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.*;
public class Main{
    public static void main(String[] args){
	new Main().run();
    }
    Scanner sc = new Scanner(System.in);

    int n;
    int[] sq;
    int ans;

    void run(){
	sq = new int[200]; // under 1024*32
	for(int i=0; i<sq.length; i++)
	    sq[i] = i*i;

	while(sc.hasNext()){
	    n = sc.nextInt();
	    if(n!=0){
		ans = 0;
		int level = sq.length-1;
		while(n < sq[level]) level--;
		int use = 0;
		solve(n, level, use);
		System.out.println(ans);
	    }
	}
    }

    void solve(int n, int level, int use){
	// hajiki kokokara
	if(level==0 || use>=4 || n<0) return;
	if(use==3 && sq[level]<n) return;
	// hajiki kokomade

	solve(n, level-1, use);

	n -= sq[level];
	use++;
	if(n==0 && use<=4){
	    ans++;
	    return;
	}

	if(n>=sq[level]) solve(n, level, use);
	else solve(n, level-1, use);
    }
}