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>

#define REP(i, n) for(long long i = 0; i < (long long) (n); i++)
#define ALL(v) (v).begin(), (v).end()
#define INF 1e9+7

using namespace std;
typedef long long ll;

int main(){
  ll n;
  while(cin >> n and n){
    int res = 0;
    REP(i, sqrt(n)+1){
      if(i == 0) continue;
      REP(j, i+1) REP(k, j+1) REP(l, k+1){
        if(i * i + j * j + k * k + l * l == n) res++;
      }
    }
    cout << res << endl;
  }
  return 0;
}