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.awt.geom.Line2D;
import java.awt.geom.Point2D;
import java.awt.geom.Point2D.Double;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.TreeSet;
import java.lang.Object;
 
public class Main {
    Scanner sc = new Scanner(System.in);
   
    public static void main(String[] args) {
        new Main(); 
    }
   
    public Main() {
        new E().doIt();
    }
    class E{
    	void doIt(){
    		int max = (1 << 15) + 1;
    		int[][] dp = new int[5][max];
            dp[0][0] = 1;
            for(int j=1; j*j<max; j++){
                for(int i=1; i<5; i++){
                    for(int k=j*j; k<max; k++){
                        dp[i][k] += dp[i-1][k-j*j];
                    }
                }
            }
    		while(true){
    			int n = sc.nextInt();
    			if(n == 0)break;
    			int sum = dp[0][n] + dp[1][n] +dp[2][n] + dp[3][n] + dp[4][n];
    			System.out.println(sum);
    		}
    	}
    }
}