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;
int main(){
    bool a[50002]={0};
    
    for(int i=2;i<25002;i++)
        for(int j=i;j*i<50002;j++)
            a[i*j]=true;
    int n;
    while(cin>>n,n){
        int co=0;
        for(int i=2;i<=n/2;i++){
            if((!a[i])&&(!a[n-i]))co++;
        }
        cout<<co<<endl;
    }
}