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 ans;

void solve(int sum,int objNum,int cnt,int nowNum){
	if(sum>objNum || cnt>4)return ;

	else if(sum == objNum){
		ans++;
		return;
	}
	else if(cnt==4)return;

	else if(cnt==3){
		int tmp = objNum-sum;
		if(nowNum*nowNum>tmp)return;
		if((int)sqrt(tmp)*(int)sqrt(tmp)==tmp)ans++;
		
		return;
	}

	else{
		for(int i=nowNum;i*i<=objNum;i++){
			solve(sum+i*i,objNum,cnt+1,i);
		}
	}
}

int main(){

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

		ans=0;
		solve(0,n,0,1);
		

		cout<<ans<<endl;
	}

	return 0;
}