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>

using namespace std;

int main()
{
	static bool era[50000];
	era[0]=era[1]=true;
	for(int i=2;i<300;i++){
		if(!era[i])for(int j=i*i;j<50000;j+=i)era[j]=true;
	}
	int sz=0;
	static int p[5133];
	for(int i=2;i<50000;i++){
		if(!era[i])p[sz++]=i;
	}

	int n;
	for(;scanf("%d",&n),n;){
		int cnt=0;
		for(int i=0;n-p[i]>=0&&p[i]<=n/2;i++){
			if(!era[n-p[i]])cnt++;
		}
		printf("%d\n",cnt);
	}

	return 0;
}