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(){
  vector<int> V;
  for(int i = 0; i*i < 1<<15; ++i) V.push_back(i*i);
  int n;
  while(cin >> n, n){
    int ans = 0;
    for(int i = 0; V[i] < n; ++i){
      for(int j = i; V[i]+V[j] < n; ++j){
	for(int k = j; V[i]+V[j]+V[k] < n; ++k){
	  for(int l = k; V[i]+V[j]+V[k]+V[l] <= n; ++l){
	    if(V[i]+V[j]+V[k]+V[l] == n) ++ans;
	  }
	}
      }
    }
    cout << ans << endl;
  }
  return 0;
}