#include <stdio.h>
int main(){

  int e,a,n,m,result;

  while(1){

    result=0;
    scanf("%d",&e);
    e *= 2;
    if(e == 0) break;

    for(n = 2; n < 50; n++){

      a=e-n*n;

      if(a > 0 && a%n == 0 && a/n%2 == 1) result++;

    }

    printf("%d\n",result);

  }

  return 0;

}