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>
#include <math.h>
#include <set>

using namespace std;

int main(void)
{
	int n;
	int k,l,t;
	int i1,i2,i3,i4;

	while(1){
		cin>>n;
		if(n==0)break;

		k=n;
		set<multiset<int> > s;

		for(i1=floor(sqrt(k));i1>0;i1--){
			k-=(i1*i1);
			l=k;
			for(i2=floor(sqrt(l));i2>=0;i2--){
				l-=(i2*i2);
				t=l;
				for(i3=floor(sqrt(t));i3>=0;i3--){
					t-=(i3*i3);
					i4=floor(sqrt(t));
					t-=(i4*i4);
					
					if(t==0) {
						//cout<<i1<<" "<<i2<<" "<<i3<<" "<<i4<<endl;
						multiset<int> m;
						m.insert(i1);
						m.insert(i2);
						m.insert(i3);
						m.insert(i4);
						s.insert(m);
					}
					t=l;
				}
				l=k;
			}
			k=n;
		}

		cout<<s.size()<<endl;
	}
	return 0;
}