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.*;

class Main {
    public static Scanner sc = new Scanner(in);
    public static Random rand=new Random();

    public void run() {
    	TCase:while(true){
    		int n=sc.nextInt();
    		if(n==0)return;
    		int res=0;
    		for(int a=0;a*a<=n;a++)
        		for(int b=a;a*a+b*b<=n;b++)
            		for(int c=b;a*a+b*b+c*c<=n;c++)
            			for(int d=c;a*a+b*b+c*c+d*d<=n;d++){
            	if(a*a+b*b+c*c+d*d==n)res++;
             }
    		ln(res);
    	}
    }
    public static void main(String[] args) {
        new Main().run();
    }

    public int[] nextIntArray(int n){
        int[] res=new int[n];
        for(int i=0;i<n;i++){
            res[i]=sc.nextInt();
        }
        return res;
    }
    public static void pr(Object o) {
        out.print(o);
    }
    public static void ln(Object o) {
        out.println(o);
    }
    public static void ln() {
        out.println();
    }
}