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 <stdio.h>

int a[100000];

int main(void)
{
	int n;
	int ans;
	for(int i = 0; i < 100000; i++){
		a[i] = 1;
	}
	for(int i = 2; i < 100000; i++){
		if(a[i]){
			for(int j = i * 2;j < 100000; j = j + i){
					a[j] = 0;
			}
		}
	}
	scanf("%d",&n);
	while(n != 0){
		ans = 0;

		for(int i = 2; i <= n / 2; i++){
			if(a[i] == 1 && a[n - i] == 1){
				ans++;
			}
		}
		printf("%d\n",ans);
		scanf("%d",&n);
	}
	return 0;
}