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 java.lang.*;
import java.io.*;

class Main
{

    private static int n;

    private static int rec(int sum,int pre,int cnt)
    {

	if(sum > n)
	    return 0;

	if(sum == n)
	    return 1;

	if(cnt >= 3)
	    {
		//return sum == n?1:0;
		   
		int dif = n-sum;
		
		    int res = (int)Math.sqrt(dif);
		    if(res >= pre){
			if(res*res == dif)return 1;
		    }
		return 0;
		
	    }


	int counter = 0;
	for(int i=pre;sum+Math.pow(i,2)<=n;i++)
	    {
		counter += rec(sum+i*i,i,cnt+1);
	    }
	return counter;
    }

      public static void main(String args[])throws IOException
    {
	BufferedReader in = new BufferedReader(new InputStreamReader(System.in));


	while(true)
	    {

		n = Integer.parseInt(in.readLine());
		if(n == 0)
		    break;
		/*
		int cnt = 0;
		for(int i=1;i*i<=n;i++)
		    {
			if(i*i == n)
			    {
				cnt++;
				break;
			    }
			for(int j=i;j*j+i*i<=n;j++)
			    {
				if(j*j+i*i == n)
				    {
					cnt++;
					continue;
				    }
				for(int k=j;k*k+j*j+i*i<=n;k++)
				    {
					if(k*k+j*j+i*i == n)
					    {
						cnt++;
						continue;
					    }
					int dif = n-(k*k+j*j+i*i);
					int res = (int)Math.sqrt(dif);
					if(res*res == dif)cnt++;

					    
				    }
			    }
		    }
		


		System.out.println(cnt);
*/
		System.out.println(rec(0,1,0));
	    }
    }

}