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 main(){
  int num[181];
  for(int i=0;i<181;i++){
    num[i]=(i+1)*(i+1);
  }

  int n;
  while(cin>>n,n){
    int cnt=0;
    int a,b,c;
    for(int i=0;i<181;i++){
      if((a=num[i])>n) continue;
      if(a==n){ cnt++; break;}
      for(int j=i;j<181;j++){
	if((b=a+num[j])>n) continue;
	if(b==n) {cnt++; break;}
	for(int k=j;k<181;k++){
	  if((c=b+num[k])>n) continue;
	  if(c==n){ cnt++; break;}
	  for(int m=k;m<181;m++){
	    if((c+num[m])==n) cnt++;
	  }
	}
      }
    }
    cout<<cnt<<endl;
  }
  return 0;
}