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 <ios>
#include <vector>
#include <algorithm>
using namespace std;
int main(void) {
    ios::sync_with_stdio(false);

    vector<int> square;
    for(int i = 0; i * i <= 32768; ++i) {
        square.push_back(i * i);
    }
    const size_t L = square.size();
    while(true) {
        int n = 0;
        cin >> n;
        if(n == 0) {
            break;
        }

        int count = 0;
        for(int i = 0; i < L; ++i) {
            for(int j = i; j < L; ++j) {
                for(int k = j; k < L; ++k) {
                    int v = n - square[i] - square[j] - square[k];
                    if(v < square[k]) {
                        break;
                    }
                    if(binary_search(square.begin(), square.end(), v)) {
                        count += 1;
                    }
                }
            }
        }
        cout << count << endl;
    }

    return 0;
}