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>

using namespace std;

int main(int argc, char const *argv[])
{
	int n;
	int cnt;
	int i1,i2,i3,i4;
	int temp1,temp2,temp3,temp4;

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

		cnt=0;
		for(i1=floor(sqrt(n));i1>0;i1--){
			temp1=n-i1*i1;
			if(temp1==0){cnt++;continue;}
			for(i2=i1;i2>0;i2--){
				temp2=temp1-i2*i2;
				if(temp2==0) {cnt++; continue;}
				else if(temp2<0) continue;
				for(i3=i2;i3>0;i3--){
					temp3=temp2-i3*i3;
					if(temp3==0) {cnt++; continue;}
					else if(temp3<0) continue;
					for(i4=i3;i4>0;i4--){
						temp4=temp3-i4*i4;
						if(temp4==0) {cnt++; break;}
					}
				}
			}
		}
		cout<<cnt<<endl;
	}
	return 0;
}