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.io.*;
import java.util.*;

public class Main{
	
	private void doit(){
		Scanner sc = new Scanner(System.in);
		while(true){
			int n = sc.nextInt();
			if(n == 0 )break;
			
			HashSet<Integer> map = new HashSet<Integer>();
			for(int i = 1; i * i <= (1 << 15); i++){
				map.add(i * i);
			}
			
			int count = 0;
			for(int i = 0; i * i <= n; i++){
				for(int j = i; j * j <= n; j++){
					for(int k = j; k * k <= n; k++){
						int temp = (i * i + j * j + k*k);
						int l = n - temp;
						if(l + temp > n){
							break;
						}
						
						if(l >=k * k && map.contains(l)){
							count++;
						}
					}
				}
			}
			System.out.println(count);
		}
	}

	public static void main(String [] args){
		new Main().doit();
	}
}