c-gcc, 94 bytes

Result

WA

Code [DL]

char*s,a;main(j,a,t){for(;gets(s);puts(a)){t=strtol(s,s,2);a=0;for(j=t;j--;)a+=j*(j+1)==t*2;}}

stdin

01110110
01011011
11110101
11001101
00000000
00111101
01100100
11111101
01010110
11100001
10001000
01010010
11100000
00011100
11011001
01110000
01101001
01110011
11011111
01101111
10000111
01011110
10011111
10011100
10111110
11010010
00000110
11100101
01001110
00101101
11010110
00100100
00010010
11100011
00110111
00010101
10101011
10011001
00001100
01000010
00001111
00001010
00000011
10000001
11010010
11100111
00000001
01101001
01111000
10100000

stdout

stderr

/tmp/code.c:1:10: warning: return type defaults to ‘int’ [-Wimplicit-int]
 char*s,a;main(j,a,t){for(;gets(s);puts(a)){t=strtol(s,s,2);a=0;for(j=t;j--;)a+=j*(j+1)==t*2;}}
          ^
/tmp/code.c: In function ‘main’:
/tmp/code.c:1:10: warning: type of ‘j’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:10: warning: type of ‘a’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:10: warning: type of ‘t’ defaults to ‘int’ [-Wimplicit-int]
/tmp/code.c:1:27: warning: implicit declaration of function ‘gets’ [-Wimplicit-function-declaration]
 char*s,a;main(j,a,t){for(;gets(s);puts(a)){t=strtol(s,s,2);a=0;for(j=t;j--;)a+=j*(j+1)==t*2;}}
                           ^
/tmp/code.c:1:35: warning: implicit declaration of function ‘puts’ [-Wimplicit-function-declaration]
 char*s,a;main(j,a,t){for(;gets(s);puts(a)){t=strtol(s,s,2);a=0;for(j=t;j--;)a+=j*(j+1)==t*2;}}
                                   ^
/tmp/code.c:1:46: warning: implicit declaration of function ‘strtol’ [-Wimplicit-function-declaration]
 char*s,a;main(j,a,t){for(;gets(s);puts(a)){t=strtol(s,s,2);a=0;for(j=t;j--;)a+=j*(j+1)==t*2;}}
                                              ^
/tmp/ccOyuFUN.o: In function `main':
code.c:(.text.startup+0x12): warning: the `gets' function is dangerous and should not be used.
/home/esolang/bin/c-gcc: line 6:    13 Done                    cat -
        14 Segmentation fault      (core dumped) | /tmp/code

strace