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;
int memo[34000][5];

int main(){

   memo[0][0]=1;
   for(int i=1; i*i<=34000; i++){
      for(int j=i*i; j<=34000; j++){
         for(int k=1; k<=4; k++){
            memo[j][k]+=memo[j-i*i][k-1];
         }
      }
   }
   while(1){
      int n;
      cin>> n;
      if(!n) break;

      int r=0;
      for(int j=1; j<=4; j++){
         r+=memo[n][j];
      }

      cout<< r<< endl;

   }
   return 0;
}