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.*;


class Main{
    public static void main(String[] args){
	BufferedReader sc=new BufferedReader(new InputStreamReader(System.in));
	int t = 1<<15;
	int[] num = new int[t+1];
	for(int i=1; i*i<=t; i++){
	    num[i*i]++;
	    for(int j=i; i*i+j*j<=t; j++){
		num[i*i+j*j]++;
		for(int k=j; i*i+j*j+k*k<=t; k++){
		    num[i*i+j*j+k*k]++;
		    for(int l=k; i*i+j*j+k*k+l*l<=t; l++){
			num[i*i+j*j+k*k+l*l]++;
		    }
		}
	    }
	}
	try {
	    while(true){
		int n = Integer.valueOf(sc.readLine());
		if(n==0)
		    break;
		System.out.println(num[n]);
	    }
	}catch(Exception e){
	    System.out.println("Error");
	}
    }
}