fish, 134 bytes

Result

AC

Code [DL]

a5*>80>2*i68*-+$1-:?v~iv
>  ^  ^            $<
  vv?:v?=,2*+1:@:{:}<:~<
   >1-              ^
  0   1
  >   >n~~1-:?v;
^             <

stdin

00101101
11111010
00000110
10110111
10100110
11110110
01011011
11100100
11101110
01111000
10100011
00010101
00011100
01110101
10000101
01000010
00001010
00111101
10101011
11010010
00000011
10110100
11110011
10000001
10111100
11111101
11111100
01101001
01011011
10111001
01100001
11001011
10001000
11000011
10110001
00001111
00000001
10111110
10011001
11100111
01001110
01101100
01010000
00101101
00001011
00000000
00100011
00110111
00100100
01000001

stdout

10100010010110011011100001011000100111111001010110

stderr

strace