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;
//2^15=32768
//2^15<184^2
int data[201];
bool num[40001];
int main(){
  data[0]=0;
  for(int i=1;i<=200;i++){
    data[i]=i*i;
    num[data[i]]=true;
  }
  int n;
  while(1){
    cin >> n;
    if(n==0) break;

    int count=0;
    for(int a=0;a<=200;a++){
      if(data[a]>n){
	break;
      }
      for(int b=a;b<=200;b++){
	if(data[a]+data[b]>n){
	  break;
	}
	for(int c=b;c<=200;c++){
	  if(data[a]+data[b]+data[c]>n) break;
	  int tmp=n-data[a]-data[b]-data[c];
	  if(tmp>n) continue;
	  if(tmp<data[c]) continue;
	  if(num[tmp]) count++;
	}
      }
    }

    cout << count << endl;
  }
  return 0;
}