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 <cstring>
#include <iostream>
using namespace std;

const int N_MAX = 1 << 15;
int results[N_MAX];

int main () {
	memset(results, 0, sizeof(results));
	for (int i = 0; i * i < N_MAX; i++) {
		for (int j = 0; j <= i && i * i + j * j < N_MAX; j++) {
			for (int k = 0; k <= j && i * i + j * j + k * k < N_MAX; k++) {
				for (int l = 0; l <= k && i * i + j * j + k * k + l * l < N_MAX; l++) {
					results[i * i + j * j + k * k + l * l]++;
				}
			}
		}
	}
	int n;
	while (cin >> n, n) {
		cout << results[n] << endl;
	}
	return 0;
}