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 p[50000];
	p[1]=false;
	for(int i=2;i<50000;i++){
		p[i]=true;
	}
	for(int j=2;j<50000;j++){
		if(p[j]){
			for(int k=j*2;k<50000;k+=j){
				p[k]=false;
			}
		}
	}
	int n;
	while(cin>>n){
		if(n==0) break;
		int count=0;
		if(p[n-2]) count++;
		for(int l=3;l<=n/2;l+=2){
			if(p[l] &&  p[n-l]) count++;
		}
		cout<<count<<endl;
	}
	return 0;
}