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{

    //int[][] memo;
    int[] square;

    void solve(){
        Scanner sc = new Scanner(System.in);

        //memo = new int[100000][5];
        //for(int i=0; i<=(2^15); i++) Arrays.fill(memo[i],-1);
        square = new int[(int)Math.sqrt(32768)+1];
        for(int i=0; i<square.length; i++) square[i] = i*i;

        while(true){
            int n = sc.nextInt();
            if(n==0) break;

            int ans = rec(n,0,(int)Math.sqrt(n));
            System.out.println(ans);
        }
    }

    int rec(int num, int cnt, int x){
        //if(memo[num][cnt]!=-1) return memo[num][cnt];
        if(num==0) return 1;
        if(cnt>=4) return 0;

        int res = 0;
        for(int i=x; i>=1; i--){
            if(num-square[i]>=0) {
                res += rec(num-square[i],cnt+1,i);
            }
        }

        return res;
    }

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