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 JAVA):

Solution:
import java.util.Scanner;

public class Main {
    static int ans;

    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        while (true) {
            int n = sc.nextInt();
            if (n == 0)
                break;
            ans = 0;
            slove(n, 0, 1);
            System.out.println(ans);
        }
    }

    public static void slove(int n, int c, int prev) {
        //System.out.println(c+" : "+n);
        if (n == 0) {
            ans++;
            return;
        }
        if (c == 4) {
            return;
        }
        for (int i = prev; i * i <= n; i++) {
            if (n - i * i >= 0)
                slove(n - i*i, c + 1, i);
        }
    }
}