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 f[50000] = {1,1};
	for(int i = 2; i < 25000; i++){
		f[i * 2] = 1;
	}
	for(int i = 3; i <= 224; i += 2){
		for(int j = 3; j * i < 50000; j += 2){
			f[i*j] = 1;
		}
	}

	int n;
	scanf("%d", &n);
	while(n){
		int count = 0;
		for(int i = n; i * 2 >= n; i--){
			if(!f[i] && !f[n-i]){
				count++;
			}
		}
		printf("%d\n", count);
		scanf("%d", &n);
	}

}