void abort() { };

                        
                                                                                                                                                          
                                                                            
extern unsigned int __VERIFIER_nondet_uint();
                        
/*@ 
    requires ((counter == 0));
    ensures ((counter == 0));
@*/
void assume_abort_if_not(int cond) {
  if(!cond) {abort();}
}
/*@ 
    requires ((1 <= cond)) && (cond != 0);
    ensures ((1 <= cond)) && (1);
@*/
void __VERIFIER_assert(int cond) {
    if (!(cond)) {
    ERROR:
        {/*@ assert(0); */;}
    }
    return;
}

int counter = 0;
/*@ 
    requires ((counter == 0));
    ensures ((\old(counter) == 0));
@*/
int main() {
    unsigned int n, p, q, r, h;

    n = __VERIFIER_nondet_uint();
    assume_abort_if_not(n < 4294967295 / 4);  // Avoid non-terminating loop

    p = 0;
    q = 1;
    r = n;
    h = 0;
/*@
loop invariant (((\old(counter) == 0) && (((((p == 0) && (n == r)) && (1 <= counter)) && (h == 0)) || ((((p == 0) && (n == r)) && (counter == 0)) && (h == 0)))));
@*/
    while (counter++<1) {
        if (!(q <= n))
            break;

        q = 4 * q;
    }
    //q == 4^n

/*@
loop invariant ((((((p == 0) && (n == r)) && (1 <= counter)) && (\old(counter) == 0)) && (h == 0)));
@*/
    while (counter++<1) {
        __VERIFIER_assert(r < 2 * p + q);
        __VERIFIER_assert(p*p + r*q == n*q);
        __VERIFIER_assert(h * h * h - 12 * h * n * q + 16 * n * p * q - h * q * q - 4 * p * q * q + 12 * h * q * r - 16 * p * q * r == 0);
        __VERIFIER_assert(h * h * n - 4 * h * n * p + 4 * (n * n) * q - n * q * q - h * h * r + 4 * h * p * r - 8 * n * q * r + q * q * r + 4 * q * r * r == 0);
        __VERIFIER_assert(h * h * p - 4 * h * n * q + 4 * n * p * q - p * q * q + 4 * h * q * r - 4 * p * q * r == 0);
        __VERIFIER_assert(p * p - n * q + q * r == 0);

        if (!(q != 1))
            break;

        q = q / 4;
        h = p + q;
        p = p / 2;
        if (r >= h) {
            p = p + q;
            r = r - h;
        }
    }
    __VERIFIER_assert(h*h*h - 12*h*n + 16*n*p + 12*h*r - 16*p*r - h - 4*p == 0);
    __VERIFIER_assert(p*p - n + r == 0);
    __VERIFIER_assert(h*h*p - 4*h*n + 4*n*p + 4*h*r - 4*p*r - p == 0);
    return 0;
}