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 main(){
	bool is_prime[1000000];
	
	is_prime[0]=is_prime[1]=false;
	for(int i=2;i<1000000;i++){
		is_prime[i]=true;
	}
	
	for(int i=2;i*i<1000000;i++){
		if(is_prime[i]){
			for(int j=i*i;j<1000000;j+=i){
				is_prime[j]=false;
				}
			}
		}
		
	while(true){
			int n,count;
			count=0;
			cin>>n;
			if(n==0)
				break;
				
			for(int i=2;i<=(n/2);i++){
				if(is_prime[i]&&is_prime[n-i]){
					count++;
				}
			}		
		cout<<count<<endl;			
	}
		
		return 0;	
}	
					