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 <map>

using namespace std;

int main()
{
    int n;

    while (cin >> n, n) {
        int ans = 0;

        for (int a = 0; a * a <= n; a++) {
            for (int b = a; b * b <= n; b++) {
                if (a * a + b * b > n)
                    break;
                for (int c = b; c * c <= n; c++) {
                    if (a * a + b * b + c * c > n)
                        break;
                    for (int d = c; d * d <= n; d++) {
                        if (a * a + b * b + c * c + d * d == n) 
                            ans++;
                        else if (a * a + b * b + c * c + d * d > n)
                            break;
                    }
                }
            }
        }
        cout << ans << endl;
    }

    return 0;
}