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 <cmath>
#include <cstdio>
#include <iostream>
using namespace std;

int main(){
	while(1){	
		int n;
		scanf(" %d", &n);
		if(n==0) break;
		
		int ans=0;
		
		for(int a=0; a*a<=n; ++a){
			int p=a*a;	
			for(int b=a; p+b*b<=n; ++b){
				int q=b*b;
				for(int c=b; p+q+c*c<=n; ++c){
					int r=c*c;
					int s=n-p-q-r;
					
					double sq=sqrt(s);
					if(sq>=c && sq-(int)sq==0){
						//printf("%d,%d,%d,%f\n", a, b, c, sq);
						ans++;
					}
					
				}
			}
		}	
		
		printf("%d\n", ans);
	}
}