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>
int main()
{
	int n;
	char prime[50001];
	for(int i = 0; i <= 50000; i++)
		prime[i] = 1;
	prime[0] = 0; prime[1] = 0;
	for(int i = 2; i <= 50000; i++){
		if(!prime[i]) continue;
		for(int j = i + i; j <= 50000; j += i)
			prime[j] = 0;
	}
	while(scanf("%d\n", &n), n){
		int cnt = 0;
		for(int i = 2; i <= n / 2; i++)
			if(prime[i] && prime[n - i])
				cnt++;
		printf("%d\n", cnt);
	}
	return 0;
}