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<cmath>
#include<cstdio>
#include<algorithm>
#include<vector>
#include<cstring>
#include<queue>

using namespace std;

#define INF 999999999
#define REP(i,n) for(int i=0; i<(int)(n); i++)

int main(){
	int n;
	int ans;
	
	while(1){
		cin >> n;
		if(!n) break;
		ans = 0;
		for(int i=0;i*i<=n;i++){
			for(int j=i;i*i+j*j<=n;j++){
				for(int k=j;i*i+j*j+k*k<=n;k++){
					for(int m=k;i*i+j*j+k*k+m*m<=n;m++){
						if(i*i+j*j+k*k+m*m==n) ans++;
					}
				}
			}
		}
		cout << ans << endl;
	}
	return 0;
}