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 <bits/stdc++.h>
#define r(i,a,n) for(int i=a;i<n;++i)
using namespace std;
int main(){
	int a[190],c=0,n;
	r(i,1,190)a[c++]=i*i;
	while(cin>>n,n){
		int c=0;
		r(i,0,n+1){
			if(a[i]>n)break;
			if(a[i]==n)c++;
			r(j,i,n+1){
				if(a[i]+a[j]>n)break;
				if(a[i]+a[j]==n)c++;
				r(k,j,n+1){
					if(a[i]+a[j]+a[k]>n)break;
					if(a[i]+a[j]+a[k]==n)c++;
					r(l,k,n+1){
                       if(a[i]+a[j]+a[k]+a[l]>n)break;
					   if(a[i]+a[j]+a[k]+a[l]==n)c++;
					}
				}
			}
		}
		cout<<c<<endl;
	}
}