python3, 47 bytes

Result

WA

Code [DL]

while 1:print(+((1+8*int(input(),2))**.5%2==0))

stdin

00001010
11010110
11100100
11001111
10101001
01101111
10101011
00101011
10011110
10001111
00111010
00111011
00100100
01001110
01111010
10101100
11100111
00011100
11000111
01110001
01011011
01000010
00110111
00001111
11100110
00010010
00101101
10001000
10001010
11010010
01111000
01010011
11111101
10001100
00000011
01100110
00000001
01101101
00000110
10011001
01101001
00000001
00010101
01000001
10110100
00000000
10011100
11010010
10111110
00011111

stdout

0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0

stderr

Traceback (most recent call last):
  File "/volume/CODE", line 1, in <module>
    while 1:print(+((1+8*int(input(),2))**.5%2==0))
EOFError: EOF when reading a line

strace