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<cstdio>
#include<cstring>
using namespace std;

#define N 50002
bool is_prime[N];

void sieve(){
	memset(is_prime,1,sizeof(is_prime));
	is_prime[0] = is_prime[1] = false;
	for(int x=2;x<N;++x){
		if(is_prime[x]){
			for(int i=x+x;i<N;i+=x){
				is_prime[i] = false;
			}
		}
	}
}

int main(){
	sieve();
	int j;
	while(scanf("%d",&j) != EOF , j){
		int t = 0;
		bool mat[j+1];
		memset(mat,0,sizeof(mat));
		for(int x=2;x<=j;++x){
			if( is_prime[x] && is_prime[j-x] && !mat[x]){
				mat[x] = true;
				mat[j-x] = true;
				t++;
			}
		}
		printf("%d\n",t);
	}
	return 0;
}