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 <cmath>
#include <vector>
#define MAX 32768
using namespace std;

vector<int> sq;
bool isSqNum[MAX+1];
void makeTable() {
  int tmp;
  for(int i = 0; i <= MAX; i++) {
    isSqNum[i] = false;
  }
  sq.clear();
  for(int i = 1; ( tmp = (int)pow((double)i, 2.0) ) <= MAX; i++) {
    sq.push_back(tmp);
    isSqNum[tmp] = true;
  }
}

int n;
int ans;

void rec(int cnt, int sum, int level) {
  if(cnt >= 4) return;
  if(sum > n) return;
  if(n-sum >= sq[level] && isSqNum[n-sum]) {
    ans++;
  }
  for(int i = level; i < sq.size() && sum+sq[i] <= n; i++) {
    rec(cnt+1, sum+sq[i], i);
  }
}

int main() {
  makeTable();
  while(1) {
    cin >> n;
    if(n == 0) break;
    ans = 0;
    rec(0,0,0);
    cout << ans << endl;
  }
  return 0;
}