d-gdc, 94 bytes

Result

WA

Code [DL]

import std.stdio,std.math;void main(){int a;for(;readf(" %b",a);)write(1-(sqrt(1+a*8.)%1>0));}

stdin

10100100
00000011
11011110
00011110
10011111
10011001
11100001
01011000
01011011
01000010
00011100
01110001
00000001
10000001
01001110
00010101
10101011
11100111
10010101
01100111
11111001
11010110
00100100
01111100
00001010
00101001
11001000
11111101
00101101
00101010
00000110
10101001
10000111
00110111
10110000
01101001
00000000
00011001
10011001
11100111
10100101
11000010
00001111
11111110
10001000
01111000
00110110
10111110
11010010
00100010

stdout

stderr

/usr/lib/gcc/x86_64-linux-gnu/5/include/d/std/format.d:582:26: error: can only * a pointer, not a 'int'
         alias A = typeof(*args[0]);
                          ^
/usr/lib/gcc/x86_64-linux-gnu/5/include/d/std/format.d:593:13: error: can only * a pointer, not a 'int'
             *args[0] = unformatValue!(A)(r, spec);
             ^
/usr/lib/gcc/x86_64-linux-gnu/5/include/d/std/stdio.d:1535:29: error: template instance std.format.formattedRead!(LockingTextReader, char, int) error instantiating
         return formattedRead(input, format, data);
                             ^
/usr/lib/gcc/x86_64-linux-gnu/5/include/d/std/stdio.d:3204:23: note: instantiated from here: readf!(int)
     return stdin.readf(format, args);
                       ^
/tmp/code.d:1:55: note: instantiated from here: readf!(int)
 import std.stdio,std.math;void main(){int a;for(;readf(" %b",a);)write(1-(sqrt(1+a*8.)%1>0));}
                                                       ^
/home/esolang/bin/d-gdc: line 6: /tmp/code: No such file or directory
rm: cannot remove '/tmp/code': No such file or directory

strace