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>
#include <string>
#include <map>
#include <algorithm>

#define REP(i,n) for(int i=0;i<(int)(n);i++)

using namespace std;

int main() {
  vector<int> v(40000);
  REP(i,200){
    for(int j=i; j<200; ++j){
      if(i*i+j*j>=40000)break;
      for(int k=j; k<200; ++k){
        if(i*i+j*j+k*k>=40000)break;
        for(int l=k; l<200; ++l){
          if(i*i+j*j+k*k+l*l>=40000)break;
          ++v[i*i+j*j+k*k+l*l];
        }
      }
    }
  }
  while(1){
    int n;
    cin>>n;
    if(!n)break;
    cout<<v[n]<<endl;
  }
  return 0;
}