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 <cstdio>
#include <cstring>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <string>
#include <algorithm>
#include <vector>
#define INF (2000000000)
using namespace std;

typedef vector<int> VI;
typedef vector<int>::iterator VII;
typedef vector<double> VD;
typedef vector<double>::iterator VDI;


int dp[5][100001];

int main()
{
	dp[0][0] = 1;
	for (int i = 1; i <= 400; i++){
		for (int j = 1; j <= 4; j++){
			for (int k = i * i; k <= 100000; k++){
				dp[j][k] += dp[j - 1][k - i * i];
			}
		}
	}
	
	int n;
	while (scanf("%d", &n), n){
		int sum = 0;
		for (int i = 1; i <= 4; i++){
			sum += dp[i][n];
		}
		
		printf("%d\n", sum);
	}
	
	return 0;
}