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
//57
#include<iostream>

using namespace std;

int main(){
  bool cmp[50001]={true,true};
  for(int i=2;i<50001;i++){
    if(!cmp[i]){
      for(int j=2;j*i<50001;j++){
	cmp[i*j]=true;
      }
    }
  }
  for(int n;cin>>n,n;){
    int ans=0;
    for(int i=0;i<=n-i;i++){
      ans+=!cmp[i]&&!cmp[n-i];
    }
    cout<<ans<<endl;
  }
  return 0;
}