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 <iostream>
using namespace std;

int p[50001] ={0};


int main()
{	
	for(int i=4;i<=50000;i++){
		if(i%2==0) p[i] = 1;
		for(int j=3;j*j<=i;j++){
			if(i % j == 0){
				p[i] = 1;
			}
		}
	}
	
	int n;
	while(cin>>n && n){
		int cnt = 0;
		for(int i=2;i<=n/2;i++){
			if( p[i]==0 && p[n-i]==0 ){
					cnt++;
			}	
		}
		
		cout<<cnt<<endl;
	}
	return 0;
}