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>
using namespace std;

long long int dp[5][40001] = {};

int main() {

  dp[0][0] = 1;

  for ( long long int i = 1; i < 200; i++ ) {

    long long int x = i * i;

    for ( long long int j = 0; j < 4; j++ ) {

      for ( long long int k = 0; k + x < 40000; k++ ) {

	dp[j+1][k+x] += dp[j][k];

      }

    }

  }

  while( true ) {

    long long int in;
    cin >> in;
    if ( in == 0 ) break;

    cout << dp[1][in] + dp[2][in] + dp[3][in] + dp[4][in] << endl;

  }

  return 0;

}