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 <algorithm>
using namespace std;

int T[256];
bool issq[70000];

int main() {
  fill(issq, issq+70000, false);
  for (auto i=0; i<256; i++) {
    int temp = i*i;
    T[i] = temp;
    issq[temp] = true;
  }
  int N;
  while (cin >> N && N) {
    int res = 0;
    for (auto i=0; i<256; i++) {
      for (auto j=i; j<256; j++) {
	for (auto k=j; k<256; k++) {
	  int s = N - (T[i] + T[j] + T[k]);
	  if (s < T[k]) break;
	  if (issq[s]) res++;
	}
      }
    }
    cout << res << endl;
  }
}