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 <bits/stdc++.h>
using namespace std;

int square(int x){
	int res = -1;
	for(int i=0; i*i<=x; ++i)
		if(i*i == x)
			res = i;
	return res;
}

void solve(int n){
	int 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)
				if(square(n-i*i-j*j-k*k) >= k){
					++ans;
//					cout << i << " " << j << " " << k << "\n";
				}
	cout << ans << "\n";
}

int main(){
//	cin.tie(0);
//	ios::sync_with_stdio(false);
	while(1){
		int n;
		cin >> n;
		if(n == 0) return 0;
		solve(n);
	}
}