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<bits/stdc++.h>
using namespace std;
int main()
{
    int  prime[50001];
    for(int i=2;i<50001;i++)prime[i]=0;
    for(int i=2;i<=sqrt(50001);i++){
        if(prime[i]==0){
            for(int j=i+i;j<50001;j+=i)prime[j]=1;
        }
    }
    int n,cou=0;
    while(cin>>n&&n!=0){
        for(int i=2;i<=n/2;i++)if(prime[i]==0&&prime[n-i]==0)cou++;
        cout<<cou<<endl;
        cou=0;

    }
}