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 CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;

int main(){

    while(1){
        int n; cin >> n;
        if(n == 0) break;
        int ans = 0;


        for(int i = 0; i <= 182; i++){
            for(int j = i; j <= 182; j++){
                for(int k = j; k <= 182; k++){
                    for(int l = k; l <= 182; l++){
                        if((i*i + j*j + k*k + l*l) == n) ans++;
                        if(i*i + j*j + k*k + l*l > n) break;
                    }
                    if(i*i + j+j + 2*k*k > n) break;
                }
                if(i*i + 3*j*j > n) break;
            }
            if(4*i*i > n) break;
        }

        cout << ans << endl;
    }
}