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;

#define MAX (1<<15)

int main()
{
    int N;
    int dp[MAX+1][5] = {};
    dp[0][0] = 1;
    for (int i = 1; i <= MAX; i++) {
        for (int j = i*i; j <= MAX; j++) {
            for (int k = 0; k < 4; k++) {
                dp[j][k+1] += dp[j-i*i][k];
            }
        }
    }
    
    while (cin >> N, N) {
        int sum = 0;
        for (int i = 1; i <= 4; i++) {
            sum += dp[N][i];
        }
        cout << sum << endl;
    }        
    return 0;
}