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 <algorithm>

using namespace std;

int main()
{
	int n, c, p=1;
	bool f, a[50001];
	
	fill(a, a+50001, false);
	for(int i = 3; i < 50000; i+=2){
		f = true;
	a[2] = true;
		for(int j = 3; j*j <= i; j+=2){
			if(i%j == 0){
				f = false;
				break;
			}
		}
		a[i] = f;
	}
	
	while(1){
		cin >> n;
		if(n == 0){
			break;
		}
		c = 0;
		for(int i = 2; i <= n/2; i++){
			if(a[i] && a[n-i]){
				c++;
			}
		}
		cout << c << endl;
	}
	
	return 0;
}