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 <vector>
int main(){
	int isprime[50001] = {0};
	isprime[2] = 1;
	std::vector<int> v;
	v.push_back(2);
	for(int i=3;i<=50000;i+=2){
		bool f = true;
		for(int j=0;v[j]*v[j]<=i;j++){
			if(i % v[j] == 0){f=false;break;}
		}
		if(f){v.push_back(i),isprime[i] = 1;}
	}

	int n, res = 0;
	while(std::cin >> n, n){
		res = 0;
		for(int i=2;i<=n/2;i++){
			if(isprime[i] && isprime[n-i])res++;
		}
		std::cout << res << std::endl;
	}
	
	return 0;
}