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 <bits/stdc++.h>
using namespace std;

int main ()
{
    int n;
    while (cin >> n, n) {
        int res = 0;
        for (int i = 1; i * i <= n; i++) {
            int s1 = i * i;
            if (s1 == n) { res++; break;}
            for (int j = i; j * j + s1 <= n; j++) {
                int s2 = j * j;
                if (s1 + s2 == n) { res++; break;}
                for (int k = j; s1 + s2 + k * k <= n; k++) {
                    int s3 = k * k;
                    if (s1 + s2 + s3 == n) { res++; break;}
                    for (int l = k; s1 + s2 + s3 + l * l <= n; l++) {
                        int s4 = l * l;
                        if (s1 + s2 + s3 + s4 == n) { res++; break;}
                    }
                }
            }
        }

        cout << res << endl;
    }


    return 0;
}