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 <cstdio>

using namespace std;

int sosu_f[50001];

void era(void){
    sosu_f[0]=sosu_f[1]=1;
    for(int i=2;i<=50000;i++){
        if(!sosu_f[i]){
            for(int j=i+i;j<=50000;j+=i){
                sosu_f[j]=1;
            }
        }
    }
}

int main(void){
    int n;
    int count;
    
    era();
    
    while(cin>>n,n!=0){
        count=0;
        for(int i=0;i<=n/2;i++){
            if(!sosu_f[i]&&!sosu_f[n-i]){
                count++;
            }
        }
        cout<<count<<endl;
    }
    return 0;
}