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;

const int maxN = 1 << 15;

typedef long long ll;

int N;
vector<ll> v;
ll dfs(int n, ll sum, int lid) {
	if (sum > N) return 0;
	if (sum == N) return 1;
	if (n >= 4) return 0;

	ll res = 0;
	for (int i = lid; i < v.size(); ++i) {
		res += dfs(n+1, sum+v[i], i);
	}
	return res;
}
int main() {
	while ( cin >> N, N ) {
		v.clear();
		for (int i = 1; i*i <= N; ++i) {
			v.push_back(i*i);
		}
		cout << dfs(0, 0, 0) << endl;
	}
}