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;

#define rep(i,n) for(int i=0; i<n; i++)
typedef long long ll;
typedef pair<int,int> pii;
typedef vector< vector<int> > vvi;

int main() {
	int n;
	while(cin >> n, n) {
		int ans = 0;
		int lim = sqrt(n);
		for(int i=0; i<=lim; i++) {
			for(int j=i; j<=lim && i*i+j*j<=n; j++) {
				for(int k=j; k<=lim && i*i+j*j+k*k<=n; k++) {
					int sq = n - i*i - j*j - k*k;
					if( k*k<=sq && ((int)sqrt(sq))*((int)sqrt(sq)) == sq ) {
						ans++;
					}
				}
			}
		}
		cout << ans << endl;
	}
	return 0;
}