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<cmath>
using namespace std;

const int MAX = 32770;//1<<15
const int SQRT = 182;

int dp[MAX][5][SQRT];

int main(){

    dp[0][0][1] = 1;
    for(int i = 0; i < MAX; i++){
        for(int j = 0; j < 5; j++){
            for(int k = 1; k < SQRT; k++) if(dp[i][j][k] > 0){
                for(int l = k; l < SQRT; l++){ // l*lを加算
                    if(i+l*l >= MAX || j + 1 >= 5)break;
                    dp[i+l*l][j+1][l] += dp[i][j][k];
                }
            }
        }
    }

    int n;
    while(cin >> n, n){
        int ans = 0;
        for(int i = 1; i < 5; i++){
            for(int j = 1; j < SQRT; j++) ans += dp[n][i][j];
        }
        cout << ans << endl;
    }
}