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 <cmath>
using namespace std;
int main(){
	int n;
	while(cin>>n){
		if(n==0) break;
		int ct=0;
		//1
		int rt=pow(n,0.5);
		if(rt*rt==n) ct++;
		//2
		for(int i=1;i<=rt+1;i++){
			for(int j=i;j<=rt+1;j++){
				if(i*i+j*j==n) ct++;
			}
		}
		//3
		for(int i=1;i<=rt+1;i++){
			for(int j=i;j<=rt+1;j++){
				for(int k=j;k<=rt+1;k++){
					if(i*i+j*j+k*k==n) ct++;
				}
			}
		}
		//4
		for(int i=1;i<=rt+1;i++){
			for(int j=i;j<=rt+1;j++){
				for(int k=j;k<=rt+1;k++){
					for(int l=k;l<=rt+1;l++){
						if(i*i+j*j+k*k+l*l==n) ct++;
					}
				}
			}
		}
		cout<<ct<<endl;
	}
    return 0;
}