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>
using namespace std;
#define MAX 10000000
typedef long long ll;

bool prime[MAX];

void calcPrime(){
	for( ll i = 2; i < MAX; i++ ) prime[i] = true;
	for( ll i = 2; i < MAX; i++ ){
		if( prime[i] ){
			for( ll j = i+i; j < MAX; j += i ) prime[j] = false;
		}
	}
}

int main(){
	calcPrime();
	int n;
	while( cin >> n, n ){
		int cnt = 0;
		for( int i = 2; i <= n/2 ; i++ ){
			if( prime[i] && prime[n-i] ) cnt++;
		}
		cout << cnt << endl;
	}
}