s478815/paranormal-or-skeptic-ISI-public
1
0
Fork 0
forked from kubapok/paranormal-or-skeptic-ISI-public
Code Issues Pull Requests Projects Releases Wiki Activity
db662285c4
paranormal-or-skeptic-ISI-p.../train/.ipynb_checkpoints/expected-checkpoint.tsv
korne 8a69cabc52 nn
2022-06-14 23:36:56 +02:00

566 KiB
Raw Blame History 

1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1