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 <bits/stdc++.h>
#define range(i,a,b) for(int (i)=(a);(i)<(b);(i)++)
using namespace std;

bool prime[50010];

void init(){
	range(i,2,50010){
		prime[i]=true;
		for(int j=2;j*j<=i;++j){
			if(i%j==0) prime[i]=false;
		}
	}
	return ;
}

int main(void){
	int n;
	init();
	while(cin >> n,n){
		int res=0;
		range(i,2,n+1){
			int j=n-i;
			if(i>j) break;
			if(prime[i]&&prime[j]) res++;
		}
		cout << res << endl;
	}
}