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;

const int Max = 1000000;
bool P[Max];

void eratos()
{
	for( int i = 0;i < Max;i++ ) P[i] = true;
	P[0] = P[1] = false;
	for( int i = 2;i * i < Max;i++ ) if( P[i] ) for( int j = 2;i * j < Max;j++) P[i * j] = false;
}
int main(int argc, char const* argv[])
{
	int n;
	eratos();

	while( cin >> n && n != 0 ){
		int answer = 0;

		for( int i = 2;i <= n/2;i++ ){
			if( P[i] == true && P[n - i] == true ){ answer++;}
		}

		cout << answer << endl;
	}
	return 0;
}