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:
// AOJ 1241

#include <iostream>
#include <vector>

using namespace std;

vector <long long> data;

int main(void)
{
	for (int i = 0; i < 200; i++){
		data.push_back(i*i);
	}
	int n;
	while (cin >> n, n){
		int ret = 0;
		for (int i = 0; i < data.size(); i++){
			for (int j = i; j < data.size(); j++){
				for (int k = j; k < data.size(); k++){
					for (int l = k; l < data.size(); l++){
						if (data[i] + data[j] + data[k] + data[l] == n){
							ret++;
						}
						if (n < data[i] + data[j] + data[k] + data[l]){
							break;
						}
					}
				}
			}
		}
		cout << ret << endl;
	}

	return 0;
}