Hugging Face's logo

Spaces:
AstraTeam
/
astra
Build error

App Files Community
8
astra / train_label.txt
suryadev1's picture
suryadev1
Upload 3 files
4509c3d
raw
history blame
124 kB
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
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
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
0
1
1
0
1
1
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
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
1
1
1
1
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
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
0
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
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
0
1
0
1
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
0
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
1
0
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
0
1
0
0
0
1
0
1
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
0
0
1
1
1
1
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
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
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
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
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
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
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
1
0
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
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
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
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
1
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
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
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
0
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
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
1
1
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
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
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
0
0
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
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
1
0
1
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
0
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
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
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
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
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
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
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
0
0
0
0
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
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
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
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
0
1
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
0
1
0
0
1
1
1
0
0
1
1
0
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
1
0
0
1
0
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
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
0
0
1
0
1
1
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
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
0
0
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
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
1
0
1
1
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
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
0
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
0
1
1
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
0
0
0
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
1
0
1
0
0
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
1
1
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
1
0
0
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
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
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
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
1
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
0
1
0
0
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
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
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
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
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
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
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
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
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
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
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
0
0
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
1
0
0
1
0
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
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
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
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
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
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
1
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
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
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
1
0
0
1
1
1
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
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
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
1
0
0
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
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
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
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
0
1
1
0
1
1
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
0
1
0
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
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
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
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
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
0
1
0
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
0
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
1
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
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
0
0
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
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
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
1
0
0
1
1
0
1
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
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
0
0
0
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
1
0
0
0
1
0
1
0
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
1
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
0
0
1
1
1
1
0
0
1
0
1
1
1
1
1
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
0
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
1
0
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
1
0
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
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
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
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
1
1
0
1
0
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
1
1
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
0
0
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
1
1
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
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
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
0
1
0
0
1
0
1
1
0
0
0
0
1
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
1
1
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
0
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
1
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
1
0
0
0
1
1
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
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
1
0
0
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
0
1
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
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
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
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
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
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
0
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0
1
0
1
0
0
1
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
1
0
1
1
0
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
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
0
0
0
1
1
1
1
1
0
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
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
1
1
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
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
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
1
1
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
0
0
1
1
0
1
1
0
1
0
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
0
1
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
0
1
1
0
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
1
0
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
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
1
1
0
1
0
0
1
0
0
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
1
0
0
0
1
1
0
0
0
1
1
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
0
0
1
0
0
1
0
0
0
0
1
1
1
0
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
0
0
0
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
1
0
1
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
0
0
1
0
1
0
1
1
1
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
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
0
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
0
0
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
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
1
0
1
1
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
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
0
1
0
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
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
1
0
1
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
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
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
1
1
0
0
1
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
1
0
1
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
0
1
1
0
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
1
1
0
0
0
1
1
1
0
0
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
0
1
1
1
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
0
0
1
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
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
0
1
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
1
1
1
1
0
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
1
1
1
0
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
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
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
1
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
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
0
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
0
1
1
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
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
0
1
0
0
0
0
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
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
0
0
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
0
0
1
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
1
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
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
1
0
1
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
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
0
1
0
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
1
0
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
1
0
1
0
0
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
1
1
0
0
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
1
0
1
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
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
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
1
1
1
0
0
1
1
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
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
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
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
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
1
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
0
1
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
0
1
0
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
1
0
0
0
1
0
1
1
1
1
1
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
0
0
0
0
0
0
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
0
0
1
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
1
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
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
1
0
1
1
1
1
0
1
0
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
0
0
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
1
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
1
1
0
1
1
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
1
1
1
0
0
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
1
1
0
1
0
1
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
1
1
1
1
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
0
1
0
0
1
1
1
0
1
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
1
1
1
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
1
0
1
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
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
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
1
0
0
1
0
1
0
1
0
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
0
0
0
1
1
0
1
0
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
0
1
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
1
0
0
0
1
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
1
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
1
1
0
1
0
0
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
0
0
1
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
0
0
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
0
0
1
1
0
0
0
1
0
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
0
1
0
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
0
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
0
0
0
1
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
0
1
0
0
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
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
1
1
1
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
1
0
0
0
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
0
1
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
0
1
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
0
0
1
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
0
1
1
0
1
0
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
0
1
0
1
1
1
0
1
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
0
0
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
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
1
1
0
0
1
1
0
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
1
1
0
1
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
1
1
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
0
0
1
0
0
0
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
0
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
1
0
1
1
0
0
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
1
0
0
1
1
0
1
0
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
1
1
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
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
1
1
0
0
1
1
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
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
1
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
1
1
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
1
0
1
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
1
0
1
0
0
1
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
1
0
0
0
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
1
1
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
0
1
1
1
1
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
0
1
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
1
1
0
0
1
1
0
1
1
0
1
0
1
0
1
1
0
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
0
0
1
1
0
0
1
0
0
1
1
1
0
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
1
0
1
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
1
0
0
1
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
1
0
0
0
0
1
0
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
0
0
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
1
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
1
1
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
1
0
0
1
0
1
0
0
0
0
0
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
0
0
1
0
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
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
1
1
0
0
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
0
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
1
0
1
1
0
0
0
1
0
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
0
1
0
0
0
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
1
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
0
0
1
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
1
0
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
1
1
1
1
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
0
0
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
1
0
0
1
0
0
0
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
0
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
0
1
0
0
0
0
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
0
1
0
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
0
1
0
1
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
0
0
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
1
0
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
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
1
0
0
0
1
0
1
0
0
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
1
1
0
1
1
0
0
1
1
0
1
0
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
0
0
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
1
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
1
1
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
1
0
1
1
0
1
1
1
0
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
1
0
1
0
1
0
0
1
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
0
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
0
1
0
1
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
1
0
0
0
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
0
1
0
0
1
0
1
0
1
1
0
0
0
0
0
0
1
0
1
1
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
0
0
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
0
0
1
0
0
1
0
1
0
0
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
0
0
0
0
0
0
1
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
0
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
1
1
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
0
0
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
0
0
0
0
1
0
1
0
1
0
0
0
0
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
0
0
1
1
0
1
0
1
1
1
0
0
0
0
1
0
0
0
1
1
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
1
0
0
0
1
1
0
1
0
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
0
1
1
1
0
0
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
1
1
0
0
0
0
0
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
1
0
1
1
1
1
1
1
0
1
1
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
1
0
1
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
1
0
1
1
0
0
1
1
1
1
0
1
0
1
1
0
0
0
0
1
0
0
0
1
0
1
1
1
0
1
0
1
0
0
0
0
1
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
0
1
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
0
0
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
0
0
1
1
0
1
1
1
1
0
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
0
1
1
0
0
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
1
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
1
0
1
1
1
0
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
0
1
0
1
0
1
1
1
1
0
1
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
1
1
0
1
0
1
0
0
1
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
1
1
1
1
1
0
1
1
1
1
1
0
1
0
1
0
1
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
0
0
1
0
0
1
1
1
0
0
0
1
0
0
0
0
1
1
1
1
1
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
1
0
0
1
0
1
0
0
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
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
0
1
0
0
1
0
0
1
1
0
1
0
1
0
0
1
0
1
0
1
1
1
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
0
0
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
0
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
1
1
1
1
1
0
1
0
0
1
1
1
1
1
1
1
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
0
1
0
0
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
0
1
0
1
0
0
1
0
0
1
0
0
1
1
1
0
1
1
0
0
1
1
0
1
1
0
1
0
0
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
1
1
0
1
1
1
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
0
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
0
1
0
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
1
1
1
1
1
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
1
1
0
1
0
0
1
1
0
0
1
0
1
0
0
1
0
0
0
1
0
1
1
0
1
0
1
1
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
1
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
0
1
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
1
1
1
0
1
1
1
0
1
1
0
0
1
1
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
1
0
0
1
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
1
0
1
1
1
1
1
0
1
1
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
1
1
0
1
0
0
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
1
0
0
0
1
0
1
1
1
1
0
1
0
1
0
1
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
1
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
1
0
0
0
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
1
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
0
1
0
1
1
0
1
1
0
0
0
1
1
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
0
1
0
1
1
0
0
1
1
1
0
0
0
1
0
1
0
0
0
0
0
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
0
1
1
1
0
1
0
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
1
0
1
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
1
0
0
0
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
0
0
0
1
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
1
0
0
0
0
1
1
0
0
0
1
1
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
1
0
0
1
0
0
1
0
0
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
0
0
1
1
1
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
1
1
0
0
0
1
0
1
0
1
1
1
1
0
0
1
0
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
0
1
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
0
0
1
0
1
1
1
0
1
1
0
1
1
0
0
1
1
0
0
0
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
1
0
1
1
0
1
0
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
1
0
1
1
1
1
0
1
0
1
1
1
1
0
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
0
0
1
0
0
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
0
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
1
1
1
0
1
1
0
1
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
0
0
0
1
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
1
1
1
0
0
0
0
1
0
0
0
1
0
1
0
1
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
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
0
1
1
0
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
0
1
0
1
0
0
1
0
1
1
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
0
1
1
0
1
1
1
1
0
1
1
1
0
1
1
1
1
0
1
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
1
0
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
1
1
0
1
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
0
0
1
1
1
0
0
0
0
0
1
1
1
0
1
0
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
1
1
0
1
1
1
1
1
0
1
1
0
0
1
0
1
0
0
1
1
0
1
1
1
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
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
1
1
1
1
1
0
0
0
0
0
0
1
1
1
0
1
1
0
0
0
1
0
1
0
0
1
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
0
1
0
1
1
1
1
0
1
0
1
0
0
0
0
0
1
0
0
1
1
1
1
0
1
1
0
0
0
0
1
0
0
0
0
1
1
0
1
1
1
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
1
0
1
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
0
0
0
0
1
0
1
1
1
1
0
1
1
0
0
0
0
1
0
1
0
0
1
0
0
1
1
0
0
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
1
0
1
1
0
1
0
0
1
1
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
0
0
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
0
0
1
0
0
1
0
1
0
1
0
1
1
0
1
1
0
0
1
1
0
0
1
0
1
1
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
0
0
1
0
1
1
1
0
1
0
1
0
1
0
0
1
0
0
0
1
1
1
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
1
1
0
0
1
1
1
0
0
1
1
0
1
1
1
0
1
1
1
1
0
1
1
0
0
0
1
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
1
1
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
0
0
0
1
1
1
0
1
0
0
0
0
0
0
1
1
0
1
1
0
1
1
1
0
1
1
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
0
1
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
0
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
1
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
0
0
0
0
0
0
1
0
1
0
1
0
0
1
0
1
0
0
0
1
0
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
0
1
0
1
0
1
0
0
0
0
0
1
0
1
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
1
0
0
1
0
1
1
0
1
1
0
0
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
0
0
0
1
0
0
1
1
1
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
1
0
1
1
1
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
1
0
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
1
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
0
1
0
1
0
1
0
1
1
1
1
1
0
1
1
1
1
1
0
0
0
1
0
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
1
0
0
1
1
1
1
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
1
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
1
0
1
0
0
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
0
1
1
0
1
0
0
0
1
0
1
0
0
0
0
0
0
1
0
1
1
1
1
0
0
1
1
1
1
1
1
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
1
0
0
0
1
0
1
1
0
0
1
0
1
0
1
1
0
1
0
1
1
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
0
0
1
0
1
1
0
1
0
0
1
0
0
1
1
0
1
1
0
0
1
1
0
1
1
1
0
1
1
0
0
1
0
1
0
1
1
1
1
1
0
0
0
1
0
0
1
0
1
0
0
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
1
0
1
1
0
1
1
0
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
1
1
0
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
0
0
1
0
1
0
1
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
0
1
1
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
1
1
1
1
1
0
0
1
0
0
1
1
1
0
1
1
1
1
0
1
1
0
1
1
0
0
1
0
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
1
1
0
1
0
0
1
1
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
0
1
1
1
1
1
1
1
0
0
0
1
0
0
0
1
0
1
0
0
1
1
0
0
0
1
0
0
0
0
1
0
0
0
0
1
1
1
1
0
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
1
0
0
1
1
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
1
0
1
1
1
0
1
1
0
1
0
1
1
0
1
1
1
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
0
1
0
0
1
0
1
1
1
0
0
0
1
1
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
0
1
1
0
1
1
1
0
0
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
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
0
0
1
1
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
0
1
0
0
1
0
0
1
1
0
0
1
1
0
0
0
1
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
1
0
1
1
0
0
0
0
0
0
0
0
0
1
0
1
1
0
0
1
0
1
1
1
1
0
0
1
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
1
0
0
0
0
0
1
1
0
1
0
0
0
0
1
1
1
1
0
0
0
1
0
1
1
1
1
1
1
0
0
0
1
1
0
1
0
0
1
0
0
0
1
1
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
1
1
0
0
0
1
0
0
0
0
1
1
1
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
0
0
1
1
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
1
1
0
1
0
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
0
1
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
1
0
1
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
1
1
1
1
1
0
0
1
1
1
1
1
0
0
1
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
1
0
1
0
1
0
1
0
1
0
0
0
0
0
1
1
1
0
0
0
0
1
1
1
1
0
0
1
0
0
1
1
1
1
1
0
0
0
1
1
1
1
1
1
1
1
0
0
1
1
0
1
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
1
0
1
1
0
0
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
0
0
0
1
1
0
0
1
1
1
1
1
0
1
1
0
0
1
0
1
1
1
1
1
0
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
0
0
0
0
1
1
0
1
1
1
1
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
1
0
1
0
0
0
0
0
1
1
1
0
1
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
1
1
0
0
0
0
1
0
0
0
0
0
1
0
1
0
1
1
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
1
1
1
1
0
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
0
1
0
1
1
1
1
0
1
1
0
1
0
1
1
0
0
0
1
1
1
1
0
1
1
0
1
1
0
1
1
0
1
0
1
1
0
0
1
0
1
0
0
0
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
1
0
1
0
1
0
1
1
0
1
1
0
1
0
0
1
1
0
0
0
0
1
1
1
0
1
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
0
0
0
1
0
0
1
1
1
1
1
1
1
0
0
1
0
0
0
0
0
1
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
1
0
0
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
0
0
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
0
1
1
0
1
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
0
1
1
0
1
1
1
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
1
0
0
0
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
0
0
0
1
0
0
0
1
0
0
0
0
0
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
1
0
0
1
0
1
0
0
1
1
0
0
0
0
0
0
0
1
1
0
1
0
1
0
1
1
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
1
1
1
0
0
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
1
1
1
0
1
0
1
1
1
0
1
1
1
1
1
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
0
1
1
1
0
0
0
0
0
1
1
0
0
0
1
0
1
0
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
1
0
0
0
1
0
0
0
0
0
1
1
1
0
1
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
0
0
1
1
1
0
0
0
0
0
0
0
0
1
1
0
1
1
0
0
1
0
1
0
0
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
0
0
1
1
0
0
0
0
0
0
1
0
0
0
0
1
1
0
0
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
1
0
1
1
0
0
1
0
0
0
1
0
0
1
0
1
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
1
0
1
1
1
0
0
1
0
1
0
0
0
0
1
1
1
1
0
0
1
1
0
1
0
0
0
0
1
1
0
0
1
0
0
1
1
1
0
0
1
0
0
1
0
0
0
1
0
0
1
1
0
1
1
1
1
0
1
1
0
1
1
1
1
1
1
0
1
1
0
0
1
1
1
0
1
0
1
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
1
0
0
0
1
1
1
1
1
0
1
0
0
0
0
0
0
1
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
1
1
1
0
1
0
1
0
1
0
0
0
1
1
0
1
0
1
1
1
1
1
1
0
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
0
1
0
1
1
0
1
0
0
0
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
1
1
1
0
1
0
1
1
0
0
1
0
1
1
1
0
1
0
1
1
1
0
1
1
0
1
0
1
0
1
1
0
1
1
1
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
0
0
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
1
0
0
1
1
1
1
1
0
1
1
0
0
0
0
0
0
1
1
0
1
0
1
1
0
0
1
1
0
0
0
1
0
0
1
1
1
1
0
1
0
0
0
0
0
1
0
0
1
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
1
1
0
0
1
1
1
1
0
0
0
0
1
1
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
1
0
1
0
1
0
1
0
0
0
1
0
0
0
1
1
0
1
1
1
0
1
0
1
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
1
0
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
0
1
0
0
1
1
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
1
1
0
0
1
0
0
0
1
1
0
0
1
1
0
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
0
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
1
1
0
0
1
1
0
0
1
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
0
1
1
0
1
1
1
0
0
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
0
1
0
0
1
0
1
1
1
1
1
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
1
1
0
0
1
1
0
1
0
1
1
0
1
1
0
1
1
1
1
1
1
0
1
0
1
1
1
0
1
1
0
1
1
0
1
1
0
1
1
1
1
0
1
0
0
1
1
0
0
1
1
0
1
0
0
0
1
1
0
0
0
1
0
1
0
1
0
1
1
1
0
0
1
1
0
0
0
1
0
0
0
1
0
0
0
1
1
1
1
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
0
1
1
1
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
0
0
1
1
0
0
1
1
0
1
1
1
1
1
0
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
0
0
0
1
1
0
0
1
0
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
1
1
1
1
1
1
0
0
0
1
1
0
1
1
1
0
1
1
1
0
1
1
0
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
0
0
0
1
0
0
0
1
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
0
0
0
1
0
0
0
0
0
1
0
1
0
0
0
0
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
0
1
1
1
0
1
1
1
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
0
0
0
0
0
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
1
1
1
1
1
0
0
1
0
1
0
0
1
1
0
1
1
0
0
0
1
1
1
0
0
0
1
1
0
1
1
1
1
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
1
0
1
1
1
1
0
1
0
1
0
1
0
1
0
0
1
1
0
1
1
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
0
1
1
0
1
0
0
0
0
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
1
0
1
1
0
0
1
0
0
0
1
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
0
0
0
1
0
0
1
0
1
1
1
1
1
1
0
1
1
0
1
0
1
0
0
1
0
0
0
0
0
0
1
1
1
0
0
0
0
0
1
1
1
0
0
0
1
0
0
0
1
0
1
1
1
0
1
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
1
1
1
1
1
1
1
1
0
0
1
1
1
0
1
0
1
0
1
0
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
0
0
0
0
1
1
1
0
0
1
1
0
0
1
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
0
0
0
0
1
1
0
1
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
1
1
0
1
1
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
1
0
0
1
1
1
0
1
0
0
1
1
0
0
1
0
0
1
0
0
0
0
1
1
0
1
0
0
1
0
0
0
1
0
1
1
1
0
1
1
1
0
0
0
1
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
0
1
0
1
0
0
0
1
1
1
0
1
1
1
1
1
1
0
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
0
0
0
0
0
1
0
1
0
0
1
0
1
0
0
1
1
0
0
1
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
1
0
1
0
1
0
1
1
0
0
1
1
0
0
1
0
1
0
0
0
0
1
1
0
0
1
1
0
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
1
0
0
0
0
1
1
0
1
1
1
1
0
0
0
1
1
0
0
1
0
0
0
0
1
1
1
0
1
0
0
1
0
0
1
1
1
1
1
0
0
1
1
0
0
1
1
0
1
1
0
0
1
1
0
0
0
0
0
0
0
0
0
1
1
0
1
0
1
1
0
1
0
0
0
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
0
0
1
1
0
1
0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
1
1
1
1
1
0
0
1
1
1
0
1
0
1
1
0
1
1
1
1
1
1
1
0
0
0
1
0
1
1
1
0
0
0
0
0
0
0
1
0
1
0
1
1
1
1
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
1
1
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
0
1
1
1
0
0
1
1
0
0
0
1
1
1
1
0
1
1
1
0
0
0
0
0
0
0
0
1
1
1
1
0
0
0
0
1
1
0
1
1
0
0
0
0
0
0
1
0
0
0
1
1
0
1
0
1
0
1
1
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
0
1
1
1
1
1
1
1
0
1
0
1
1
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
1
1
0
0
1
0
1
1
0
0
1
1
1
0
1
0
0
1
0
1
0
0
1
0
0
0
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
0
1
1
0
1
1
1
1
0
1
0
1
1
1
0
0
0
0
1
1
1
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
1
1
0
1
1
0
0
0
0
1
0
1
1
0
0
0
0
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
0
1
0
1
0
0
0
0
1
0
0
1
0
0
1
1
0
0
1
0
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
1
1
0
0
1
0
1
0
0
1
0
0
1
1
0
1
0
0
0
1
0
0
1
0
1
0
1
1
0
1
0
1
0
1
1
0
1
0
0
1
0
1
1
0
1
0
1
0
0
1
1
0
1
0
0
1
1
1
0
1
0
0
1
1
0
1
1
1
1
1
0
1
0
1
1
0
0
0
1
1
1
1
1
0
1
0
1
1
1
1
1
1
0
1
0
0
1
1
0
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
1
0
0
1
1
1
1
1
1
0
1
0
0
0
0
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
1
0
1
1
1
0
0
1
0
1
0
0
0
0
0
0
1
1
1
1
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
0
1
1
1
1
0
0
0
1
1
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
0
0
1
0
1
0
0
1
1
0
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
1
0
1
0
1
0
1
0
1
1
1
1
0
1
1
1
1
0
0
0
1
0
1
1
0
1
1
0
0
1
1
0
1
0
1
1
1
0
1
0
0
0
0
1
0
0
1
0
1
1
0
1
1
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
1
0
1
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
1
0
0
1
1
1
1
0
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
1
1
1
1
1
0
0
0
0
0
0
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
1
1
1
0
1
0
0
0
0
1
1
0
1
0
1
1
1
0
1
0
1
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
1
0
1
1
1
1
1
1
0
1
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
0
1
0
0
0
0
0
1
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
0
0
0
1
1
0
0
1
1
0
0
0
1
0
0
1
0
0
1
1
1
1
0
0
0
1
1
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
0
0
1
1
1
1
0
0
0
1
1
1
1
0
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
1
0
0
1
1
1
0
1
1
1
0
0
1
1
0
1
0
0
1
1
1
1
1
1
1
0
0
1
1
1
0
0
1
1
0
0
0
1
0
1
0
1
0
0
0
0
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
0
1
1
1
0
1
1
0
0
1
1
1
0
0
0
0
0
1
0
0
0
1
1
1
1
1
1
1
1
0
1
0
1
1
0
1
1
1
1
0
1
0
0
0
0
1
0
1
0
0
1
1
1
1
0
1
1
0
1
1
1
0
1
0
1
1
1
1
1
1
1
1
1
1
0
1
0
1
0
0
1
0
1
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
0
0
0
0
1
0
0
1
0
1
0
0
0
1
0
0
0
1
0
1
0
0
0
0
0
1
0
1
1
0
1
0
1
1
1
1
1
0
1
0
0
0
0
0
1
0
1
0
1
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
0
1
0
0
1
0
1
1
1
1
0
1
1
1
0
0
0
0
1
1
0
0
1
1
0
1
1
0
1
0
1
1
1
1
1
1
1
0
1
0
0
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
0
0
0
1
1
0
1
0
0
1
1
0
0
0
0
1
0
1
1
1
0
1
1
1
0
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
1
0
0
0
1
1
1
1
1
1
0
0
1
1
0
0
1
1
1
1
0
1
1
1
1
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
0
0
0
0
1
1
0
1
1
0
0
1
0
0
0
0
1
0
1
0
1
1
1
1
1
1
1
0
0
1
0
1
0
1
0
1
0
1
1
1
0
0
1
1
1
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
0
0
1
0
0
0
1
1
1
0
1
1
1
0
1
0
1
0
0
0
0
0
0
1
0
0
1
1
0
0
0
0
1
1
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
1
0
0
0
0
0
0
0
0
1
0
1
1
1
1
1
0
0
0
0
0
1
1
0
0
0
1
1
0
0
0
1
1
0
1
0
0
0
0
0
1
0
1
0
1
1
1
1
0
1
1
1
1
1
0
1
1
0
1
0
0
0
0
1
1
1
0
1
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
1
0
1
1
0
0
0
1
0
0
1
1
1
0
1
1
0
1
1
0
1
0
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
1
1
0
0
0
0
1
0
0
1
0
0
0
0
1
1
1
1
0
1
1
1
1
0
1
1
1
1
0
0
0
0
0
1
1
0
0
1
1
1
1
0
0
1
0
0
0
1
0
0
1
1
1
0
0
0
1
1
1
0
1
0
0
1
0
1
0
0
0
0
1
1
1
1
1
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
0
1
1
1
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
1
0
0
1
0
1
0
0
1
0
0
0
0
0
1
1
0
0
0
0
0
0
0
1
1
1
1
0
1
0
1
0
0
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
0
1
1
1
1
1
1
0
0
0
0
0
0
0
1
0
1
0
0
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
1
0
0
0
0
0
0
1
1
0
1
1
0
1
0
1
0
0
0
0
0
1
1
1
1
0
1
1
1
1
0
0
1
1
1
1
0
1
0
0
0
1
1
1
0
1
0
1
0
1
1
0
0
0
0
1
0
1
1
1
1
1
1
1
1
0
0
1
0
1
1
1
0
1
1
1
0
0
1
0
0
1
1
0
0
0
0
0
0
1
0
1
1
1
1
0
1
0
0
1
0
1
0
1
0
0
1
1
1
1
1
0
1
1
1
0
0
1
1
1
1
0
1
0
1
0
1
1
0
0
0
1
1
1
0
0
1
0
0
0
0
0
0
0
1
1
1
1
1
1
0
1
1
1
1
0
1
0
1
1
1
0
1
0
0
1
1
1
1
0
0
1
1
1
0
0
0
1
1
0
0
0
1
0
1
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
1
1
0
0
0
0
0
1
0
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
0
0
1
0
1
1
0
1
1
0
1
1
1
1
0
1
1
0
1
0
0
1
1
1
1
1
1
0
0
1
1
1
0
1
1
0
1
0
1
0
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0
1
1
0
1
1
1
0
0
1
1
1
0
0
0
1
0
0
1
0
1
0
0
1
0
0
0
0
1
1
1
1
1
0
1
1
1
0
1
1
0
1
0
0
0
1
1
1
1
0
0
0
1
0
0
0
0
1
0
1
1
0
1
0
0
1
0
0
0
0
0
0
1
0
1
0
1
0
1
1
1
1
1
0
1
0
0
1
0
0
1
1
1
0
0
1
1
0
0
1
1
0
1
0
1
1
0
1
0
0
1
0
1
0
1
1
1
0
1
0
0
0
0
0
1
0
1
1
0
1
1
0
1
1
1
0
0
0
1
1
1
0
1
0
0
0
1
0
1
0
0
0
0
1
0
0
0
0
0
1
1
1
0
1
0
1
1
0
0
0
0
0
1
1
1
1
0
1
1
0
1
0
0
1
0
0
0
0
0
1
1
1
1
1
0
1
0
1
1
0
1
1
0
0
0
1
0
1
1
0
0
0
0
1
1
0
0
1
1
1
0
1
0
1
0
0
1
1
1
0
1
0
1
0
0
0
1
0
0
0
1
0
0
0
0
1
0
1
0
1
1
1
0
0
1
1
0
1
1
1
1
1
1
0
1
0
0
1
0
0
0
0
0
0
0
1
0
1
0
1
1
0
1
1
1
1
0
0
0
0
1
0
0
1
1
0
0
1
1
1
0
1
1
1
0
0
0
0
1
0
0
1
1
1