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<cstring>
using namespace std;

bool prime[50001];

void seive(int s){
	memset(prime,true,sizeof(prime));
	prime[0]=prime[1]=false;
	for(int i=2;i<=s;i++){
		if(prime[i]==true){
			for(int j=i*2;j<=s;j+=i)prime[j]=false;
		}
	}
}

int main(void){
	seive(50000);
	while(1){
		int n,ans=0;
		scanf("%d",&n);
		if(n==0)break;
		if(n<=3)printf("0\n");
		else{
			for(int i=2;i<=n/2;i++){
				if(prime[i]==true && prime[n-i]==true)ans++;
			}
			printf("%d\n",ans);
		}
	}
    return 0;
}