mirror of
https://git.sb/baoshuo/OI-codes.git
synced 2024-12-26 05:51:59 +00:00
50001 lines
98 KiB (Stored with Git LFS)
Plaintext
50001 lines
98 KiB (Stored with Git LFS)
Plaintext
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
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
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
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
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
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
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
0
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
1
|
|
0
|
|
1
|
|
1
|
|
1
|
|
0
|