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>
using namespace std;

int main(){
	int n;
	const int max = 50000;
	int a[max];
	a[1] = 0;
	for(int i = 2; i < max; i++) a[i] = 1;
	for(int i = 2; i * i <= max; i++){
		for(int j = 2; j*i <= max; j++){
			a[i*j] = 0;
		}
	}
	while(cin >> n){
		if(n == 0) break;
		int count = 0;
		if(n % 2 == 1){
			if(a[n-2]){
				cout << 1 << endl;
			}else{
				cout << 0 << endl;
			}
		}else{
			for(int i = 2; i <= n-i; i++)
				if(a[i] && a[n-i])
					count++;
			cout << count <<endl;
		}
	}
	return 0;
}