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<vector>
using namespace std;
int main(){
    vector<bool>L(50000);
    for(int i=0;i<50000;i++)L[i]=true;
    L[0]=L[1]=false;
    for(int i=2;i<50000;i++){
        if(L[i]){
            for(int j=i*2;j<50000;j+=i)L[j]=false;
        }
    }
    int n;
    while(cin>>n&&n){
        if(n%2){
            cout<<L[n-2]<<endl;
            continue;
        }
        int cnt=0;
        for(int i=2;i<=n/2;i++){
            if(L[i]&&L[n-i])cnt++;
        }
        cout<<cnt<<endl;
    }


}