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 <cstdio>
#include <cmath>
using namespace std;

int ans, sum, n, z;
 
void subsetsum(int x, int y)
{
  for(int i = x; i <= z; i++){
    if(y){
      sum += i*i;
      if(sum > n){
        sum -= i*i;
        return;
      }else if(sum == n){
        ans++;
        sum -= i*i;
        return;
      }
      subsetsum(i,y-1);
      sum -= i*i;
    }else{
      return;
    }
  }
}
 
int main()
{
  while(1){
    ans = sum = 0;
    scanf("%d", &n);
    if(n == 0) break;
    z = (int)sqrt(n);
    subsetsum(1,4);
    printf("%d\n", ans);
  }
}