#include <stdlib.h>

// some not necessarily correct math function
extern long math(long a)
{
    long l = 0;
    long h = a;
    for (int i = 0; i < 18; i++) {
        long m = l + (h - l) / 2;
        if (a > m * m)
            l = m + 1;
        else
            h = m;
    }
    return l;
}