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>
#include <math.h>

using namespace std;

void solve()
{
	double n;
	while(cin >> n, n)
	{
		int ans = 0;
		int k = sqrt(n);
		for(int a = 1; a <= k; ++a)
		{
			if(a * a > n)
			{
				break;
			}
			if(a * a == n)
			{
				++ans;
			}
			for(int b = a; b <= k; ++b)
			{
				if(a * a + b * b > n)
				{
					break;
				}
				if(a * a + b * b == n)
				{
					++ans;
				}
				for(int c = b; c <= k; ++c)
				{
					if(a * a + b * b + c * c > n)
					{
						break;
					}
					if(a * a + b * b + c * c == n)
					{
						++ans;
					}
					for(int d = c; d <= k; ++d)
					{
						if(a * a + b * b + c * c + d * d > n)
						{
							break;
						}
						if(a * a + b * b + c * c + d * d == n)
						{
							++ans;
						}
					}
				}
			}
		}
		cout << ans << endl;
	}
}

int main()
{
	solve();
	return(0);
}