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;

bool isp(int n){
  if(n<2)return 0;
  if(n==2)return 1;
  if(n%2==0)return 0;
  for(int i=3;i*i<=n;i+=2){
    if(n%i==0)return 0;
  }
  return 1;
}

int main(){
  int n[50001]={0},sum,a;
  for(int i=1;i<=50000;i++){
    if(isp(i)){
      n[i]=1;
    }
  }
  while(1){
    cin>>a;
    if(a==0)break;
    sum=0;
    for(int i=2;i<=a/2;i++){
      if(n[i]==1&&n[a-i]==1)sum++;
    }
    cout<<sum<<endl;
  }
  return 0;
}