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>
#include <cstdio>
using namespace std;

#define N 50000

int main(){
	bool prime[N+1];
	
	for(long i=2; i<=N; ++i) prime[i]=true;

	for(long i=2; i<=N; ++i){
		if(prime[i]){
			for(long j=2; i*j<=N; ++j) prime[i*j]=false;
		}
	}
	
	while(1){
		long n, ans=0;
		
		scanf(" %ld", &n);
		if(n==0) break;
		
		for(long i=2; i<=n/2; ++i){		
			if(prime[i] && prime[n-i]) ++ans;	
		}
		
		printf("%ld\n", ans);	
	}
	
	return 0;
}