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>

int solve(int n) {
  int res = 0;
  for(int i = 0; i < 256; ++i) {
    if( i * i > n ) break;
    for(int j = i; j < 256; ++j) {
      if( i * i + j * j > n ) break;
      for(int k = j; k < 256; ++k) {
        if( i * i + j * j + k * k > n ) break;
        for(int w = k; w < 256; ++w) {
          if( i * i + j * j + k * k + w * w > n ) break;
          if( i * i + j * j + k * k + w * w == n ) {
            res += 1;
          }
        }
      }
    }
  }
  return res;
}

int main() {

  int n;
  for(;;) {
    std::cin >> n;
    if( n == 0 ) break;
    std::cout << solve(n) << std::endl;
  }
 
  return 0;
}