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 unsigned LIMIT = 50000;

int main(){
	bool table[ LIMIT ] = { false };
	table[ 2 ] = true;
	for ( int i = 3; i < LIMIT; i += 2 ){
		table[ i ] = true;
	}
	for ( int i = 3; i < LIMIT; i += 2 ){
		if ( !table[ i ] ) continue;
		for ( int j = i + i; j < LIMIT; j += i ){
			table[ j ] = false;
		}
	}

	int n;
	while ( cin >> n ){
		if ( !( n ) ) break;

		int cnt = 0;
		if ( table[ n - 2 ] ) ++cnt;
		for ( int i = 3; i <= n / 2; i += 2 ){
			if ( !table[ i ] ) continue;
			if ( table[ n - i ] ) ++cnt;
		}

		cout << cnt << endl;
	}
	return 0;
}