MATH ANALYSIS - ON COMPUTERIZED SHUFFLE

❃

000000

 0 0 0 0 0 0 

  0  0  0  0  0  0  

   0   0   0   0   0   0   

    0    0    0    0    0    0    

     0     0     0     0     0     0     

- - - - - - - - - - - - -  - - - - - - - - - - - - -  - - - - - - - - - - - - -  - - - - - - - - - - - - - 

1
00
111
00
11
0
11
0
1
0000
1
0
11111
0
1
0000
11111111
0
11
0
11
00
1
0000000
1
000
111
0000
1
0
111111
00
1
00
1
00
11
00
111
000
11
0
111
0
1
00
111
00
1
00
1
00000
11
00
11
00
11
0
111
000000
1
0000
1
0
1
00
11
0000
111
0
1
000
1
0
1
0000000
11
0
1
00
1
000
1
000
11111
00
11
00
1
00
111
000
111
00000
1
0
111
00
1
000
1
000
1
0
1
0
111
0
1
000
11
000000
1
0
1
00
111
00
111
00
1
0
1
0
1
0
1111
00
1
000000
111
0
111
000
1
0
11
0
1
0
11
000
1
0
1
0000
1
00
1
00
11111
000000
111
00
1
0
1
000
1
00
11111
0
1
000
111
0000
111
0
1111
00
1
0
1111111
0000
1
0
11
000
1
0
1
0
1
0
11
00
1
00
11
00000
1
0
1
00
1
00000
1
0
1
0
111
000
11
00000
1
00
1111
0
1
0
1
00
1111
0
1111
0
11
00
1
00
1
00
111
000000
1
000
11
00
11
0
1
00
11
0
111
00
1
00
1
00
111
0
11
0
1
00
1111111
00
1
0
1
00
111
00
111111111
0
1
0
11111
0
1
0
11
0
1
000
1
00
11
0
111
0
1
0000
11
00
1111
0
11
0000
1
0
1
0
111111
00
111
00
1
00
1
000
1
00
1
00
1
0
11
000
1
0000
111
00000
11
0
1
00
1
00000000
1
0
1
00
1
0
1
00000
1
0000
1
000000
1
00
11
0000000
1
00
1
0
1
0
1111
00
1
00
11
0
1111
00
1
00
111
0
111
000
11111
000
1
00000
1
0
1
0
111
0
1
0
11
0
1
000
1
000
1
00
1
00
1
0
1
00
1
0
11
00
1
0
1
00
1
00
1
0
11
0
1
0
11
00
1
00
1
0
11
00000
1
0
1
0
111
0
1
0
1
00
1
0
1
0
11
0
1
000
1
000000000
11
0000
11
0
1
00
1
0
1
00
1
0
1
000
1
0
1111
0
1111
0
1
0000
1
00
11
000
1
0
1
00
11
00
1
000
111
0
1
0000
1
0
11
0
1
0
11
00
111111
0
111
0
1
000000
111
0
1
0
11
0000
1
0
1
0
1
00
111
0
1
00
111
0
1
0000
111
0
1
0
11
00
1
00
11111
0000000
1
0
1
0
1
000000
1
000
11111
0
1
0
1
000
111
00
1
00
1
0
111111
00
111111
0
11
000000
111
0
1
0
1111
0
1
0
1
0
1
0
1
0
1
0
11
0
1111
000
1
0
1
00
111
0
1
0
111
0
1
00
1
0
1
0
11
0
1
00
111
0
1
00
1
0
1
0
1111
0
1
00
11
0
1
00000000
11
000
11111
0
11
000000
1
00
11
0
11
000
1
0
1
0
1
00
1
0
1
00
1
0
11
0
11
0
1
0
111
0
1
000
1
0
11
000
1
00000000
111
00
11
0
1
000
111
0
1
0000
111
0
11
0
11
0
11
0
1
0
1111
0
11
0
1111
0
11
00000
1
0
1
00
1
00
1
00
11
0
1
0
111
0
11
00
11
00000000
1111
00
1
0
11111
000
1
00
111
0
11
0
1
0
11
0
1111
0
1111
0
1
0
111
0
11
0000000
11
0
1
0000000
1
0
1111
0
1
00
11
00
11
0
1
0
11111
000
1
00000
11
00
1
000
1
000
1111
00
1
00000
111
0
11
0
1
0000
111111111
00
11
000
1
00
1
0
111
0
1
0
1111
0
1
00
1
0
11
00
1
00000
1
0
1
0
1
0
1
00
1
00
1
0
1
0
1
0
1
00000
1
0
1
00
111
0
111
0
111
0
1111
0
1111
0
1
0
1
0
11
0
1111
0
11
00000
1111
0
1
0
11
0000
1
0
111
0
1
00
1
00000
111
0
1
0
1
0
11
00
1
00
11
00
1
00
1
0
11
0
11
0
1
0
1
0
111
000
1
00
1
0
11
0
111
0
1
0000
11
0
11
00
1
00
11
00
11111
0
111
00
1
00
1
00
1
0
1
0
1
1
0
11
0
1
0
1
00
1
00
1
0
111
00
1
0
11111
00
111
00
1111
0000
1
00
11
00
1
000000
1
0
1
0
1
00
11
0
1
000
1
00
11
0
1


Grey
Common
Uncommon
Rare
Epic
Mythical
Legendary