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.io.*;

public class Main{
	public static void main(String[] args){
		new Main().solve();
	}

	void solve(){

		Scanner cin = new Scanner(System.in);
		int MAX = 1 << 15;
		MAX += 1;
		int[][] dp = new int[MAX][5];
		dp[0][0] = 1;
		for(int i=1;i*i<=MAX;i++){
			int a = i * i;
			for(int j=0;j+a<MAX;j++){
				for(int k=0;k<4;k++){
					dp[j+a][k+1] += dp[j][k];
				}
			}
		}

		while(true)
		{
			int n = cin.nextInt();
			if(n==0) return;
			int ret = 0;
			for(int i=0;i<5;i++) ret += dp[n][i];
			System.out.println(ret);
		}
	}
}