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 <vector>
#include <iostream>
#include <utility>
#include <algorithm>
#include <string>
#include <deque>
#include <tuple>
#include <queue>
#include <functional>
#include <cmath>
#include <iomanip>
#include <map>
//cin.sync_with_stdio(false);
//streambuf
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
int a[4][1 << 16];
int main() {
	for (int i = 1; i < 256; i++) {
		a[0][i*i] = 1;
		for (int j = 1; j + i*i < (1 << 16); j++) {
			for (int k = 1; k < 4; k++) {
				a[k][j + i*i] += a[k - 1][j];
			}
		}
	}
	int n;
	while(cin >> n, n) {
		cout << a[0][n] + a[1][n] + a[2][n] + a[3][n] << endl;;
	}
	return 0;
}