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 <cmath>
using namespace std;
bool flg[10000001];

int main(){

	for(int i=0;i <= 1000000;i++){
		if(i<=1)flg[i]=false;
		else flg[i]=true;
	}
	for(int i=2;i <= 1001 ;i++){
		if(flg[i]==true){
			for(int j=i*2 ; j<=1000000 ; j=j+i){
				flg[j] = false;
			}
		}
	}
    while(1){
        int n=0,ans=0;
		cin>>n;
		if(!n)break;
		for(int i=2;i<=n;i++){
            if(flg[i]==true&&flg[n-i]==true&&i<=n-i)ans++;
		}
		cout<<ans<<endl;

	}
}