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;

//Lagrange's Four-Square Theorem
public class Main{

	void run(){
		Scanner sc = new Scanner(System.in);
		for(;;){
			int n = sc.nextInt();
			if(n==0)break;
			int c = 0;
			for(int i=0;i<=n;i++){
				if(n<i*i)break;
				for(int j=i;j<=n;j++){
					if(n<i*i+j*j)break;
					for(int k=j;k<=n;k++){
						if(n<i*i+j*j+k*k)break;
						for(int l=k;l<=n;l++){
							if(n<i*i+j*j+k*k+l*l)break;
							c+=i*i+j*j+k*k+l*l==n?1:0;
						}
					}
				}
			}
			System.out.println(c);
		}
	}
	
	public static void main(String[] args) {
		new Main().run();
	}
}