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;
#define N 1000010
int main()
{
    int a[N]={0},n,i,j,count;
    for(i=2;i<=N/2;i++){
	if(a[i]==0){
	    for(j=2;j*i<=N;j++){
		a[i*j]=1;	     
    	    }
	}
    }
    while(1){
    	cin>>n;
	if(n==0)break;
    	count=0;
	for(i=2;i<=n/2;i++){
	    if(a[i]==0&&a[n-i]==0)count++;
	}   
	cout<<count<<endl; 
    }
    return 0;	
}