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 <algorithm>
#include <queue>
using namespace std;
typedef long long ll;

int dp[1<<15+1][4];

int main(){
	cin.tie(nullptr);
	ios::sync_with_stdio(false);
	for(int i=1;i*i<=(1<<15);i++){
		for(int j=0;j<3;j++){
			if(j==0){
				dp[i*i][j]=1;
			}
			for(int k=1;k<=(1<<15);k++){
				if(k+i*i<=(1<<15)){
					dp[k+i*i][j+1]+=dp[k][j];
				}
			}
		}
	}
	int n;
	while(cin >> n,n){
		ll res=dp[n][0]+dp[n][1]+dp[n][2]+dp[n][3];
		cout << res << endl;
	}
}