A double-square number is an integer X which can be expressed as the sum of two perfect squares. For example, 10 is a double-square because 10 = 32+ 12. Your task in this problem is, given X, determine the number of ways in which it can be written as the sum of two squares. For example, 10 can only be written as 32 + 12 (we don’t count 12 + 32 as being different). On the other hand, 25 can be written as 52 + 02 or as 42 + 32.

Input

You should first read an integer N, the number of test cases. The next N lines will contain N values of X.

Constraints

0 ≤ X ≤ 2147483647
1 ≤ N ≤ 100

Output

For each value of X, you should output the number of ways to write X as the sum of two squares.

Sample input:

5
10
25
3
0
1

Sample output:

1
2
0
1
1

Code (C++):

//============================================================================
// Name        : doublesquare.cpp
// Author      : Francesco Laurita
// Version     : 1.0
// Copyright   : Francesco Laurita
// Description :
//============================================================================

#include <iostream>
#include <fstream>
#include <math.h>
using namespace std;

bool check(const int a, const int b, const int c) {
	return pow(a,2) + pow(b,2) == c;
}
int main(int argc, char **argv) {

	ifstream fp(argv[1]);
	if (!fp){
		cerr << "Unable to open file!\n";
		return 1;
	}

	int ntest;
	fp >> ntest;
	fp.ignore();
	int a, b;
	for (int i = 0; i < ntest; i++) {
		int current, found;
		fp >> current;
		b = sqrt(current);
		a = sqrt(current - (pow(b,2)));
		found = 0;
		while (a <= b && b >= 0) {
			if (check(a, b, current)) {
				found++;
			}
			b--;
			a = sqrt(current - (pow(b,2)));
		}
		cout << found << endl;
	}
	fp.close();
	return 0;
}

© 2013 Francesco Laurita' s blog Suffusion theme by Sayontan Sinha