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 <vector>
#include <algorithm>
#include <complex>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cmath>
#include <queue>
#include <set>
#include <map>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
const int INF = 1<<29;

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 res = 0;
    REP(i, v.size()) {
      if (v[i] > n) break;
      REP(j, i+1) {
        if (v[i]+v[j] > n) break;
        REP(k, j+1) {
          if (v[i]+v[j]+v[k] > n) break;
          REP(l, k+1) {
            if (v[i]+v[j]+v[k]+v[l] > n) break;
            if (v[i]+v[j]+v[k]+v[l] == n)
              res++;
          }
        }
      }
    }
    cout << res << endl;
  }
}