It is known that even numbers greater than or equal to 4 can be represented by the sum of two prime numbers. This is called the Goldbach's conjecture, and computer calculations have confirmed that it is correct up to a fairly large number. For example, 10 can be represented by the sum of two prime numbers, 7 + 3 and 5 + 5.

Write a program that inputs the integer n and outputs how many combinations of n are the sum of two prime numbers. However, n must be 4 or more and 50,000 or less. Also, the n entered is not always even.



Input

Given multiple datasets. Each dataset is given n on one row. When n is 0, it is the last input. The number of datasets does not exceed 10,000.

Output

For each dataset, output the number of combinations in which n is the sum of two prime numbers on one line.

Example

Input

10
11
0


Output

2
0
#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<string>
using namespace std;
bool F[50005];
int main(){
	for(int i=3;i<=50002;i+=2){F[i]=true;
		for(int j=3;j*j<=i;j+=2)
			if(i%j==0)F[i]=false;
	}
	F[2]=true;

	int n;
	while(1){
		cin>>n;if(n==0)break;
		int c=0;int P=n/2;

		for(int i=2;i<=P;i++)
		{if(F[i]==true&&F[n-i]==true)c++;}
		cout<<c<<endl;
	}
	return 0;
}