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 <iostream>
#include <vector>
#include <cstring>
#include <string>
#include <algorithm>
#include <iomanip>
#include <cmath>
#include <cassert>
using namespace std;
int dp[2][(1 << 15) + 10][5];

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

	vector<int> s;
	for(int i = 1; i < 1 << 8 && i * i <= 1 << 15; i++) {
		s.push_back(i * i);
	}

	dp[0][0][0] = 1;
	for(int i = 0; i < s.size(); i++) {
		for(int j = 0; j <= 1 << 15; j++) {
			for(int k = 0; k <= 4; k++) {
				if(dp[0][j][k] == 0) continue;
				for(int l = 0; k + l <= 4; l++) {
					if(j + l * s[i] < (1 << 15) + 10) {
						dp[1][j + l * s[i]][k + l] += dp[0][j][k];
					}
				}
			}
		}
		swap(dp[0], dp[1]);
		for(int j = 0; j <= 1 << 15; j++) {
			for(int k = 0; k <= 4; k++) {
				dp[1][j][k] = 0;
			}
		}
	}

	int n;
	while(cin >> n, n) {
		int ans = 0;
		for(int i = 1; i <= 4; i++) {
			ans += dp[0][n][i];
		}
		cout << ans << endl;
	}
}