s460985/paranormal-or-skeptic4
1
0
Fork 0
Code Issues Pull Requests Releases Wiki Activity
73a1b8862f
paranormal-or-skeptic4/train/expected.tsv
Filip Gralinski 73a1b8862f Switching to O/1
2020-03-30 18:28:23 +02:00

566 KiB
Raw Blame History 

1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1