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(void){
    int n;
    while (cin>>n) {
        if (n==0) {
            break;
        }
        int count=0;
        for (int i=1;i*i<=n;i++) {
            if (i*i==n) {
                count++;
            }
            for (int j=i;i*i+j*j<=n;j++) {
                if (i*i+j*j==n) {
                    count++;
                }
                for (int k=j;i*i+j*j+k*k<=n;k++) {
                    if (i*i+j*j+k*k==n) {
                        count++;
                    }
                    for (int l=k;i*i+j*j+k*k+l*l<=n;l++) {
                        if (i*i+j*j+k*k+l*l==n) {
                            count++;
                        }
                    }
                }
            }
        }
        cout<<count<<endl;
    }
}