s443930/paranormal-or-skeptic
1
0
Fork 0
Code Issues Pull Requests Projects Releases Wiki Activity
587808bce9
paranormal-or-skeptic/train/out.tsv
s443930 587808bce9 s443930
2022-05-26 22:57:14 +02:00

848 KiB
Raw Blame History 

0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
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
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
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
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
0
0
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
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
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
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
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
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
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
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
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
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
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
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
1
0
1
1
0
1
1
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
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
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
0
1
0
0
1
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
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
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
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
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
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
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
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
1
1
1
0
0
0
1
0
0
1
0
1
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
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
0
0
1
0
0
0
1
0
0
0
0
1
1
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
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
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
0
0
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
1
1
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
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
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
0
0
0
0
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
1
0
0
0
0
0
1
1
0
0
0
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
0
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
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
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
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
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
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
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
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
1
1
1
0
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
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
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
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
1
1
0
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
0
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
0
1
0
0
0
1
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
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
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
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
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
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
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
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
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
0
0
0
1
0
0
0
0
0
0
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
1
0
0
0
0
0
1
0
1
0
0
0
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
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
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
1
0
0
1
1
0
1
0
1
0
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
0
0
1
0
1
0
0
0
1
1
0
0
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
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
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
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
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
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
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
1
0
0
1
0
0
1
0
1
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
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
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
0
1
0
0
0
1
0
0
0
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
1
0
1
0
0
0
0
0
0
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
0
1
1
0
0
1
0
1
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
0
0
1
0
0
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
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
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
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
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
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
0
0
1
0
0
1
0
0
0
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
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
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
1
1
1
0
0
0
1
1
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
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
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
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
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
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
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
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
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
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
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
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
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
1
0
0
1
1
1
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
0
1
0
0
1
1
1
0
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
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
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
1
0
0
1
0
0
1
1
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
0
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
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
0
0
1
1
0
1
0
1
0
0
0
0
0
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
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
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
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
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
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
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
1
0
0
0
0
0
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
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
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
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
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
0
1
0
0
0
1
0
0
0
1
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
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
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
1
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
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
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
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
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
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
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
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
0
0
0
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
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
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
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
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
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
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
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
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
1
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
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
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
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
0
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
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
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
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
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
0
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
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
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
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
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
1
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
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
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
0
0
0
0
0
0
1
0
0
0
1
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
1
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
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
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
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
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
0
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
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
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
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
0
0
0
0
0
0
0
0
1
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
1
0
0
1
0
1
1
0
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
0
0
0
1
1
0
1
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
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
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
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
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
1
0
0
0
0
0
0
1
0
1
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
1
0
0
0
0
1
0
0
0
0
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
0
0
1
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
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
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
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
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
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
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
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
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
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
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
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
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
0
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
0
0
0
0
1
0
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
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
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
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
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
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
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
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
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
0
1
0
1
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
0
0
0
1
0
0
1
0
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
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
1
0
0
0
1
0
1
1
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
1
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
1
1
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
0
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
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
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
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
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
0
1
1
0
0
1
0
1
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
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
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
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
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
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
1
1
0
1
0
0
0
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
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
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
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
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
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
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
0
0
1
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
0
1
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
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
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
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
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
1
0
0
0
1
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
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
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
1
0
1
1
0
0
1
1
1
0
0
0
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
0
0
1
1
0
0
0
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
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
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
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
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
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
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
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
1
1
1
1
1
1
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
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
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
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
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
1
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
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
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
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
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
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
1
0
1
0
0
1
1
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
0
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
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
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
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
0
0
0
0
0
1
1
0
0
1
0
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
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
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
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
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
0
0
1
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
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
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
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
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
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
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
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
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
0
0
0
1
1
1
0
0
0
0
0
0
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
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
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
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
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
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
0
1
0
0
0
0
0
0
0
1
1
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
1
0
0
0
0
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
0
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
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
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
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
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
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
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
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
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
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
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
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
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
0
0
0
0
1
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
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
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
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
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
0
0
0
0
0
1
0
1
0
0
0
0
0
1
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
0
0
0
1
0
0
1
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
0
1
0
0
0
0
0
0
0
1
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
0
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
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
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
0
0
0
0
0
0
1
0
0
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
0
0
0
0
1
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
1
0
0
0
1
0
0
1
0
1
0
0
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
1
0
0
0
0
0
0
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
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
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
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
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
0
1
1
0
0
1
0
1
1
1
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
0
1
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
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
1
0
0
0
1
0
0
1
0
0
0
0
0
0
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
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
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
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
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
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
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
1
0
0
0
0
0
1
1
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
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
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
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
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
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
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
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
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
1
1
0
0
0
1
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
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
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
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
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
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
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
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
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
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
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
1
1
0
0
0
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
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
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
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
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
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
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
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
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
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
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
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
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
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
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
1
0
0
0
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
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
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
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
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
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
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
0
0
1
0
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
1
0
0
0
1
0
0
0
1
0
1
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
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
0
0
0
0
0
1
0
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
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
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
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
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
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
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
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
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
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
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
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
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
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
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
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
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
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
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
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
1
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
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
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
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
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
0
0
1
0
0
0
0
0
0
0
0
1
0
1
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
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
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
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
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
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
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
1
0
0
1
1
0
0
0
0
1
1
0
1
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
0
0
0
0
1
1
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
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
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
1
1
0
1
0
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
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
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
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
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
0
0
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
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
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
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
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
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
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
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
0
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
1
0
0
0
0
1
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
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
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
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
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
0
0
0
1
1
0
0
0
0
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
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
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
0
0
0
0
1
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
0
0
0
0
0
0
0
1
0
1
0
1
0
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
1
1
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
0
1
0
1
0
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
1
0
0
1
0
0
0
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
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
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
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
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
1
0
1
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
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
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
1
0
0
0
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
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
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
1
0
1
0
0
0
0
1
1
1
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
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
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
0
1
0
0
0
0
1
0
0
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
1
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
0
0
0
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
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
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
1
1
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
1
0
0
0
0
1
0
1
0
0
1
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
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
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
1
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
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
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
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
0
0
0
0
0
0
0
1
1
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
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
1
0
0
0
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
0
0
0
1
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
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
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
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
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
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
0
0
0
0
0
0
1
0
1
0
0
0
0
0
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
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
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
1
0
0
0
0
1
1
0
1
0
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
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
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
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
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
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
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
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
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
0
1
1
1
0
0
1
1
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
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
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
0
1
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
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
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
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
1
1
0
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
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
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
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
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
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
0
0
1
1
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
0
1
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
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
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
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
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
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
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
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
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
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
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
0
0
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
0
0
0
0
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
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
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
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
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
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
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
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
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
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
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
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
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
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
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
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
1
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
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
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
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
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
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
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
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
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
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
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
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
1
1
0
0
0
0
0
0
1
0
1
0
1
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
1
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
0
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
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
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
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
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
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
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
0
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
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
0
0
1
0
0
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
0
1
0
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
1
1
1
1
0
0
1
0
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
1
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
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
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
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
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
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
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
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
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
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
1
0
0
0
1
0
0
0
1
1
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
1
1
0
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
0
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
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
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
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
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
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
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
0
0
0
0
0
0
0
1
0
1
0
0
0
1
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
1
1
0
1
1
1
0
0
1
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
0
0
1
1
0
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
0
1
1
1
0
0
0
0
1
0
0
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
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
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
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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
0
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
1
0
1
1
0
1
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
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
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
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
0
0
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
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
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
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
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
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
1
0
0
0
0
0
0
0
1
0
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
0
1
0
0
0
1
0
1
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
0
0
0
1
1
1
0
1
0
1
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
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
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
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
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
0
0
0
0
1
0
0
1
0
1
0
0
1
0
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
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
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
0
0
0
0
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
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
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
0
1
1
1
1
0
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
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
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
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
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
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
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
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
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
0
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
0
1
0
1
0
0
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
0
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
1
0
1
0
1
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
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
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
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
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
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
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
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
0
0
0
0
0
0
0
1
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
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
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
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
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
1
0
0
0
0
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
0
0
0
1
1
0
0
1
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
0
1
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
1
1
0
0
1
0
0
1
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
1
1
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
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
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
1
0
1
0
0
0
0
1
1
0
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
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
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
0
1
1
0
0
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
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
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
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
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
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
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
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
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
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
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
0
0
0
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
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
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
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
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
0
0
0
0
0
0
1
1
0
0
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
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
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
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
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
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
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
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
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
0
0
1
0
0
1
0
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
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
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
1
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
1
0
0
0
1
1
0
1
1
1
0
0
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
0
0
1
1
1
0
0
1
0
1
1
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
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
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
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
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
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
0
1
0
0
0
0
0
0
1
1
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
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
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
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
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
1
0
0
0
0
0
1
0
1
0
1
1
0
0
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
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
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
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
0
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
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
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
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
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
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
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
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
1
1
1
0
0
0
0
0
0
0
0
0
1
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
0
1
1
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
1
0
1
1
0
0
0
0
1
1
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
0
0
0
0
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
0
0
0
1
0
1
1
0
1
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
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
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
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
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
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
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
1
1
0
1
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
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
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
0
0
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
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
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
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
1
0
0
0
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
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
1
1
0
0
1
1
1
1
1
0
1
1
0
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
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
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
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
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
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
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
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
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
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
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
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
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
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
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
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
1
0
1
0
0
0
1
0
0
0
1
1
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
1
0
0
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
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
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
0
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
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
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
0
1
0
1
0
0
0
1
0
0
1
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
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
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
1
1
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
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
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
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
0
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
1
1
0
0
0
0
0
1
0
0
0
1
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
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
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
1
0
0
0
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
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
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
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
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
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
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
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
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
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
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
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
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
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
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
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
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
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
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
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
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
0
0
1
1
0
0
0
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
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
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
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
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
1
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
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
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
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
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
0
1
0
0
0
0
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
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
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
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
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
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
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
0
0
0
0
0
1
0
0
1
0
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
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
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
0
1
1
0
0
1
0
0
1
0
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
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
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
1
1
0
1
1
0
1
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
0
1
0
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
0
0
0
0
0
1
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
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
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
1
0
1
0
1
1
1
0
0
1
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
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
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
0
0
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
1
1
0
1
0
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
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
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
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
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
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
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
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
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
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
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
0
0
0
0
0
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
1
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
0
1
1
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
1
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
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
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
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
0
1
0
1
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
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
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
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
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
0
0
0
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
1
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
1
0
0
0
0
0
0
0
0
0
1
0
1
1
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
1
0
0
0
0
0
0
0
0
0
0
1
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
1
0
1
1
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
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
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
1
1
0
1
0
1
0
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
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
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
0
0
0
0
0
1
1
0
0
1
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
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
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
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
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
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
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
0
1
1
0
0
0
0
1
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
0
0
0
0
1
0
0
0
0
1
1
0
0
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
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
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
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
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
0
0
1
0
0
1
0
0
1
0
0
0
0
0
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
1
0
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
1
0
0
0
0
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
0
0
1
0
0
0
1
1
1
0
0
1
0
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
0
0
0
0
0
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
1
0
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
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
1
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
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
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
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
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
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
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
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
0
1
0
1
0
0
1
0
0
0
1
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
1
0
0
0
0
0
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
0
0
0
1
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
0
0
1
0
0
1
0
0
0
1
0
0
1
1
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
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
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
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
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
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
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
1
0
0
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
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
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
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
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
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
1
1
0
1
0
1
0
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
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
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
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
0
1
1
0
0
0
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
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
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
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
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
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
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
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
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
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
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
0
0
0
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
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
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
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
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
0
0
0
0
1
1
0
1
0
0
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
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
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
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
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
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
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
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
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
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
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
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
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
0
1
0
0
0
0
0
0
1
0
0
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
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
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
0
1
1
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
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
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
1
0
1
0
0
0
0
0
0
0
1
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
1
0
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
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
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
1
0
1
0
1
1
0
1
0
1
0
0
0
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
1
1
1
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
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
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
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
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
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
1
0
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
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
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
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
0
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
0
0
0
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
0
0
0
0
1
1
1
1
0
1
0
0
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
0
1
0
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
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
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
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
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
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
0
0
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
0
1
1
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
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
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
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
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
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
1
0
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
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
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
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
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
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
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
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
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
0
0
0
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
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
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
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
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
1
1
1
0
0
0
1
1
1
0
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
0
0
1
0
1
1
1
0
1
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
0
1
1
1
0
1
0
1
1
1
1
0
0
0
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
0
0
0
0
0
0
0
0
0
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
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
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
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
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
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
1
1
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
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
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
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
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
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
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
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
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
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
0
1
0
1
0
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
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
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
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
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
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
0
0
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
0
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
1
0
1
1
0
1
0
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
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
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
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
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
0
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
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
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
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
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
0
0
1
0
0
0
0
1
0
0
1
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
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
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
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
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
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
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
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
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
1
1
0
1
1
0
1
0
1
1
0
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
1
0
1
0
0
0
0
0
1
0
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
1
1
1
0
0
0
1
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
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
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
0
0
0
1
0
0
0
0
0
0
0
1
0
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
1
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
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
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
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
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
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
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
0
1
0
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
0
0
0
0
1
0
0
1
1
0
1
0
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
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
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
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
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
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
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
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
0
0
0
1
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
0
0
0
1
1
1
0
0
0
1
0
0
1
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
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
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
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
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
0
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
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
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
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
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
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
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
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
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
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
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
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
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
1
0
0
1
1
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
1
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
1
1
0
1
0
0
1
1
1
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
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
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
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
0
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
0
0
0
1
1
1
0
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
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
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
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
1
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
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
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
1
1
1
0
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
1
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
0
0
0
0
0
1
1
1
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
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
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
0
1
0
0
1
0
0
0
1
0
1
1
1
1
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
1
0
0
0
0
0
1
1
0
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
0
1
0
0
0
1
0
0
0
0
1
0
1
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
0
0
0
1
0
0
0
0
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
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
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
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
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
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
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
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
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
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
0
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
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
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
1
0
0
0
0
1
0
0
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
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
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
1
0
0
1
0
0
0
0
0
1
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
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
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
1
0
0
0
1
1
1
1
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
1
1
0
0
0
1
0
0
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
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
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
0
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
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
0
0
0
0
0
1
1
0
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
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
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
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
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
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
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
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
1
0
0
0
0
0
1
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
0
1
0
1
1
0
1
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
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
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
0
0
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
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
1
0
1
0
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
1
0
0
0
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
0
1
0
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
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
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
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
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
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
0
1
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
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
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
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
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
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
1
1
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
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
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
0
0
0
0
0
0
1
1
1
0
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
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
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
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
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
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
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
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
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
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
1
0
0
0
1
0
0
0
1
1
0
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
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
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
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
0
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
1
0
0
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
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
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
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
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
1
0
0
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
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
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
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
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
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
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
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
1
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
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
1
0
0
1
1
1
0
1
0
1
0
0
0
0
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
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
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
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
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
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
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
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
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
0
0
0
1
1
1
1
0
0
0
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
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
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
0
1
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
0
0
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
1
0
0
0
0
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
0
0
0
0
0
1
0
0
0
1
1
0
0
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
0
0
0
1
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
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
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
0
1
1
0
0
1
0
1
1
0
0
1
1
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
1
1
1
0
0
0
1
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
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
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
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
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
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
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
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
1
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
1
0
0
1
1
0
0
0
0
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
1
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
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
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
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
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
0
0
0
0
0
0
1
0
0
1
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
1
0
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
0
0
1
0
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
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
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
0
0
0
0
1
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
0
0
1
0
0
0
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
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
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
1
0
0
0
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
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
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
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
0
0
1
1
0
0
0
0
1
0
0
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
1
0
1
1
0
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
1
1
1
0
1
0
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
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
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
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
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
1
0
0
1
1
1
0
0
1
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
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
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
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
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
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
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
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
0
0
0
0
0
1
1
0
0
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
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
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
0
0
0
1
1
0
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
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
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
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
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
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
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
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
0
1
0
0
0
0
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
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
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
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
1
0
0
0
0
0
0
1
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
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
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
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
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
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
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
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
0
0
0
0
1
0
1
0
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
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
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
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
0
0
0
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
0
1
0
0
1
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
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
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
0
0
1
0
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
0
0
0
1
1
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
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
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
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
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
0
1
0
0
0
1
0
1
1
1
0
0
0
1
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
0
0
1
1
0
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
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
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
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
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
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
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
1
0
1
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
0
0
0
1
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
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
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
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
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
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
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
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
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
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
0
0
0
0
0
0
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
1
0
1
0
0
0
0
0
1
1
0
0
1
1
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
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
0
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
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
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
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
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
1
0
0
1
0
0
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
1
0
0
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
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
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
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
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
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
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
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
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
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
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
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
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
0
1
0
1
0
0
0
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
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
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
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
1
0
0
0
0
1
0
0
1
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
0
0
1
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
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
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
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
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
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
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
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
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
0
0
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
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
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
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
1
0
0
0
0
1
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
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
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
1
0
1
1
1
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
0
0
0
0
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
0
0
1
0
0
0
1
1
1
0
1
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
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
1
0
0
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
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
0
0
1
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
0
0
0
1
1
0
1
0
1
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
1
0
1
0
0
1
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
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
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
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
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
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
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
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
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
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
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
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
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
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
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
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
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
0
0
0
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
1
0
1
1
1
0
1
1
0
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
0
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
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
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
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
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
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
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
1
0
1
1
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
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
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
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
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
0
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
0
0
0
1
0
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
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
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
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
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
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
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
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
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
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
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
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
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
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
0
0
0
1
0
0
0
0
1
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
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
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
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
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
1
0
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
1
0
1
1
1
0
1
0
1
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
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
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
0
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
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
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
0
1
0
1
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
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
1
0
0
0
0
1
0
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
1
0
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
1
0
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
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
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
1
0
0
0
0
1
1
0
1
0
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
0
0
0
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
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
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
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
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
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
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
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
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
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
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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
0
0
1
1
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
1
1
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
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
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
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
0
0
1
0
0
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
1
0
1
1
0
0
0
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
1
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
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
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
0
1
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
0
0
1
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
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
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
1
0
0
0
1
1
1
1
0
1
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
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
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
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
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
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
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
0
0
0
0
0
0
0
0
0
1
1
0
1
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
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
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
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
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
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
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
0
0
0
0
0
0
1
1
1
0
1
0
0
1
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
1
1
0
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
0
0
0
0
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
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
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
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
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
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
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
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
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
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
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
0
0
1
0
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
0
0
1
0
1
0
0
0
1
0
1
1
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
0
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
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
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
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
0
0
0
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
1
0
0
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
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
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
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
0
1
0
0
0
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
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
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
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
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
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
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
0
1
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
0
0
0
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
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
0
0
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
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
0
0
1
1
0
1
1
1
0
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
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
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
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
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
1
0
0
0
1
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
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
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
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
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
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
0
0
1
0
1
1
0
0
1
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
1
0
1
0
0
0
1
1
0
0
1
0
1
0
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
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
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
1
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
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
0
0
0
0
1
1
1
0
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
0
0
0
1
0
0
0
0
0
1
0
1
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
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
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
0
0
0
0
0
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
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
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
0
0
1
0
0
1
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
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
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
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
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
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
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
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
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
0
0
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
0
0
0
0
0
0
0
1
1
0
1
0
1
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
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
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
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
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
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
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
0
0
1
1
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
0
0
0
0
1
0
0
1
0
1
0
0
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
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
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
0
1
1
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
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
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
1
0
0
0
1
0
0
1
0
1
1
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
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
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
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
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
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
0
0
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
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
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
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
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
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
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
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
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
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
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
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
0
0
1
1
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
0
0
1
1
0
0
0
0
0
0
0
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
0
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
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
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
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
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
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
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
0
0
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
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
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
1
1
0
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
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
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
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
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
0
1
0
0
0
0
0
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
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
0
0
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
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
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
1
0
1
1
0
0
1
0
0
0
1
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
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
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
0
0
0
1
0
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
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
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
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
1
0
0
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
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
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
1
0
0
0
0
0
1
0
0
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
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
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
0
0
0
0
0
1
0
1
1
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
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
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
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
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
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
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
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
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
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
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
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
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
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
1
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
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
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
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
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
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
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
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
1
1
0
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
0
0
0
1
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
0
1
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
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
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
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
0
0
0
0
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
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
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
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
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
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
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
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
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
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
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
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
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
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
0
0
0
1
0
0
0
0
0
1
1
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
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
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
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
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
1
0
0
0
0
0
0
1
0
0
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
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
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
1
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
1
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
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
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
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
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
1
1
0
0
1
0
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
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
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
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
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
1
0
0
0
0
0
0
1
0
0
0
0
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
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
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
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
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
0
1
1
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
1
1
1
1
1
1
1
1
0
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
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
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
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
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
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
1
0
1
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
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
1
0
0
0
1
1
1
1
1
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
1
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
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
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
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
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
1
1
0
0
0
1
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
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
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
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
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
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
0
0
1
0
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
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
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
1
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
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
1
0
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
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
1
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
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
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
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
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
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
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
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
1
1
0
0
0
0
1
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
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
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
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
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
0
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
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
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
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
1
0
0
0
0
0
0
0
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
1
0
1
0
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
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
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
1
0
0
0
0
0
0
1
0
0
0
1
0
0
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
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
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
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
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
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
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
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
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
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
1
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
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
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
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
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
0
0
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
0
0
0
0
1
0
1
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
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
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
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
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
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
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
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
1
0
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
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
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
1
0
1
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
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
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
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
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
1
0
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
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
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
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
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
0
1
0
1
1
0
0
1
1
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
1
0
1
0
0
1
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
0
0
1
0
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
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
1
0
1
1
1
1
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
1
0
1
0
0
0
1
0
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
0
0
0
0
0
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
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
1
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
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
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
1
0
0
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
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
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
0
1
0
0
1
1
0
0
1
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
1
1
0
0
1
0
0
0
0
0
1
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
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
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
0
1
1
0
0
0
0
0
1
0
1
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
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
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
1
1
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
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
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
1
0
0
1
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
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
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
0
1
0
0
0
1
0
0
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
0
0
0
1
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
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
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
1
0
0
1
0
0
1
1
1
0
0
0
1
1
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
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
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
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
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
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
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
0
0
0
1
0
0
1
1
0
0
0
1
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
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
0
0
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
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
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
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
0
0
1
0
0
0
0
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
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
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
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
1
0
0
0
1
1
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
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
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
0
0
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
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
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
0
0
0
0
0
0
1
1
1
1
1
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
1
1
1
1
0
0
0
0
1
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
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
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
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
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
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
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
0
0
0
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
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
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
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
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
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
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
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
1
0
0
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
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
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
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
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
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
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
0
1
0
1
0
0
1
0
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
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
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
0
1
0
1
0
0
0
1
0
0
1
1
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
0
0
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
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
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
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
1
0
0
0
0
1
0
1
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
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
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
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
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
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
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
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
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
1
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
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
1
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
0
1
0
0
0
0
1
0
1
1
0
0
1
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
0
1
1
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
1
0
1
1
0
0
1
1
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
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
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
1
0
0
0
0
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
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
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
0
1
0
0
0
0
1
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
1
0
0
1
1
0
0
0
0
0
1
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
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
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
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
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
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
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
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
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
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
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
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
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
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
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
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
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
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
0
0
0
0
0
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
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
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
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
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
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
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
1
0
0
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
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
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
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
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
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
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
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
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
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
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
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
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
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
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
0
0
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
1
1
0
1
0
0
1
1
0
0
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
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
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
0
1
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
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
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
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
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
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
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
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
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
0
0
1
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
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
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
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
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
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
1
1
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
1
1
0
0
0
0
1
0
1
1
0
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
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
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
0
0
0
0
1
0
1
0
0
1
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
0
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
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
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
1
0
0
0
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
0
0
1
0
1
1
0
0
0
0
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
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
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
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
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
0
0
0
0
0
1
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
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
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
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
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
1
0
1
1
0
0
1
0
1
1
1
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
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
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
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
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
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
1
1
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
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
0
0
1
1
1
1
0
0
1
0
0
1
0
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
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
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
1
0
0
1
0
0
0
0
1
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
1
1
1
1
0
0
0
1
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
0
1
0
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
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
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
1
0
0
0
0
0
0
0
0
0
1
1
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
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
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
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
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
0
0
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
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
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
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
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
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
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
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
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
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
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
0
0
1
0
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
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
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
0
1
0
1
1
1
1
0
0
0
0
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
0
0
1
0
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
1
1
1
0
0
1
0
1
1
0
0
0
0
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
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
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
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
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
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
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
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
0
1
1
1
1
0
0
0
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
0
0
0
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
1
1
1
1
0
0
1
0
0
0
0
1
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
0
1
1
0
1
0
0
0
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
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
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
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
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
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
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
1
0
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
0
1
0
0
0
0
0
1
0
1
1
0
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
1
0
0
1
1
1
0
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
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
1
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
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
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
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
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
1
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
1
1
0
0
0
0
0
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
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
0
1
0
1
0
0
1
1
0
0
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
0
1
1
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
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
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
0
1
0
0
1
1
0
0
0
0
0
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
0
0
0
0
1
0
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
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
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
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
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
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
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
0
0
0
0
1
0
1
0
1
0
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
1
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
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
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
1
0
1
0
0
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
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
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
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
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
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
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
0
0
0
1
1
0
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
1
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
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
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
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
1
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
1
0
1
0
0
1
1
0
0
1
0
1
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
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
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
0
0
0
0
0
1
1
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
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
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
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
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
0
1
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
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
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
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
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
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
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
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
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
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
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
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
1
1
1
0
0
0
1
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
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
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
0
0
0
1
0
0
1
1
1
0
0
1
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
1
0
0
1
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
1
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
0
0
0
1
0
0
0
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
0
0
0
0
0
0
1
0
1
1
0
1
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
0
1
0
0
0
0
0
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
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
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
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
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
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
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
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
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
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
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
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
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
0
0
0
0
0
1
0
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
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
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
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
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
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
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
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
1
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
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
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
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
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
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
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
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
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
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
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
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
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
0
0
0
1
0
1
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
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
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
1
0
0
1
0
0
1
0
0
0
1
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
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
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
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
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
0
1
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
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
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
0
0
0
0
0
0
1
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
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
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
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
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
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
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
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
0
0
0
0
1
1
1
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
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
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
1
0
0
0
0
1
0
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
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
0
0
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
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
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
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
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
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
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
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
0
1
1
1
0
0
0
0
0
1
0
1
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
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
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
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
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
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
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
1
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
1
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
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
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
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
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
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
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
0
0
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
1
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
0
0
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
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
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
1
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
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
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
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
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
1
0
1
0
0
0
1
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
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
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
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
0
0
1
0
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
0
1
0
0
0
0
1
0
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
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
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
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
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
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
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
0
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
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
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
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
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
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
1
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
0
0
0
0
0
0
1
0
1
1
1
0
1
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
1
1
1
0
0
0
0
1
0
1
1
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
0
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
1
1
0
0
1
0
0
1
1
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
1
0
0
1
1
0
0
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
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
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
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
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
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
0
0
0
0
0
0
1
1
0
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
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
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
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
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
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
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
1
1
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
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
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
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
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
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
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
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
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
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
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
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
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
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
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
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
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
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
0
0
1
1
1
0
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
0
0
1
0
0
0
1
0
0
1
0
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
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
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
0
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
1
0
0
1
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
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
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
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
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
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
1
1
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
0
0
0
1
0
0
0
1
0
0
0
1
0
0
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
1
0
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
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
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
0
0
0
1
1
1
1
0
0
0
1
0
0
0
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
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
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
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
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
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
1
0
1
0
1
1
0
0
0
1
1
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
1
0
1
1
1
0
0
0
0
1
1
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
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
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
1
0
0
0
0
1
0
0
0
1
0
1
0
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
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
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
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
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
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
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
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
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
1
0
1
0
0
1
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
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
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
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
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
1
0
0
1
1
0
0
1
0
0
0
0
1
1
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
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
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
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
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
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
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
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
0
1
0
0
0
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
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
0
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
0
0
0
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
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
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
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
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
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
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
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
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
0
1
0
0
0
0
1
0
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
1
0
1
0
0
0
0
0
0
1
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
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
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
1
0
0
1
0
0
1
0
1
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
0
1
0
1
0
0
0
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
1
0
0
0
1
1
0
1
1
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
1
0
1
0
0
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
0
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
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
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
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
1
1
0
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
1
1
1
1
1
0
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
1
0
0
0
0
1
0
0
0
0
0
0
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
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
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
1
1
1
0
1
0
0
0
1
1
0
0
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
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
0
0
1
0
0
0
1
0
0
0
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
1
0
1
0
0
0
1
1
0
0
1
0
1
1
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
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
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
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
0
0
0
0
0
0
0
1
0
1
1
0
0
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
1
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
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
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
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
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
0
0
0
1
1
0
0
0
1
0
1
0
0
1
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
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
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
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
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
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
1
0
0
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
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
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
1
1
0
1
0
0
0
1
1
0
0
1
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
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
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
1
0
0
1
0
1
0
1
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
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
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
1
0
1
0
0
1
1
0
1
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
0
1
0
1
1
0
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
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
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
1
1
0
1
0
0
0
0
0
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
0
0
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
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
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
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
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
0
1
0
1
0
0
1
1
0
1
1
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
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
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
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
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
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
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
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
1
0
0
0
1
1
1
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
0
0
1
0
1
0
1
0
1
0
0
1
0
1
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
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
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
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
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
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
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
0
0
0
0
1
0
1
0
0
0
0
0
0
1
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
1
0
1
0
0
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
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
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
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
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
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
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
0
1
0
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
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
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
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
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
0
0
0
0
1
0
1
0
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
1
0
1
0
0
1
0
0
0
1
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
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
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
0
1
1
0
0
1
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
0
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
0
0
0
0
0
1
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
0
1
0
1
1
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
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
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
0
1
0
0
1
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
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
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
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
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
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
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
1
0
0
1
1
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
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
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
1
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
1
1
0
0
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
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
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
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
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
0
1
0
0
1
1
1
0
0
1
0
0
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
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
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
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
0
1
0
0
1
1
0
1
0
0
0
0
0
1
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
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
1
1
0
0
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
1
0
1
1
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
1
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
1
0
0
0
0
1
1
1
0
0
0
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
0
0
0
1
0
0
0
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
1
1
0
1
0
1
0
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
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
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
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
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
1
1
0
0
0
0
1
0
0
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
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
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
0
0
0
0
1
1
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
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
0
0
1
1
0
0
0
0
0
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
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
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
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
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
0
0
1
0
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
1
0
1
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
0
0
1
1
1
0
0
1
0
0
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
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
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
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
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
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
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
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
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
0
0
0
0
0
1
0
1
1
0
0
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
1
0
0
0
0
1
0
0
0
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
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
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
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
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
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
1
1
0
1
0
1
0
1
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
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
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
0
0
1
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
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
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
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
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
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
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
1
1
1
0
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
0
1
0
0
0
1
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
0
0
0
0
1
1
1
0
0
1
1
0
1
0
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
1
0
0
1
0
0
0
0
1
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
0
1
0
1
0
0
0
0
0
1
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
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
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
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
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
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
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
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
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
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
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
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
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
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
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
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
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
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
0
0
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
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
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
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
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
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
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
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
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
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
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
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
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
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
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
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
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
1
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
1
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
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
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
0
0
1
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
1
0
0
0
0
0
0
1
0
0
1
1
0
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
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
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
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
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
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
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
1
0
1
1
0
1
1
0
1
0
1
0
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
0
0
1
1
1
0
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
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
1
0
1
1
1
0
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
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
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
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
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
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
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
0
0
0
1
1
1
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
0
0
1
0
0
0
0
1
1
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
0
1
0
1
1
1
0
1
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
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
0
0
0
0
0
0
1
0
0
1
0
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
0
0
0
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
0
0
1
1
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
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
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
1
0
0
0
0
0
1
0
0
1
0
1
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
0
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
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
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
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
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
0
1
0
1
1
1
1
0
0
0
1
0
1
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
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
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
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
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
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
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
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
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
0
0
0
0
1
1
0
1
0
1
0
1
0
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
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
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
0
0
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
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
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
0
0
0
1
0
0
0
1
0
0
0
1
0
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
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
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
1
0
1
1
0
0
0
1
0
0
1
1
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
0
0
0
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
0
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
0
1
1
0
0
1
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
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
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
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
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
0
1
1
0
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
1
0
0
0
0
1
1
0
0
1
0
1
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
0
1
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
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
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
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
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
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
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
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
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
0
0
0
0
0
1
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
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
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
1
0
1
0
0
1
0
1
1
0
1
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
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
0
0
0
1
0
1
0
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
1
0
1
0
0
1
0
1
0
0
0
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
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
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
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
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
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
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
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
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
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
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
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
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
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
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
0
0
1
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
0
0
0
0
1
0
0
0
0
0
1
0
0
1
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
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
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
0
1
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
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
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
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
1
0
1
1
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
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
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
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
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
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
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
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
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
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
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
0
0
0
1
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
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
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
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
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
0
1
0
0
1
0
0
0
1
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
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
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
1
0
1
1
0
0
1
1
1
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
1
1
0
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
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
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
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
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
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
0
0
0
1
0
0
0
1
1
0
0
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
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
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
1
1
1
0
1
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
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
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
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
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
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
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
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
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
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
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
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
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
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
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
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
0
1
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
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
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
1
1
1
0
0
0
0
0
0
1
0
0
1
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
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
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
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
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
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
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
0
1
1
1
0
0
1
1
0
1
1
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
1
0
0
1
0
0
0
0
0
0
0
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
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
1
0
0
1
1
0
0
0
0
0
0
1
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
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
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
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
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
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
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
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
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
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
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
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
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
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
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
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
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
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
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
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
0
0
0
0
0
0
0
1
0
1
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
1
1
0
0
1
0
0
0
0
0
1
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
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
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
0
0
0
0
1
0
0
1
0
1
1
0
0
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
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
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
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
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
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
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
0
1
1
1
0
0
0
0
0
0
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
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
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
0
1
0
0
0
0
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
0
0
0
0
0
1
1
1
0
1
0
1
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
0
0
0
1
0
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
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
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
0
0
0
0
1
1
1
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
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
1
0
0
0
0
0
0
0
1
1
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
0
0
0
0
0
0
1
1
0
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
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
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
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
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
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
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
1
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
1
0
1
0
0
1
0
1
1
0
1
0
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
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
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
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
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
0
0
1
0
1
1
0
0
1
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
0
0
0
0
0
0
0
0
1
0
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
0
1
1
1
0
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
0
1
0
1
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
0
1
0
0
0
0
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
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
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
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
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
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
0
1
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
0
0
0
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
1
0
0
0
0
0
1
0
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
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
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
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
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
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
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
0
1
0
0
0
1
1
1
1
0
1
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
0
0
0
0
0
0
0
1
0
0
0
1
1
0
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
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
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
0
0
0
0
1
0
1
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
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
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
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
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
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
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
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
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
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
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
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
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
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
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
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
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
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
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
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
0
1
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
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
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
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
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
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
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
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
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
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
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
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
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
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
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
1
0
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
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
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
1
0
0
0
0
0
1
1
0
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
1
0
1
0
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
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
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
0
0
0
1
0
1
1
1
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
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
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
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
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
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
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
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
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
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
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
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
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
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
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
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
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
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
0
0
1
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
1
0
0
0
0
0
0
1
0
0
1
0
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
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
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
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
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
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
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
1
1
0
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
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
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
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
1
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
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
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
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
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
1
1
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
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
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
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
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
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
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
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
1
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
1
0
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
0
0
0
0
0
1
0
0
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
0
0
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
0
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
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
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
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
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
1
0
0
0
1
1
1
0
1
0
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
1
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
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
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
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
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
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
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
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
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
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
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
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
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
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
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
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
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
0
1
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
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
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
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
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
1
1
0
0
0
1
0
1
1
1
0
0
0
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
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
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
1
0
1
1
0
0
0
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
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
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
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
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
1
1
0
1
1
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
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
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
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
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
0
0
0
1
1
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
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
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
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
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
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
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
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
1
0
0
0
0
0
1
1
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
0
0
0
0
0
0
1
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
1
0
1
0
1
1
1
0
0
0
0
0
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
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
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
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
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
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
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
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
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
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
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
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
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
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
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
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
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
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
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
1
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
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
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
0
0
0
1
1
0
0
0
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
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
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
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
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
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
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
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
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
1
1
0
1
1
1
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
1
0
0
1
0
1
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
0
1
0
0
0
0
0
0
1
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
0
0
0
0
1
0
1
1
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
1
1
0
0
1
0
0
1
1
1
1
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
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
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
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
0
0
0
0
1
0
1
0
1
0
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
1
0
1
0
0
0
0
0
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
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
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
0
0
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
0
0
0
1
0
0
0
1
1
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
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
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
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
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
0
0
1
0
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
1
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
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
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
0
0
0
1
1
0
0
1
1
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
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
1
0
0
0
0
1
0
1
1
1
1
0
1
1
0
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
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
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
0
0
0
0
0
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
0
0
0
0
1
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
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
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
0
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
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
0
0
0
1
1
0
0
0
0
0
0
0
1
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
0
0
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
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
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
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
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
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
0
0
1
1
1
0
0
1
0
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
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
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
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
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
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
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
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
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
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
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
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
0
0
1
1
0
1
0
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
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
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
1
1
1
0
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
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
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
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
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
1
0
1
0
0
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
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
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
1
0
0
0
0
1
0
1
0
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
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
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
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
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
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
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
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
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
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
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
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
1
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
1
1
0
0
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
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
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
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
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
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
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
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
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
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
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
0
0
0
1
0
0
0
1
0
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
0
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
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
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
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
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
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
1
0
0
1
0
0
0
0
0
1
0
0
0
1
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
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
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
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
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
1
1
0
1
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
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
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
0
1
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
0
0
1
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
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
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
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
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
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
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
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
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
0
1
0
0
1
1
0
0
0
1
1
1
1
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
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
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
0
0
1
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
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
0
1
1
1
0
0
1
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
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
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
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
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
1
0
0
1
0
0
0
0
1
0
0
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
1
0
0
1
0
1
0
0
0
1
0
1
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
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
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
1
0
0
0
1
1
0
0
0
0
1
0
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
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
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
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
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
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
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
0
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
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
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
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
1
1
1
0
1
1
0
1
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
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
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
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
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
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
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
1
1
1
0
1
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
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
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
1
0
1
1
0
0
0
1
0
1
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
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
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
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
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
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
0
0
0
0
0
0
1
0
0
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
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
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
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
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
1
1
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
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
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
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
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
1
0
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
0
0
0
0
1
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
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
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
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
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
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
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
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
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
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
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
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
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
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
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
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
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
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
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
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
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
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
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
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
0
1
0
0
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
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
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
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
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
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
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
1
0
0
1
1
0
1
0
0
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
1
0
1
0
0
0
1
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
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
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
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
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
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
0
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
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
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
0
0
0
1
0
1
1
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
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
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
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
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
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
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
0
0
1
1
0
1
0
0
1
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
1
0
0
1
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
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
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
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
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
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
0
1
0
0
0
1
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
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
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
1
0
0
1
0
1
1
1
1
1
1
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
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
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
1
0
0
1
0
0
1
0
1
1
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
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
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
1
0
1
0
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
0
0
0
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
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
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
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
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
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
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
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
0
1
0
1
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
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
1
1
1
0
0
1
0
0
0
1
1
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
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
0
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
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
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
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
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
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
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
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
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
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
0
1
1
0
1
1
1
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
0
1
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
1
0
0
0
1
1
0
0
1
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
1
1
1
0
0
1
1
0
0
0
0
1
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
1
0
0
1
1
1
0
0
0
0
1
0
0
1
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
1
0
0
1
0
0
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
1
1
1
1
1
0
0
0
1
0
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
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
0
0
0
1
0
1
0
0
0
0
1
0
0
0
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
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
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
1
1
0
1
0
0
0
0
1
0
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
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
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
0
0
1
0
1
0
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
1
0
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
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
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
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
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
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
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
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
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
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
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
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
1
0
0
1
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
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
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
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
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
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
1
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
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
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
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
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
0
1
1
1
0
0
0
0
0
0
1
0
0
1
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
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
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
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
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
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
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
1
1
0
0
0
1
1
1
0
1
0
1
0
1
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
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
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
0
0
0
0
1
0
1
1
0
0
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
1
0
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
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
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
0
0
1
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
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
0
0
0
1
1
0
0
1
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
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
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
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
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
0
1
0
0
0
1
1
0
0
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
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
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
1
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
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
1
0
0
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
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
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
0
0
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
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
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
0
0
1
0
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
0
1
0
0
0
1
0
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
0
1
1
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
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
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
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
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
1
0
0
0
1
1
0
1
0
0
1
1
1
0
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
1
0
1
0
0
0
0
1
1
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
1
0
0
0
0
1
0
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
0
0
1
0
1
0
0
0
0
0
1
0
1
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
0
1
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
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
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
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
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
1
1
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
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
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
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
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
0
0
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
0
0
0
0
0
0
1
0
1
1
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
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
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
1
0
0
0
0
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
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
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
0
0
0
0
0
0
0
0
1
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
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
0
0
1
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
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
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
0
0
0
0
0
1
0
1
0
0
1
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
0
0
1
0
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
1
0
0
1
1
0
0
0
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
0
1
0
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
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
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
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
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
1
0
1
0
0
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
1
1
0
0
0
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
1
0
0
0
0
0
1
0
0
0
0
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
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
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
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
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
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
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
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
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
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
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
0
0
1
1
1
1
1
0
0
0
1
0
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
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
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
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
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
0
0
0
0
0
1
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
1
0
0
0
0
0
0
1
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
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
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
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
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
0
0
0
0
0
0
0
0
0
0
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
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
1
0
1
0
0
0
0
0
0
0
0
1
1
0
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
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
0
0
0
1
0
0
0
1
1
0
0
0
0
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
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
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
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
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
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
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
0
0
1
1
0
0
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
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
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
0
0
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
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
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
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
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
1
0
1
0
1
1
1
0
1
1
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
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
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
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
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
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
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
1
1
1
0
1
0
1
0
0
1
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
0
1
0
1
1
1
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
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
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
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
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
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
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
0
1
1
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
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
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
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
1
1
0
0
0
0
0
1
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
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
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
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
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
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
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
1
0
1
0
0
1
1
0
1
1
0
0
0
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
0
0
0
0
0
1
0
0
0
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
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
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
1
0
0
1
0
0
1
0
0
1
1
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
1
0
0
0
1
1
0
0
0
0
0
1
1
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
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
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
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
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
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
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
1
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
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
1
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
0
0
0
0
0
0
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
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
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
1
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
1
0
0
1
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
0
0
0
0
1
1
0
1
1
0
0
1
1
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
0
0
1
0
1
1
1
0
0
0
0
0
1
0
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
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
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
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
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
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
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
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
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
1
1
0
1
0
0
0
0
1
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
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
0
0
0
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
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
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
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
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
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
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
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
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
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
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
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
1
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
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
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
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
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
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
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
0
0
1
0
0
0
1
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
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
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
1
1
0
0
1
1
0
1
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
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
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
1
0
0
0
1
0
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
0
1
0
1
1
0
1
0
1
0
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
1
1
0
0
0
1
0
0
0
1
0
0
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
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
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
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
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
0
0
0
0
0
1
1
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
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
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
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
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
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
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
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
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
0
0
0
1
1
0
0
0
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
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
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
0
0
0
1
1
0
1
0
0
0
0
0
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
0
0
0
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
0
1
1
0
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
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
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
1
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
1
1
0
0
1
0
0
1
1
1
0
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
1
1
0
0
0
1
0
1
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
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
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
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
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
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
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
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
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
0
1
0
1
0
0
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
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
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
0
1
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
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
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
1
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
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
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
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
1
0
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
1
1
0
1
0
1
0
1
0
1
1
0
1
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
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
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
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
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
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
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
1
0
0
0
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
0
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
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
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
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
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
0
0
1
0
1
0
0
0
1
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
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
0
0
1
0
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
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
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
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
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
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
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
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
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
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
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
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
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
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
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
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
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
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
0
0
1
1
0
1
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
0
0
0
0
1
1
0
1
0
0
0
0
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
0
0
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
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
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
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
1
0
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
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
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
0
0
0
0
0
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
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
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
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
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
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
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
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
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
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
1
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
1
0
0
0
1
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
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
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
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
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
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
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
1
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
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
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
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
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
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
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
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
0
1
0
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
0
0
0
0
0
1
0
1
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
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
1
0
0
0
0
0
0
0
1
1
0
0
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
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
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
0
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
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
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
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
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
1
0
0
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
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
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
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
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
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
1
0
0
0
1
0
0
0
0
1
0
0
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
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
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
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
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
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
1
0
0
1
0
0
0
0
1
0
1
1
1
1
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
1
0
0
0
0
1
1
1
0
1
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
1
1
0
0
1
0
1
0
1
0
0
0
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
0
0
1
0
1
0
1
1
1
0
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
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
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
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
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
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
0
1
0
1
0
0
0
0
0
1
0
1
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
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
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
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
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
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
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
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
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
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
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
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
1
0
1
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
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
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
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
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
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
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
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
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
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
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
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
1
1
0
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
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
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
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
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
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
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
1
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
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
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
0
1
0
0
0
0
0
1
0
0
0
1
1
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
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
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
0
1
0
0
0
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
0
0
0
1
0
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
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
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
0
1
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
0
0
0
0
0
1
0
0
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
0
0
0
1
0
1
0
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
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
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
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
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
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
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
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
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
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
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
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
1
0
1
0
0
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
1
0
0
0
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
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
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
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
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
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
1
1
1
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
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
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
1
0
0
1
0
0
0
0
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
1
0
1
0
1
0
1
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
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
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
0
0
1
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
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
0
1
0
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
0
0
0
0
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
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
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
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
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
1
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
0
1
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
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
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
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
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
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
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
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
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
1
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
1
0
0
0
1
0
1
0
0
0
0
0
1
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
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
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
0
1
1
1
0
0
0
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
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
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
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
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
0
1
0
1
0
0
1
1
1
1
0
0
0
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
1
0
1
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
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
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
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
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
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
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
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
1
0
0
0
1
0
0
0
0
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
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
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
0
0
0
1
1
0
1
0
0
0
0
0
0
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
0
1
0
0
0
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
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
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
0
0
1
1
1
1
0
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
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
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
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
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
0
1
0
0
0
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
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
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
1
1
0
0
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
0
0
0
0
1
0
0
0
1
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
0
0
0
0
1
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
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
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
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
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
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
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
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
1
0
0
0
0
0
0
1
0
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
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
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
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
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
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
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
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
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
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
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
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
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
0
0
0
0
1
0
1
0
0
0
1
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
1
1
1
1
0
1
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
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
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
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
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
0
1
0
1
1
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
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
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
1
0
1
0
0
0
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
0
0
1
1
1
1
0
1
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
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
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
0
1
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
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
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
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
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
1
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
0
0
0
0
0
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
0
1
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
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
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
0
1
0
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
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
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
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
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
1
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
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
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
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
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
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
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
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
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
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
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
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
0
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
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
0
0
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
1
0
0
1
0
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
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
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
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
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
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
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
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
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
0
1
0
0
0
0
0
1
1
0
0
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
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
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
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
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
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
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
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
0
1
1
0
0
1
0
1
1
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
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
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
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
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
0
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
0
0
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
1
0
0
0
1
1
0
0
1
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
1
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
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
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
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
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
0
0
0
0
0
1
0
0
0
1
1
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
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
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
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
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
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
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
0
0
0
0
0
1
1
0
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
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
1
1
0
1
0
1
0
0
0
0
1
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
0
0
1
0
0
0
1
1
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
0
0
0
0
1
0
0
0
1
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
1
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
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
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
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
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
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
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
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
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
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
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
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
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
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
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
1
1
0
0
1
1
0
1
0
0
0
0
1
0
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
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
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
0
1
0
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
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
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
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
1
0
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
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
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
1
0
0
0
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
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
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
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
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
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
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
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
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
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
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
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
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
1
1
0
0
0
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
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
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
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
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
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
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
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
0
0
0
1
0
1
1
0
1
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
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
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
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
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
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
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
1
0
1
1
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
1
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
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
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
1
0
1
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
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
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
1
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
0
0
0
0
0
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
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
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
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
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
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
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
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
1
1
0
1
1
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
1
1
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
1
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
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
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
1
1
0
0
0
1
0
0
0
0
0
0
0
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
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
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
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
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
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
0
1
1
0
0
0
1
0
0
1
0
0
1
1
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
0
0
0
0
1
0
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
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
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
0
1
0
0
1
0
0
1
0
0
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
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
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
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
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
1
0
1
1
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
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
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
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
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
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
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
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
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
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
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
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
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
1
1
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
0
0
0
1
0
0
1
1
0
1
0
0
1
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
0
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
1
0
1
1
0
0
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
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
0
1
1
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
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
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
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
0
0
1
1
0
0
1
0
0
1
0
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
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
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
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
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
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
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
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
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
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
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
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
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
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
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
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
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
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
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
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
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
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
1
0
1
0
0
0
0
0
0
0
0
0
1
1
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
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
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
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
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
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
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
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
0
1
0
1
1
0
1
0
1
0
1
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
1
1
0
1
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
0
1
0
0
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
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
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
0
0
0
0
0
1
1
0
0
0
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
0
1
0
1
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
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
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
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
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
0
0
0
0
0
0
0
0
0
0
0
1
0
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
1
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
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
0
1
1
0
0
1
1
1
0
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
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
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
1
0
0
0
0
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
0
0
0
0
0
1
0
0
0
0
1
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
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
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
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
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
1
1
1
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
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
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
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
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
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
1
1
1
1
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
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
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
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
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
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
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
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
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
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
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
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
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
1
0
0
1
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
0
0
0
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
0
0
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
0
0
0
0
1
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
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
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
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
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
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
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
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
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
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
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
0
0
0
0
0
1
0
0
0
1
0
1
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
0
0
1
1
0
0
1
1
0
0
0
0
0
1
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
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
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
1
1
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
1
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
1
0
1
0
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
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
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
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
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
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
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
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
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
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
1
1
0
1
0
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
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
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
0
0
0
1
0
0
0
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
0
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
0
0
0
0
0
0
0
1
0
1
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
1
1
0
1
0
0
0
1
0
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
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
0
0
0
0
1
0
0
1
1
0
1
1
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
1
1
0
0
0
0
1
1
0
0
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
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
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
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
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
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
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
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
0
0
0
0
0
0
1
0
1
0
1
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
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
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
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
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
0
1
0
1
0
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
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
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
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
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
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
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
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
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
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
0
1
1
1
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
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
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
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
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
0
0
0
0
1
1
0
0
0
0
0
0
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
1
0
1
0
0
0
0
0
1
1
0
1
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
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
0
0
0
1
1
0
0
0
0
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
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
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
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
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
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
0
0
1
0
1
0
1
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
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
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
0
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
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
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
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
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
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
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
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
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
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
1
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
0
0
0
0
0
1
0
1
0
0
0
1
0
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
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
1
0
0
0
0
0
1
1
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
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
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
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
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
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
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
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
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
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
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
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
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
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
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
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
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
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
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
0
0
1
1
0
0
0
1
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
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
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
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
0
0
0
0
0
0
1
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
0
0
1
1
0
1
0
0
0
0
1
0
1
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
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
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
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
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
0
0
0
1
0
1
1
1
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
0
0
1
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
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
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
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
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
1
0
0
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
0
0
1
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
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
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
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
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
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
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
1
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
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
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
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
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
1
0
0
0
1
0
1
1
0
0
0
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
0
1
1
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
1
0
0
0
0
0
0
1
0
1
0
0
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
1
0
0
0
1
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
0
1
0
1
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
0
1
0
0
0
1
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
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
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
1
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
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
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
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
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
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
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
1
1
0
1
1
0
0
0
0
0
1
0
1
0
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
0
0
1
0
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
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
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
1
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
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
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
1
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
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
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
0
0
0
0
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
0
0
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
0
0
0
0
0
0
1
1
1
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
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
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
0
0
1
0
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
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
0
0
0
0
0
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
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
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
1
0
0
1
1
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
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
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
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
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
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
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
0
0
0
0
0
1
0
1
0
1
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
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
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
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
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
1
0
1
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
0
0
0
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
0
1
1
1
1
0
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
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
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
0
0
1
0
1
0
0
0
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
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
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
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
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
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
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
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
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
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
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
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
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
1
1
0
0
0
0
1
0
1
0
0
1
1
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
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
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
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
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
0
0
0
0
1
1
0
0
0
0
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
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
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
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
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
0
0
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
0
1
0
1
0
1
1
1
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
0
1
0
0
1
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
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
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
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
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
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
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
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
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
1
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
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
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
1
1
1
0
0
1
0
0
0
0
1
1
0
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
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
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
1
0
0
1
0
1
0
0
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
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
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
0
0
1
0
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
0
0
0
0
1
0
0
0
0
1
0
1
0
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
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
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
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
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
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
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
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
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
0
0
0
0
0
0
0
1
1
0
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
0
1
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
0
1
0
0
1
0
0
1
0
0
0
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
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
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
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
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
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
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
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
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
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
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
1
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
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
0
0
0
0
0
0
0
0
1
0
0
0
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
1
1
0
0
0
0
1
1
0
0
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
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
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
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
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
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
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
0
0
0
1
1
0
1
0
0
0
0
0
0
0
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
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
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
1
0
0
1
0
0
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
0
1
1
0
0
1
1
0
0
1
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
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
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
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
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
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
1
0
0
0
1
0
0
0
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
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
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
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
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
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
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
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
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
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
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
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
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
1
1
0
0
0
0
0
0
0
1
1
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
0
0
0
1
0
0
0
1
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
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
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
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
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
0
0
0
0
1
0
1
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
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
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
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
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
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
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
0
0
1
0
1
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
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
1
0
0
0
0
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
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
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
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
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
1
1
0
0
0
0
1
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
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
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
0
0
0
0
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
0
1
0
0
1
1
1
0
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
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
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
1
0
0
1
0
0
0
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
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
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
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
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
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
0
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
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
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
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
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
0
0
0
0
1
0
1
1
0
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
0
0
0
1
1
1
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
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
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
0
0
0
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
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
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
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
0
0
0
1
0
0
0
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
0
0
1
0
1
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
0
0
0
0
1
0
1
0
1
0
0
0
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
0
0
0
0
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
0
0
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
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
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
1
0
1
0
1
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
1
1
1
1
0
1
0
1
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
1
0
1
1
0
0
0
1
0
0
0
0
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
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
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
1
0
1
0
0
1
1
0
0
0
0
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
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
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
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
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
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
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
1
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
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
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
0
1
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
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
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
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
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
1
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
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
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
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
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
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
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
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
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
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
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
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
0
0
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
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
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
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
0
0
0
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
1
0
1
1
0
1
0
0
0
0
1
0
0
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
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
0
1
0
0
0
0
0
1
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
1
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
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
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
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
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
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
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
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
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
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
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
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
0
0
0
1
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
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
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
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
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
0
0
1
0
0
0
0
0
0
0
0
0
0
1
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
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
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
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
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
0
0
0
1
0
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
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
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
1
0
0
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
1
0
1
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
1
0
0
0
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
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
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
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
0
1
0
0
0
0
0
1
0
0
1
0
0
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
1
0
1
0
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
0
0
0
0
0
0
0
0
1
0
0
1
0
0
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
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
1
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
0
1
0
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
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
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
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
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
1
0
1
0
1
0
0
0
0
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
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
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
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
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
1
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
1
0
1
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
0
0
1
1
0
0
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
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
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
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
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
1
1
1
1
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
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
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
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
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
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
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
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
0
0
0
1
0
0
0
0
0
0
0
0
1
1
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
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
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
0
0
1
0
0
0
1
0
0
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
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
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
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
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
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
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
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
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
0
0
0
0
0
0
1
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
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
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
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
0
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
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
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
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
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
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
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
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
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
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
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
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
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
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
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
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
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
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
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
1
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
1
0
0
0
1
0
0
1
1
0
0
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
1
0
1
0
1
1
0
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
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
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
0
0
0
0
1
0
1
0
0
0
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
0
0
0
1
0
0
1
0
0
1
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
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
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
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
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
1
1
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
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
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
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
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
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
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
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
1
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
1
1
1
0
0
1
0
1
0
1
1
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
1
1
0
0
0
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
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
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
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
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
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
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
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
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
0
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
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
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
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
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
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
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
0
0
0
1
0
1
0
0
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
0
0
1
1
0
1
1
1
0
0
0
0
0
0
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
0
0
0
0
1
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
0
0
0
1
0
0
0
0
0
0
0
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
1
0
0
0
1
1
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
1
0
0
0
1
0
1
0
0
0
0
0
1
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
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
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
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
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
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
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
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
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
0
0
0
0
0
0
1
1
0
1
1
0
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
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
1
0
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
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
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
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
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
0
0
1
1
0
0
0
0
1
0
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
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
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
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
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
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
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
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
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
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
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
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
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
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
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
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
0
0
0
0
0
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
0
0
0
1
0
0
0
0
0
0
0
0
1
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
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
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
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
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
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
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
0
0
0
1
0
1
0
0
0
0
0
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
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
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
0
0
1
1
0
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
1
0
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
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
0
0
1
0
0
1
0
1
0
1
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
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
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
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
0
0
0
0
1
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
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
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
1
1
0
1
1
0
0
1
0
0
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
1
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
0
1
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
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
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
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
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
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
0
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
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
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
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
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
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
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
1
1
1
1
1
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
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
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
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
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
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
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
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
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
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
0
0
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
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
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
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
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
0
0
1
0
1
1
0
0
0
0
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
0
0
0
1
0
1
0
1
0
0
1
0
0
0
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
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
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
0
0
0
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
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
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
1
1
0
0
1
0
0
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
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
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
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
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
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
0
1
0
0
0
0
1
0
1
1
0
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
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
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
0
1
1
0
0
0
1
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
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
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
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
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
1
0
0
0
1
0
0
0
1
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
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
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
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
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
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
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
1
0
0
0
0
1
0
0
1
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
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
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
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
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
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
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
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
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
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
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
1
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
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
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
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
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
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
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
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
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
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
0
0
0
0
0
0
1
0
0
0
0
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
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
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
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
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
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
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
1
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
1
0
0
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
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
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
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
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
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
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
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
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
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
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
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
0
0
0
0
1
1
1
0
1
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
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
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
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
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
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
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
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
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
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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
1
0
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
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
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
1
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
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
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
1
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
0
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
1
0
0
0
0
0
1
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
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
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
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
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
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
0
1
1
0
1
0
0
0
1
1
0
1
0
0
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
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
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
0
1
0
0
0
1
0
1
1
0
0
0
1
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
1
0
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
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
0
1
0
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
0
0
1
1
1
1
1
1
0
0
1
0
1
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
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
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
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
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
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
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
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
0
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
1
0
1
0
0
1
1
1
0
1
0
0
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
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
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
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
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
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
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
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
1
1
0
0
0
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
0
0
0
0
1
1
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
1
1
0
0
1
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
0
0
1
0
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
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
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
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
1
1
0
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
1
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
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
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
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
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
0
0
0
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
1
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
1
1
1
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
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
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
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
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
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
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
1
0
0
0
1
0
1
1
0
0
1
0
1
0
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
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
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
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
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
1
1
0
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
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
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
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
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
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
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
1
0
0
1
0
0
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
1
1
1
1
0
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
0
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
1
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
1
0
1
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
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
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
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
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
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
0
1
0
0
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
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
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
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
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
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
1
0
0
0
0
0
1
0
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
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
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
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
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
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
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
0
0
0
1
0
0
0
1
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
0
0
0
0
0
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
1
1
0
0
0
0
0
1
0
1
1
1
1
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
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
0
1
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
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
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
1
0
1
0
0
0
1
0
0
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
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
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
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
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
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
0
0
1
0
1
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
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
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
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
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
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
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
0
0
1
0
1
1
1
1
1
0
0
1
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
0
0
0
0
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
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
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
1
0
0
0
1
1
0
0
1
1
1
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
0
0
0
0
1
1
1
0
0
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
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
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
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
1
1
0
0
0
0
1
0
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
0
1
1
1
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
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
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
0
1
1
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
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
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
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
1
0
0
0
1
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
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
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
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
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
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
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
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
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
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
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
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
1
1
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
0
0
0
0
0
1
1
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
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
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
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
0
0
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
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
0
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
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
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
0
1
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
0
1
0
0
1
0
1
0
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
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
0
1
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
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
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
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
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
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
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
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
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
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
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
1
1
0
1
0
1
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
1
1
0
0
1
0
0
0
0
0
0
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
0
0
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
1
0
1
0
0
0
1
0
0
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
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
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
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
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
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
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
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
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
1
0
0
0
1
0
1
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
1
0
0
0
0
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
0
1
1
0
0
1
0
0
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
1
0
0
0
0
1
0
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
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
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
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
1
1
1
1
0
0
1
0
0
0
0
1
1
1
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
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
1
0
0
1
0
1
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
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
1
0
1
0
0
0
0
0
0
0
1
0
1
1
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
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
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
0
0
0
0
0
0
1
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
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
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
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
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
0
1
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
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
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
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
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
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
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
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
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
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
1
0
0
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
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
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
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
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
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
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
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
0
0
0
0
0
1
0
1
1
1
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
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
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
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
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
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
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
1
0
0
0
0
1
0
0
1
0
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
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
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
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
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
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
0
0
0
0
0
0
0
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
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
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
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
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
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
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
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
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
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
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
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
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
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
1
0
0
0
0
1
0
1
0
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
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
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
0
1
0
0
1
1
0
0
1
0
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
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
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
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
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
0
1
0
0
1
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
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
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
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
1
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
1
0
0
0
1
1
0
0
0
1
0
0
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
0
0
0
1
0
0
0
1
0
1
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
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
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
0
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
1
0
0
1
0
0
0
1
0
1
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
1
0
1
0
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
1
0
0
0
1
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
0
0
0
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
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
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
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
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
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
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
1
0
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
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
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
1
0
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
0
1
0
1
0
0
1
1
1
1
1
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
0
0
0
0
0
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
0
0
0
0
1
1
1
0
1
0
1
0
1
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
1
0
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
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
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
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
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
0
0
0
1
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
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
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
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
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
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
0
0
0
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
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
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
1
0
1
1
0
0
1
1
1
0
1
0
0
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
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
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
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
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
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
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
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
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
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
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
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
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
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
0
0
1
1
0
0
1
1
0
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
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
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
0
0
0
1
0
0
1
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
1
0
1
0
1
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
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
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
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
0
0
0
1
0
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
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
1
0
0
1
1
0
0
1
0
1
1
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
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
1
0
0
0
1
0
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
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
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
1
0
0
1
0
1
0
0
1
0
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
1
0
1
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
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
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
0
0
0
0
0
0
0
0
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
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
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
0
0
0
0
0
1
0
0
0
0
1
0
1
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
1
0
0
0
1
0
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
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
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
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
0
0
1
0
1
0
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
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
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
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
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
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
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
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
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
0
1
1
0
0
0
0
1
0
1
0
0
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
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
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
0
1
1
0
0
0
0
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
1
1
1
0
0
0
0
0
0
0
1
0
1
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
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
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
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
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
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
1
0
0
1
1
0
0
1
0
0
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
1
0
0
0
1
0
0
0
1
0
1
0
0
0
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
1
0
1
0
0
1
0
0
0
1
1
0
1
0
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
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
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
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
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
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
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
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
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
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
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
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
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
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
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
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
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
1
0
0
0
0
0
0
1
1
1
0
0
0
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
1
0
0
0
0
0
0
0
0
1
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
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
1
1
0
0
0
0
1
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
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
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
0
0
0
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
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
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
0
0
0
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
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
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
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
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
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
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
1
1
1
1
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
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
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
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
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
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
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
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
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
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
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
0
0
0
0
1
0
0
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
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
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
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
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
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
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
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
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
1
0
0
0
1
1
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
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
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
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
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
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
0
1
1
0
0
0
0
0
0
0
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
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
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
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
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
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
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
1
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
0
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
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
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
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
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
0
0
0
0
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
0
0
0
0
1
0
0
1
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
0
1
0
0
0
0
1
0
0
1
0
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
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
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
1
0
1
1
0
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
0
0
0
0
1
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
0
0
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
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
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
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
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
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
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
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
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
1
0
1
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
1
0
0
0
0
0
0
0
0
0
1
0
0
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
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
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
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
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
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
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
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
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
1
1
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
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
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
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
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
0
0
1
1
1
1
1
1
0
0
1
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
0
0
0
1
0
1
0
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
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
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
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
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
1
0
0
0
1
0
1
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
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
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
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
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
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
1
1
0
0
1
0
0
0
0
0
0
1
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
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
1
0
1
0
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
0
1
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
0
1
0
0
0
0
0
0
0
0
0
1
0
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
0
0
0
1
0
1
0
1
0
0
1
0
1
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
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
1
0
0
1
0
0
1
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
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
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
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
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
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
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
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
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
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
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
1
0
1
1
0
1
0
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
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
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
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
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
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
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
1
1
1
0
0
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
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
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
1
1
0
1
0
0
0
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
0
1
1
0
0
1
0
0
0
1
0
0
1
1
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
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
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
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
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
0
0
0
0
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
0
0
0
1
1
0
1
0
0
1
0
1
0
1
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
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
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
0
1
1
0
0
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
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
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
0
0
0
0
1
0
0
1
1
1
1
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
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
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
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
0
0
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
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
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
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
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
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
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
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
1
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
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
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
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
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
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
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
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
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
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
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
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
0
0
1
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
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
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
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
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
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
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
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
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
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
0
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
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
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
0
0
0
0
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
0
0
0
0
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
1
0
0
0
0
1
0
0
0
1
1
0
1
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
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
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
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
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
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
0
1
0
0
0
0
1
0
0
0
1
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
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
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
1
1
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
1
1
0
0
0
1
0
1
0
0
1
0
1
0
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
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
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
1
0
1
0
1
0
1
0
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
1
0
0
0
0
0
0
0
0
1
1
1
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
1
0
1
0
0
0
1
1
0
1
1
0
0
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
1
0
1
0
0
0
1
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
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
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
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
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
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
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
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
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
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
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
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
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
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
0
0
1
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
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
1
0
1
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
0
1
1
0
0
0
1
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
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
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
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
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
0
0
0
0
1
0
0
1
0
1
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
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
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
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
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
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
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
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
0
1
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
0
0
0
0
1
0
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
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
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
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
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
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
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
1
0
0
1
1
0
1
0
1
1
1
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
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
0
1
0
0
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
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
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
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
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
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
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
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
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
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
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
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
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
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
0
0
0
0
0
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
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
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
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
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
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
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
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
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
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
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
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
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
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
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
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
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
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
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
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
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
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
0
0
0
0
0
0
1
0
1
0
0
0
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
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
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
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
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
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
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
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
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
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
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
0
0
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
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
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
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
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
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
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
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
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
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
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
0
1
0
0
0
1
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
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
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
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
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
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
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
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
0
0
0
0
0
1
1
0
0
0
0
0
0
0
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
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
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
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
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
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
1
0
1
0
1
0
0
1
0
0
1
0
1
1
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
1
0
1
1
0
0
1
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
0
0
1
0
0
1
0
0
0
0
0
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
1
0
1
1
0
1
1
1
1
0
0
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
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
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
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
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
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
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
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
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
0
0
0
0
1
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
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
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
1
0
0
1
1
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
0
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
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
1
1
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
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
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
0
1
0
0
0
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
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
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
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
0
1
1
1
0
1
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
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
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
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
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
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
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
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
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
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
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
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
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
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
0
1
0
0
0
0
0
0
0
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
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
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
0
0
1
1
0
0
1
1
0
1
0
0
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
0
0
0
1
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
1
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
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
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
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
1
0
0
1
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
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
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
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
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
1
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
1
1
0
0
1
0
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
1
0
0
1
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
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
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
0
0
0
0
0
0
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
1
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
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
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
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
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
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
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
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
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
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
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
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
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
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
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
0
0
0
1
0
0
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
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
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
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
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
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
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
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
0
0
1
0
1
0
1
0
0
1
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
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
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
0
0
0
1
1
1
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
0
0
1
0
0
0
0
1
0
0
1
1
1
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
1
0
1
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
1
0
0
1
0
1
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
0
0
1
0
0
1
1
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
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
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
0
0
1
0
0
0
1
1
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
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
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
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
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
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
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
0
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
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
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
1
0
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
0
1
0
0
0
0
0
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
1
1
1
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
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
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
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
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
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
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
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
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
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
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
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
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
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
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
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
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
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
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
1
1
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
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
1
1
1
0
0
0
0
0
0
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
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
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
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
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
0
1
0
0
0
1
1
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
0
0
1
0
0
1
0
0
1
0
0
1
0
0
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
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
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
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
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
0
0
1
0
0
0
1
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
0
0
1
1
0
0
1
0
0
1
1
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
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
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
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
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
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
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
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
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
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
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
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
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
1
0
0
1
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
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
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
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
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
1
1
0
1
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
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
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
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
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
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
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
1
0
0
1
0
0
0
0
0
0
0
0
1
1
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
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
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
0
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
1
0
0
0
0
0
1
0
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
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
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
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
1
0
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
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
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
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
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
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
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
1
0
0
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
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
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
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
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
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
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
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
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
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
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
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
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
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
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
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
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
0
0
0
1
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
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
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
1
0
1
0
0
1
0
1
0
0
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
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
0
0
0
0
0
0
1
1
0
0
0
0
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
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
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
0
0
1
1
1
0
0
0
0
0
0
0
0
1
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
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
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
0
0
0
1
1
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
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
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
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
0
0
0
0
1
1
0
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
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
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
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
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
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
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
0
1
0
0
0
0
1
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
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
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
1
1
0
0
0
0
0
0
0
0
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
1
0
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
1
1
0
0
0
1
0
1
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
1
1
1
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
0
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
0
1
1
0
0
1
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
0
1
0
0
0
0
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
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
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
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
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
0
1
1
0
0
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
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
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
1
0
0
0
0
0
0
1
1
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
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
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
0
0
0
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
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
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
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
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
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
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
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
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
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
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
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
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
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
0
1
0
0
1
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
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
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
0
0
0
0
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
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
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
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
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
1
0
0
0
1
0
1
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
0
1
1
1
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
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
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
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
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
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
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
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
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
0
0
0
0
0
1
0
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
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
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
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
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
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
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
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
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
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
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
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
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
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
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
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
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
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
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
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
1
1
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
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
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
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
1
1
0
0
0
1
1
0
0
0
0
1
0
0
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
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
1
0
1
1
0
0
1
1
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
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
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
0
0
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
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
1
0
1
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
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
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
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
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
1
0
0
1
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
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
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
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
1
1
1
0
0
0
1
0
0
0
1
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
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
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
1
1
1
0
0
1
0
0
1
0
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
0
0
1
0
1
0
0
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
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
0
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
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
1
1
0
1
1
1
0
0
0
0
1
0
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
1
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
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
0
0
0
0
1
0
1
0
1
1
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
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
1
0
0
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
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
0
0
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
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
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
0
0
0
1
0
1
1
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
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
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
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
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
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
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
1
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
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
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
0
0
0
1
0
0
0
1
0
0
1
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
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
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
1
0
0
0
1
0
1
0
1
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
0
0
0
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
0
0
0
0
1
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
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
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
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
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
1
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
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
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
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
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
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
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
0
0
0
0
0
1
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
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
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
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
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
0
0
0
0
1
1
0
0
1
1
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
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
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
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
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
0
0
1
1
0
1
1
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
1
0
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
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
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
0
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
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
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
0
0
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
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
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
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
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
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
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
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
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
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
0
0
0
0
1
1
1
1
1
0
1
0
0
0
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
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
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
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
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
0
0
0
0
0
1
0
0
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
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
1
0
0
1
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
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
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
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
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
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
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
1
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
0
0
0
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
1
1
0
1
0
0
0
0
1
1
1
0
1
1
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
0
1
0
1
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
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
1
1
0
0
0
0
1
0
0
0
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
1
1
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
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
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
1
0
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
0
1
0
0
1
0
0
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
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
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
0
0
0
0
1
1
0
0
0
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
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
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
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
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
1
0
1
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
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
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
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
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
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
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
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
0
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
0
0
0
1
1
0
1
0
1
0
1
1
0
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
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
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
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
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
0
1
0
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
0
0
0
0
0
1
0
1
1
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
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
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
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
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
0
0
0
0
0
0
0
0
0
1
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
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
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
1
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
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
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
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
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
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
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
1
0
0
0
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
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
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
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
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
0
0
0
0
0
0
0
1
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
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
1
0
0
0
0
0
1
0
0
1
0
0
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
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
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
1
1
1
0
1
1
0
0
0
0
0
0
1
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
1
0
0
0
1
0
1
1
1
0
1
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
1
0
0
1
1
1
1
0
0
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
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
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
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
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
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
0
0
1
0
0
0
1
0
0
1
1
0
1
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
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
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
0
1
1
1
1
0
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
0
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
0
1
1
0
1
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
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
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
0
1
0
1
0
0
1
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
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
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
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
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
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
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
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
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
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
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
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
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
0
0
0
1
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
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
0
1
1
1
1
0
1
1
1
1
0
1
1
0
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
1
1
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
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
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
0
1
0
0
1
0
0
0
0
1
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
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
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
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
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
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
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
0
0
1
0
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
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
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
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
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
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
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
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
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
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
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
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
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
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
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
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
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
0
1
1
0
0
1
0
1
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
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
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
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
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
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
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
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
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
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
1
0
0
0
0
1
0
0
0
0
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
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
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
1
1
0
1
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
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
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
0
1
1
0
1
1
1
0
1
0
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
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
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
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
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
0
0
1
0
0
0
0
1
1
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
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
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
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
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
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
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
1
0
0
0
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
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
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
0
0
0
0
0
0
0
0
1
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
0
0
0
1
0
0
0
0
1
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
0
1
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
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
1
1
1
1
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
0
0
0
1
0
1
1
0
1
0
0
0
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
0
1
0
1
0
1
0
0
1
1
0
1
0
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
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
1
0
0
1
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
1
1
1
0
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
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
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
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
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
0
0
1
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
0
1
0
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
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
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
1
1
0
1
1
0
0
0
0
0
1
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
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
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
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
0
0
0
1
1
1
0
0
0
0
1
1
0
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
0
0
0
1
0
0
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
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
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
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
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
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
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
1
0
1
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
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
1
1
1
1
1
1
1
0
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
1
0
1
0
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
1
0
0
0
0
0
1
1
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
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
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
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
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
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
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
0
0
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
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
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
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
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
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
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
1
0
1
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
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
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
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
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
1
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
1
1
1
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
1
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
1
1
0
0
0
1
1
0
1
0
1
0
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
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
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
0
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
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
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
1
1
0
0
0
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
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
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
1
1
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
1
0
0
0
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
1
1
1
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
0
0
0
1
1
0
0
0
0
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
0
1
0
0
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
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
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
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
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
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
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
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
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
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
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
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
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
0
1
0
0
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
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
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
1
0
0
1
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
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
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
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
0
0
1
1
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
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
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
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
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
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
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
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
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
1
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
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
0
1
1
0
1
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
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
0
0
0
1
1
0
0
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
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
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
0
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
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
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
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
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
0
0
1
1
0
0
0
1
0
0
1
0
0
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
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
1
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
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
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
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
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
0
0
0
0
0
0
1
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
0
0
0
0
0
1
0
0
0
0
0
0
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
0
0
1
0
0
0
0
1
0
0
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
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
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
1
0
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
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
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
1
0
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
0
0
0
1
0
1
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
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
0
0
1
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
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
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
1
1
0
1
1
0
0
0
0
0
0
1
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
0
0
0
0
1
0
0
1
1
0
0
0
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
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
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
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
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
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
1
0
1
1
0
0
0
1
1
1
0
0
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
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
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
0
0
0
1
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
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
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
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
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
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
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
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
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
0
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
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
1
0
1
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
0
1
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
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
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
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
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
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
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
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
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
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
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
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
0
0
0
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
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
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
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
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
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
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
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
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
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
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
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
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
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
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
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
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
0
1
1
0
0
0
0
0
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
0
1
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
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
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
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
0
0
0
0
1
0
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
0
0
1
0
0
0
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
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
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
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
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
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
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
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
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
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
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
1
0
0
1
1
0
1
0
0
1
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
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
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
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
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
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
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
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
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
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
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
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
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
0
0
1
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
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
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
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
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
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
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
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
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
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
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
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
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
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
1
0
0
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
1
1
0
0
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
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
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
0
1
0
0
0
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
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
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
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
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
0
0
1
0
1
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
0
0
1
0
1
0
1
0
1
1
0
0
1
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
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
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
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
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
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
0
0
1
0
0
0
1
0
0
0
0
0
1
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
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
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
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
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
0
0
0
0
0
0
1
0
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
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
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
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
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
1
1
0
0
0
0
0
0
1
0
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
0
1
0
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
0
0
0
1
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
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
0
0
0
0
1
0
0
0
0
0
0
0
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
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
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
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
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
0
1
1
0
0
0
1
0
0
1
1
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
1
0
0
1
0
0
0
0
1
1
0
0
0
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
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
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
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
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
1
1
0
0
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
1
0
0
0
0
0
1
0
0
1
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
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
0
1
0
0
0
0
1
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
1
0
0
0
0
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
0
0
0
0
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
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
1
0
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
0
0
1
0
0
1
0
1
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
0
1
0
1
0
0
1
0
0
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
0
0
1
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
1
0
0
0
0
0
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
0
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
1
0
0
0
1
0
1
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
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
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
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
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
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
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
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
1
1
1
1
1
1
1
1
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
1
0
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
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
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
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
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
1
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
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
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
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
0
0
1
1
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
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
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
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
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
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
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
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
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
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
1
1
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
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
1
0
0
0
0
1
0
0
0
1
0
0
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
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
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
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
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
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
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
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
1
0
0
1
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
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
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
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
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
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
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
0
0
1
0
0
0
0
0
0
0
0
0
1
0
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
1
1
0
0
1
0
0
0
1
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
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
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
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
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
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
1
0
0
1
0
0
1
0
0
0
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
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
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
0
0
0
1
0
1
0
0
0
0
0
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
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
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
1
0
0
0
0
0
0
1
0
0
1
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
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
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
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
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
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
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
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
0
0
1
0
0
1
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
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
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
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
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
0
1
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
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
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
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
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
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
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
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
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
1
1
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
1
0
0
1
0
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
0
0
0
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
1
0
0
1
1
1
0
0
0
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
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
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
1
1
0
1
0
0
1
1
0
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
0
0
1
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
0
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
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
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
1
1
0
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
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
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
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
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
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
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
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
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
0
1
0
1
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
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
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
1
1
1
1
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
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
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
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
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
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
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
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
0
0
1
0
0
1
0
0
0
0
1
0
0
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
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
0
0
0
0
1
1
0
0
0
1
0
1
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
0
0
0
0
0
0
0
1
0
0
0
0
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
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
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
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
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
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
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
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
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
1
0
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
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
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
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
1
0
0
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
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
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
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
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
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
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
1
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
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
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
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
1
0
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
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
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
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
0
0
0
0
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
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
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
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
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
0
1
0
0
0
1
1
0
1
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
1
0
0
1
0
1
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
0
0
0
0
0
0
0
1
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
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
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
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
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
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
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
1
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
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
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
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
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
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
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
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
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
1
1
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
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
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
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
0
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
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
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
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
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
0
0
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
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
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
1
0
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
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
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
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
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
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
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
1
1
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
1
0
0
0
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
0
0
1
1
0
0
0
1
1
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
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
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
0
0
0
0
1
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
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
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
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
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
1
0
0
0
0
0
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
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
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
0
0
0
0
1
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
0
0
1
1
1
0
0
0
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
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
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
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
1
1
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
1
1
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
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
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
1
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
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
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
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
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
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
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
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
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
0
0
0
0
1
0
0
0
1
1
1
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
0
0
0
0
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
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
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
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
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
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
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
1
0
0
0
1
0
1
1
0
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
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
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
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
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
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
0
0
0
0
0
1
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
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
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
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
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
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
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
0
0
1
1
0
1
1
1
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
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
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
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
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
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
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
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
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
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
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
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
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
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
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
1
0
0
0
0
0
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
0
1
0
0
1
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
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
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
1
1
0
1
0
1
0
0
0
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
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
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
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
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
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
0
0
0
1
1
0
1
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
1
1
0
0
0
0
0
0
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
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
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
1
0
1
0
1
0
1
0
0
0
1
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
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
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
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
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
1
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
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
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
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
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
0
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
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
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
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
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
1
0
1
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
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
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
0
0
1
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
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
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
0
0
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
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
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
0
0
1
0
0
1
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
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
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
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
1
0
0
0
0
0
0
1
1
0
1
0
0
0
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
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
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
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
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
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
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
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
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
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
1
0
0
1
0
1
0
0
0
0
0
1
0
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
1
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
0
1
0
1
0
0
0
0
0
0
0
1
1
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
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
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
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
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
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
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
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
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
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
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
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
0
0
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
0
1
0
1
0
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
0
1
1
0
0
0
0
0
1
0
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
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
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
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
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
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
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
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
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
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
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
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
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
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
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
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
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
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
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
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
0
0
1
0
0
1
0
0
0
1
0
0
1
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
1
1
0
0
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
1
1
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
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
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
0
1
1
0
0
0
1
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
0
0
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
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
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
0
0
0
1
0
1
0
0
1
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
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
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
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
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
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
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
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
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
0
0
1
0
1
0
0
0
0
1
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
0
1
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
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
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
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
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
0
1
1
0
0
0
1
0
1
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
1
0
1
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
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
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
1
0
0
0
1
1
1
0
1
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
0
1
0
0
1
1
0
1
1
1
0
1
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
0
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
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
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
0
1
1
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
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
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
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
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
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
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
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
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
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
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
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
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
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
1
0
0
0
0
0
1
1
0
0
0
0
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
0
1
0
1
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
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
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
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
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
0
0
0
1
1
1
1
1
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
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
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
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
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
1
0
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
0
0
1
1
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
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
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
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
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
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
0
1
0
0
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
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
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
0
0
1
0
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
0
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
0
0
0
0
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
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
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
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
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
1
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
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
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
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
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
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
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
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
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
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
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
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
0
0
0
0
0
0
0
1
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
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
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
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
0
0
0
1
0
0
0
1
0
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
0
0
1
0
0
1
0
0
1
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
0
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
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
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
0
1
1
0
0
1
1
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
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
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
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
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
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
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
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
0
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
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
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
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
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
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
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
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
1
0
1
0
0
0
0
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
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
1
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
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
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
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
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
0
0
0
0
1
0
0
0
0
0
1
1
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
0
0
0
0
0
1
0
1
1
0
0
0
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
1
1
1
1
0
0
0
0
1
1
0
1
1
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
0
0
1
0
0
1
1
1
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
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
0
1
1
0
0
0
0
0
0
0
0
1
0
0
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
1
1
1
0
0
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
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
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
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
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
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
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
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
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
1
0
1
0
0
0
1
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
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
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
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
0
0
1
1
1
0
1
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
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
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
1
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
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
0
1
0
0
0
0
0
0
1
0
0
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
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
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
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
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
0
0
0
0
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
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
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
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
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
1
0
0
0
0
0
1
1
0
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
0
0
0
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
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
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
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
0
0
0
0
0
1
1
0
0
1
0
1
1
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
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
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
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
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
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
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
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
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
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
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
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
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
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
1
1
0
1
1
1
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
0
1
1
0
0
1
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
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
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
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
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
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
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
0
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
1
0
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
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
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
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
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
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
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
0
1
0
0
0
0
1
0
0
1
0
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
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
1
0
0
0
1
1
0
1
0
0
1
0
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
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
0
0
0
0
0
0
0
1
0
1
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
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
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
0
0
1
0
0
1
0
1
0
1
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
1
0
1
1
0
1
0
0
1
0
1
0
0
0
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
1
1
0
0
1
0
1
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
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
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
1
1
1
0
0
0
0
0
1
0
0
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
0
1
0
0
0
0
0
1
0
0
1
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
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
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
0
0
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
0
0
1
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
0
0
0
0
0
0
0
0
0
0
0
0
1
1
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
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
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
1
1
0
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
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
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
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
0
0
1
1
0
0
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
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
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
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
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
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
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
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
1
0
0
0
1
1
1
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
0
0
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
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
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
1
1
0
1
0
1
0
0
1
1
1
1
0
0
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
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
0
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
1
1
0
0
0
0
1
0
0
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
1
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
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
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
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
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
0
0
0
0
0
1
0
1
0
0
1
0
1
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
0
0
0
1
0
1
0
0
1
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
0
0
0
0
0
0
1
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
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
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
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
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
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
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
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
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
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
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
0
1
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
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
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
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
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
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
1
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
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
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
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
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
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
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
1
1
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
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
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
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
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
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
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
1
0
1
0
0
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
1
0
1
0
0
0
1
0
0
1
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
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
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
1
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
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
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
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
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
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
0
0
0
0
0
0
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
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
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
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
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
1
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
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
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
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
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
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
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
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
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
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
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
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
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
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
1
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
0
0
0
0
1
0
0
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
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
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
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
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
0
0
0
1
0
0
1
1
1
0
1
1
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
0
0
1
0
0
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
0
0
0
0
0
0
1
0
1
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
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
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
1
1
0
1
0
0
0
1
1
1
1
1
1
1
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
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
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
0
0
0
0
1
1
0
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
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
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
0
0
1
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
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
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
0
1
0
0
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
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
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
0
0
1
0
1
1
1
0
0
0
0
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
1
0
1
0
0
1
0
1
0
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
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
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
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
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
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
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
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
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
0
1
0
0
1
1
0
0
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
0
0
0
1
0
0
1
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
1
1
1
0
0
1
0
0
1
1
0
1
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
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
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
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
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
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
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
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
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
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
1
0
0
0
0
1
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
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
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
0
0
0
0
0
1
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
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
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
1
1
0
1
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
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
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
0
0
0
1
1
0
0
1
0
1
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
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
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
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
0
0
0
0
0
0
1
0
1
1
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
0
0
1
1
0
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
0
0
0
1
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
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
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
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
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
1
0
0
0
0
0
0
0
1
0
0
0
0
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
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
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
0
1
0
0
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
1
0
0
0
0
1
0
0
0
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
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
0
1
0
0
1
0
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
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
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
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
1
0
0
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
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
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
1
0
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
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
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
0
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
1
0
0
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
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
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
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
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
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
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
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
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
1
0
1
0
1
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
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
1
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
1
0
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
1
0
1
1
0
0
0
0
1
0
0
1
1
1
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
1
1
1
0
1
0
1
0
1
1
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
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
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
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
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
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
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
1
0
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
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
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
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
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
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
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
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
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
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
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
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
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
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
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
0
0
0
0
0
0
0
0
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
0
0
0
0
0
0
1
0
0
0
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
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
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
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
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
0
0
0
1
0
1
0
1
0
0
0
1
0
0
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
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
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
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
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
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
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
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
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
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
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
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
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
0
0
1
1
0
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
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
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
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
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
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
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
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
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
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
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
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
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
0
1
0
1
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
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
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
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
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
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
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
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
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
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
0
0
1
0
1
1
0
0
0
0
0
0
0
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
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
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
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
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
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
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
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
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
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
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
1
0
1
1
0
1
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
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
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
1
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
1
1
0
0
1
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
1
0
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
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
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
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
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
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
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
0
0
1
0
0
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
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
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
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
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
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
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
1
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
0
0
0
0
0
0
1
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
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
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
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
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
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
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
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
1
0
1
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
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
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
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
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
0
0
0
1
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
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
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
1
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
0
0
0
0
1
0
1
1
1
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
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
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
1
1
0
0
0
1
0
1
1
0
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
1
0
0
0
0
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
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
1
0
0
1
0
0
1
1
0
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
0
0
0
0
1
0
1
0
0
0
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
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
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
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
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
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
1
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
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
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
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
0
1
0
1
1
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
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
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
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
0
0
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
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
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
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
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
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
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
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
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
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
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
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
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
1
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
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
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
1
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
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
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
1
1
1
0
0
0
0
0
0
1
0
0
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
0
0
0
0
1
0
1
1
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
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
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
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
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
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
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
1
0
0
0
1
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
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
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
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
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
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
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
0
1
0
0
0
1
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
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
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
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
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
1
0
0
1
0
1
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
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
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
1
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
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
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
0
0
0
0
1
0
1
0
1
0
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
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
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
1
0
1
0
0
1
0
0
1
0
1
0
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
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
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
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
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
1
0
0
0
0
1
0
0
0
0
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
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
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
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
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
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
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
0
1
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
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
0
0
0
0
0
0
0
0
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
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
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
0
0
0
0
0
0
0
1
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
0
1
0
0
0
0
0
1
1
0
0
0
0
0
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
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
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
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
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
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
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
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
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
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
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
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
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
1
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
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
0
0
0
0
0
0
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
0
0
1
0
1
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
1
0
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
1
1
1
0
1
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
1
0
0
1
0
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
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
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
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
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
0
0
0
1
0
0
0
0
0
0
0
1
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
0
1
0
0
0
1
0
0
0
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
1
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
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
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
1
0
0
1
1
0
0
0
0
0
0
1
1
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
1
0
1
0
0
0
0
0
0
0
0
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
0
1
0
0
0
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
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
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
0
0
0
1
0
1
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
0
1
1
0
0
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
0
0
1
0
0
0
0
0
0
0
0
1
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
1
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
0
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
1
0
0
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
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
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
1
1
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
0
0
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
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
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
0
0
0
0
0
0
0
0
1
1
1
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
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
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
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
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
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
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
0
0
0
1
0
1
0
1
0
1
0
0
0
1
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
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
0
1
1
0
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
0
0
0
1
0
1
0
0
0
1
1
0
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
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
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
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
0
0
0
0
0
0
0
0
0
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
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
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
0
0
0
0
1
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
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
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
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
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
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
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
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
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
1
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
0
0
0
0
1
1
1
1
1
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
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
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
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
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
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
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
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
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
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
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
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
1
0
1
1
0
0
0
0
0
1
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
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
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
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
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
1
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
1
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
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
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
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
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
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
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
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
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
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
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
0
0
0
0
1
0
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
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
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
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
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
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
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
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
1
0
0
0
0
0
1
0
0
0
1
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
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
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
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
0
1
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
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
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
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
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
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
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
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
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
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
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
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
0
0
0
0
1
0
0
1
0
0
0
0
1
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
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
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
0
0
1
0
0
1
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
0
0
0
1
0
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
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
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
0
0
0
0
0
0
0
0
1
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
0
1
0
0
0
0
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
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
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
0
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
1
1
1
1
0
0
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
1
1
0
0
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
1
0
0
1
0
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
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
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
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
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
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
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
0
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
1
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
0
0
0
1
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
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
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
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
1
0
0
1
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
0
1
0
0
0
1
1
0
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
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
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
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
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
1
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
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
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
0
0
0
1
0
0
0
0
0
0
0
0
1
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
1
1
1
0
0
0
1
0
1
0
1
0
1
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
1
0
1
0
1
0
0
1
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
0
0
0
1
0
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
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
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
0
1
0
0
0
0
0
0
0
0
1
0
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
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
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
0
1
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
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
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
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
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
0
0
0
1
1
1
1
1
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
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
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
0
0
0
0
0
1
0
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
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
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
1
0
1
0
0
0
0
1
1
1
0
0
0
0
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
0
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
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
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
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
0
1
0
0
0
0
0
1
0
1
0
0
0
1
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
0
0
1
0
0
1
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
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
1
0
0
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
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
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
1
0
0
1
1
0
1
0
0
1
0
0
0
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
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
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
0
0
0
0
0
0
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
1
1
0
0
0
1
0
1
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
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
0
1
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
0
0
0
0
0
0
0
1
0
1
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
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
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
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
1
1
1
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
1
1
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
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
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
0
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
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
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
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
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
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
0
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
1
1
1
0
0
1
0
1
0
1
0
1
1
1
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
1
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
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
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
0
0
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
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
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
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
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
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
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
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
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
0
0
0
0
0
0
0
0
0
0
0
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
0
0
1
0
0
0
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
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
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
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
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
1
0
0
0
1
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
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
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
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
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
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
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
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
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
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
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
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
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
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
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
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
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
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
1
0
0
0
1
1
0
1
0
0
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
1
0
0
0
0
1
1
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
1
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
0
1
0
0
0
0
0
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
1
0
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
0
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
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
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
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
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
0
0
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
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
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
0
0
0
1
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
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
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
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
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
1
1
0
0
1
0
0
0
1
0
1
1
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
0
1
0
1
1
0
0
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
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
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
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
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
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
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
0
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
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
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
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
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
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
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
0
0
0
0
0
1
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
0
1
0
1
0
0
1
1
0
0
1
1
0
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
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
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
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
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
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
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
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
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
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
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
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
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
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
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
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
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
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
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
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
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
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
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
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
1
0
0
1
0
1
0
0
0
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
0
0
0
0
0
1
1
0
1
1
1
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
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
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
0
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
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
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
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
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
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
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
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
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
0
1
1
1
1
1
0
0
0
1
0
0
1
0
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
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
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
1
0
0
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
0
0
0
0
0
0
0
1
0
0
0
1
0
1
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
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
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
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
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
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
0
0
0
1
1
0
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
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
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
0
0
0
0
0
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
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
0
0
0
0
1
0
0
1
0
0
0
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
1
0
1
1
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
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
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
0
0
0
0
0
1
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
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
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
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
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
0
0
1
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
1
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
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
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
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
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
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
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
0
0
0
0
0
0
0
1
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
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
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
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
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
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
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
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
0
0
0
0
1
0
1
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
0
0
0
1
1
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
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
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
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
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
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
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
0
0
0
1
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
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
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
0
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
1
0
1
1
1
1
0
1
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
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
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
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
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
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
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
0
0
0
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
0
0
1
0
0
1
1
0
0
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
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
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
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
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
0
0
0
0
0
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
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
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
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
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
0
0
0
1
0
1
0
0
0
0
0
0
1
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
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
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
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
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
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
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
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
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
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
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
1
1
0
1
0
0
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
1
0
1
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
1
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
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
0
0
1
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
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
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
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
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
1
0
0
1
1
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
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
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
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
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
1
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
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
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
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
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
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
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
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
0
1
0
1
0
0
0
0
0
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
0
1
0
1
1
1
0
0
0
1
1
1
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
0
0
0
0
0
0
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
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
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
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
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
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
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
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
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
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
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
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
0
1
1
0
0
0
0
1
0
1
0
1
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
0
0
0
0
0
0
1
0
0
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
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
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
1
1
1
0
0
1
0
0
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
0
0
0
0
1
0
1
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
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
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
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
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
0
0
0
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
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
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
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
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
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
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
1
0
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
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
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
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
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
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
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
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
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
0
1
0
0
1
0
1
1
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
0
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
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
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
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
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
0
1
0
1
0
0
1
0
0
1
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
0
1
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
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
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
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
0
0
0
1
0
1
0
1
0
0
1
0
0
0
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
1
0
0
1
0
0
0
0
0
0
1
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
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
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
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
1
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
0
0
0
1
1
1
1
0
1
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
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
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
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
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
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
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
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
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
0
1
0
0
1
0
0
0
1
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
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
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
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
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
0
1
1
0
0
0
0
0
1
0
0
1
1
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
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
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
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
0
0
0
0
1
0
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
0
0
0
0
0
1
0
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
1
0
0
0
0
1
0
0
0
0
1
1
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
1
0
1
1
0
0
0
0
1
0
0
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
0
0
1
0
0
0
0
1
0
0
1
1
1
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
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
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
1
0
0
0
1
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
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
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
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
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
1
1
0
1
0
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
1
1
0
0
0
1
0
0
0
1
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
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
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
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
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
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
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
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
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
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
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
0
0
1
1
0
0
1
1
0
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
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
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
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
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
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
1
1
0
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
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
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
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
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
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
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
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
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
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
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
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
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
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
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
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
1
0
0
0
1
0
1
0
0
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
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
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
0
1
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
0
0
0
0
0
0
0
0
0
1
1
0
1
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
0
0
0
0
0
0
1
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
1
0
0
0
0
0
0
0
1
1
0
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
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
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
0
0
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
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
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
0
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
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
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
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
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
1
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
1
0
0
0
0
0
0
0
0
1
0
1
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
0
0
0
0
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
1
0
0
0
1
0
1
1
0
0
0
0
0
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
1
0
0
0
0
0
0
0
1
1
0
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
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
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
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
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
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
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
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
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
1
0
0
1
0
0
0
0
1
1
1
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
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
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
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
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
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
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
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
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
0
0
0
0
1
0
0
0
0
0
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
0
0
0
1
0
0
0
1
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
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
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
0
1
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
0
0
0
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
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
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
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
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
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
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
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
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
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
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
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
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
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
0
0
0
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
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
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
1
0
0
0
0
1
1
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
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
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
1
0
0
0
0
0
0
0
1
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
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
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
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
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
1
0
1
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
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
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
0
0
0
0
0
1
1
1
0
1
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
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
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
0
0
0
0
1
1
0
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
1
0
0
0
0
1
0
1
0
1
0
0
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
1
0
0
0
0
1
0
0
1
0
1
0
0
1
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
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
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
0
1
1
1
0
0
1
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
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
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
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
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
1
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
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
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
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
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
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
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
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
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
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
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
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
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
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
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
1
1
0
1
1
0
0
1
1
0
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
1
0
1
0
1
1
0
1
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
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
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
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
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
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
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
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
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
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
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
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
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
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
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
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
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
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
0
0
1
0
0
1
1
0
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
0
0
1
0
1
0
0
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
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
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
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
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
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
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
0
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
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
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
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
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
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
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
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
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
0
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
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
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
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
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
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
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
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
0
0
1
0
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
1
0
0
0
0
1
0
1
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
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
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
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
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
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
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
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
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
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
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
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
0
0
1
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
0
0
0
1
1
0
0
0
0
1
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
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
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
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
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
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
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
0
0
1
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
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
0
0
0
0
0
1
1
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
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
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
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
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
0
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
0
1
1
1
0
0
0
0
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
1
1
1
1
0
0
0
1
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
1
0
1
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
0
1
1
0
0
0
1
1
1
1
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
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
1
0
0
0
0
1
0
0
0
0
1
1
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
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
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
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
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
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
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
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
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
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
1
1
1
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
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
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
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
0
0
0
1
1
1
1
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
0
0
1
0
0
0
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
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
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
0
0
0
0
1
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
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
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
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
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
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
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
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
1
0
1
1
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
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
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
1
0
0
0
0
0
1
1
1
1
1
0
0
1
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
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
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
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
1
1
1
0
1
0
1
0
1
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
1
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
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
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
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
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
1
1
0
0
1
1
0
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
0
1
0
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
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
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
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
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
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
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
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
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
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
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
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
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
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
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
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
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
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
0
1
0
1
1
1
1
0
1
0
0
1
0
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
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
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
0
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
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
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
0
0
1
0
0
0
0
0
1
1
0
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
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
1
0
1
0
0
1
0
0
1
1
1
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
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
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
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
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
0
0
1
0
0
0
1
1
0
0
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
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
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
0
0
0
0
1
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
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
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
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
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
1
0
1
0
1
0
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
0
0
0
0
0
1
0
0
1
0
0
0
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
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
0
0
0
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
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
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
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
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
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
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
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
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
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
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
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
0
0
0
1
0
1
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
1
0
1
0
0
0
0
0
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
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
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
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
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
1
0
0
0
0
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
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
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
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
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
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
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
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
0
1
0
0
0
0
1
1
0
0
0
0
0
0
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
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
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
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
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
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
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
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
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
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
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
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
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
1
1
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
1
0
0
1
1
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
1
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
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
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
1
0
1
1
0
0
0
1
0
0
0
0
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
0
0
0
1
0
0
1
1
0
1
0
1
0
0
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
0
0
0
0
0
0
0
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
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
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
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
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
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
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
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
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
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
0
0
0
0
0
1
0
0
0
0
0
0
0
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
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
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
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
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
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
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
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
1
1
0
0
0
0
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
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
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
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
1
0
1
0
0
1
0
1
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
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
1
0
1
0
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
0
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
0
1
0
0
0
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
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
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
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
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
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
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
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
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
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
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
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
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
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
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
1
1
0
0
0
1
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
0
0
1
1
1
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
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
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
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
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
0
1
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
1
0
0
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
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
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
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
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
1
1
0
0
0
0
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
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
1
0
0
0
1
0
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
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
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
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
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
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
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
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
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
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
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
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
1
0
0
1
0
1
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
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
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
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
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
0
1
1
1
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
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
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
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
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
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
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
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
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
0
0
1
0
0
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
1
0
0
1
0
1
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
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
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
0
1
0
1
0
0
1
0
0
0
0
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
1
0
0
1
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
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
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
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
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
1
1
0
1
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
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
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
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
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
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
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
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
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
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
1
1
0
0
0
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
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
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
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
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
1
0
0
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
1
1
1
1
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
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
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
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
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
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
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
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
0
0
0
0
1
0
1
0
1
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
1
0
1
1
1
1
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
1
0
0
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
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
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
1
1
0
1
0
1
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
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
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
0
1
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
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
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
1
0
1
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
0
1
0
0
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
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
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
0
0
0
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
1
0
1
0
1
0
0
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
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
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
0
1
0
0
0
1
0
1
0
0
1
0
0
0
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
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
0
1
1
1
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
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
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
1
0
1
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
1
0
0
1
1
1
0
1
0
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
1
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
0
0
0
0
0
0
1
0
1
0
1
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
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
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
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
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
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
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
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
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
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
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
0
0
0
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
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
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
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
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
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
1
0
1
1
0
0
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
1
0
0
1
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
0
0
0
1
1
0
0
0
0
0
1
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
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
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
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
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
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
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
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
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
0
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
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
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
0
0
0
1
0
1
0
0
0
1
1
0
0
0
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
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
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
1
1
1
0
0
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
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
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
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
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
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
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
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
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
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
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
1
1
1
0
0
1
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
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
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
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
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
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
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
1
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
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
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
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
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
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
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
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
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
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
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
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
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
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
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
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
1
0
0
0
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
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
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
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
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
1
0
0
0
1
0
1
0
0
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
1
0
1
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
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
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
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
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
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
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
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
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
1
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
1
1
0
0
1
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
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
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
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
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
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
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
0
0
0
0
0
1
0
0
0
0
0
0
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
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
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
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
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
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
1
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
0
0
0
0
1
0
0
1
0
0
0
0
0
0
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
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
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
1
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
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
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
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
1
0
0
1
1
0
0
0
1
1
0
0
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
0
0
0
0
0
0
0
0
0
0
0
1
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
1
0
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
0
1
0
0
0
0
1
1
1
1
1
0
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
0
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
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
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
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
1
0
0
0
1
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
0
1
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
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
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
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
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
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
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
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
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
1
0
1
0
0
0
0
0
0
0
1
0
0
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
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
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
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
1
1
1
1
0
0
0
1
1
0
0
0
1
1
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
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
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
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
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
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
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
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
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
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
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
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
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
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
0
0
0
1
1
0
1
0
0
0
1
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
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
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
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
1
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
0
0
0
1
0
1
0
1
0
1
1
1
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
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
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
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
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
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
0
0
0
0
1
0
1
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
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
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
1
0
1
0
0
0
1
1
0
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
0
0
0
0
0
0
1
1
1
0
0
1
1
1
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
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
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
1
0
0
0
1
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
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
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
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
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
0
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
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
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
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
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
1
0
0
0
1
0
0
0
1
1
0
0
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
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
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
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
0
0
0
0
0
0
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
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
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
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
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
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
0
0
1
0
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
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
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
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
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
1
0
0
0
0
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
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
1
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
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
0
1
0
0
1
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
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
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
1
0
1
0
1
0
1
0
0
1
0
0
0
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
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
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
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
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
0
1
0
1
1
1
1
0
0
1
0
1
1
1
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
0
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
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
0
0
1
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
0
1
1
1
0
1
1
1
0
1
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
0
0
0
0
0
1
0
1
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
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
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
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
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
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
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
0
0
1
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
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
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
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
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
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
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
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
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
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
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
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
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
0
0
1
0
0
1
0
0
0
1
0
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
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
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
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
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
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
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
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
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
0
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
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
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
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
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
1
0
1
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
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
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
1
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
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
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
0
0
0
1
0
0
0
1
1
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
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
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
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
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
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
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
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
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
0
1
0
1
0
0
1
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
0
0
0
0
1
0
0
1
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
1
0
0
0
1
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
0
0
0
1
1
0
1
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
0
0
0
1
0
0
1
0
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
1
0
0
0
1
1
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
1
0
1
0
0
0
0
1
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
1
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
1
0
1
0
0
1
0
1
1
0
0
0
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
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
1
1
0
0
0
1
0
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
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
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
0
0
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
0
0
0
0
0
0
1
1
0
1
0
1
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
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
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
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
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
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
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
1
0
0
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
1
1
0
0
1
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
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
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
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
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
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
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
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
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
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
1
1
0
0
0
1
0
1
0
1
0
0
0
0
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
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
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
1
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
1
0
0
0
0
0
0
0
1
0
1
0
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
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
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
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
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
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
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
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
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
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
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
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
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
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
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
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
0
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
0
0
1
0
1
0
0
0
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
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
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
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
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
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
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
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0