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 <stdio.h>
#include <cmath>
#include <algorithm>
#include <stack>
#include <queue>
#include <vector>

using namespace std;




int main(){

	int table[32769];

	for(int i = 0; i <= 32768; i++)table[i] = 0;

	for(int i = 1; i <= 181; i++){
		table[i*i]++;
		for(int k = i; k <= 181; k++){
			if(i*i+k*k > 32768)break;
			table[i*i+k*k]++;
			for(int p = k; p <= 181;p++){
				if(i*i+k*k+p*p > 32768)break;
				table[i*i+k*k+p*p]++;
				for(int a = p; a <= 181; a++){
					if(i*i+k*k+p*p+a*a > 32768)break;
					table[i*i+k*k+p*p+a*a]++;
				}
			}
		}
	}

	int n;

	while(true){
		scanf("%d",&n);
		if(n == 0)break;

		printf("%d\n",table[n]);

	}

	return 0;
}