s478831/paranormal-or-skeptic
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
master
paranormal-or-skeptic/train/expected.tsv
JulianZablonski 9792a7b140 task
2022-05-24 11:09:21 +02:00

566 KiB
Raw Permalink 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