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 ;

int ans[50010] = {};
int prime[50010] = {};
vector<int> VC;

void calc(){
	
	prime[0] = prime[1] = 1;
	for( int i=2 ; i<=50000 ; i++ ){
		if( !prime[i] ){
			VC.push_back(i) ;
			for( int j=2 ; i*j<=50000 ; j++ ){
				prime[i*j] = 1;
			}
		}
	}
	
	for( int i=4 ; i<=50000 ; i++ ){
		for( int j=0 ; VC[j] <= i/2 ; j++ ){
			if( !prime[i-VC[j]] ) ans[i]++;
		}
	}
	
}

int main(){
	
	calc();
	
	int n;
	while( cin >> n , n ){
		cout << ans[n] << endl ;
	}
	
	return 0;
}