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.*;
import static java.lang.System.*;

public class Main {

	Scanner sc = new Scanner(in);
	
	boolean isSquare(int n) {
		for (int i = (int)Math.sqrt(n); i*i <= n; i++) {
			if (i*i == n) return true;
		}
		return false;
	}
	
	void run() {
		int n;
		while (true) {
			n = sc.nextInt();
			if (n == 0) break;
			int ans = 0;
			
			for (int i = 1; i*i <= n; i++) {
				if (n-i*i == 0) ans++;
				for (int j = i; j*j <= n-i*i; j++) {
					if (n-i*i-j*j == 0) ans++;
					for (int k = j; k*k <= n-i*i-j*j; k++) {
						if (n-i*i-j*j-k*k == 0) ans++;
						else if (k*k <= n-i*i-j*j-k*k && isSquare(n-i*i-j*j-k*k)) ans++;
					}
				}
			}
			
			out.println(ans);
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}

}