Problem: The fact that any positive integer has a representation as the sum of at most four positive squares (i.e. squares of positive integers) is known as Lagrange’s Four-Square Theorem. The first published proof of the theorem was given by Joseph-Louis Lagrange in 1770. Your mission however is not to explain the original proof nor to discover a new proof but to show that the theorem holds for some specific numbers by counting how many such possible representations there are.

For a given positive integer n, you should report the number of all representations of n as the sum of at most four positive squares. The order of addition does not matter, e.g. you should consider 42 + 32 and 32 + 42 are the same representation.

For example, let’s check the case of 25. This integer has just three representations 12 +22 +22 +42 , 32 + 42 , and 52 . Thus you should report 3 in this case. Be careful not to count 42 + 32 and 32 + 42 separately.



Input

The input is composed of at most 255 lines, each containing a single positive integer less than 215 , followed by a line containing a single zero. The last line is not a part of the input data.

Output

The output should be composed of lines, each containing a single integer. No other characters should appear in the output.

The output integer corresponding to the input integer n is the number of all representations of n as the sum of at most four positive squares.

Example

Input

1
25
2003
211
20007
0


Output

1
3
48
7
738

Solution (in CPP):

Solution:
#include <cmath>
#include <cstdlib>
#include <iostream>
using namespace std;

int main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	for(int n; cin >> n, n;) {
		int ans = 0;
		for(int a = 0; a * a <= n; ++a) {
			for(int b = a; b * b <= n; ++b) {
				for(int c = b; c * c <= n; ++c) {
					const int d2 = n - a * a - b * b - c * c;
					if(d2 < 0)
						continue;

					const int d = (int)sqrt(d2);
					if(c <= d && d * d == d2)
						++ans;
				}
			}
		}

		cout << ans << endl;
	}

	return EXIT_SUCCESS;
}