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 <iostream>
#include <vector>

using namespace std;

int main(){
    int n = 1 << 15;
    vector<int> mem(n, 0);
    for(int x=0; x*x < n - x; ++x){
        for(int y=x; x*x + y*y < n - x - y; ++y){
            for(int z=y; x*x + y*y + z*z < n - x - y - z; ++z){
                for(int w=z; x*x + y*y + z*z + w*w < n; ++w){
                    mem[x*x + y*y + z*z + w*w]++;
                }
            }
        }
    }
    while(cin >> n, n)cout << mem[n] << '\n';
    return 0;
}