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<iostream>
using namespace std;

int main()
{
	int n;
	while (cin >> n && n != 0)
	{
		int ans = 0;
		for (int i = 1; i * i <= n; i++)
		{
			int sumI = i * i;
			if (sumI == n)ans++;
			for (int j = i; j * j <= n; j++)
			{
				int sumJ = sumI + j * j;
				if (sumJ == n)ans++;
				for (int k = j; k * k <= n; k++)
				{
					int sumK = sumJ + k * k;
					if (sumK == n)ans++;
					for (int l = k; l * l <= n; l++)
					{
						int sumL = sumK + l * l;
						if (sumL == n)
						{
							ans++;
						}
					}
				}
			}
		}

		cout << ans << endl;
	}
	return 0;
}