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 <algorithm>
#define N 50000
using namespace std;

int main(){
  bool ip[N];
  int p[N];
  for(int i=0;i<N;i++) ip[i]=true;
  int q=0;
  ip[0]=ip[1]=false;
  for(int i=0;i<N;i++){
    if(ip[i]){
      p[q++]=i;
      for(int j=i*2;j<N;j+=i) ip[j]=false;
    }
  }
  int n,a;
  while(1){
    cin>>n;
    a=0;
    if(n==0) break;
    if(n%2){
      if(binary_search(p,p+min(n,q),n-2)) a=1;
    }
    else{
      for(int i=0;p[i]<=n/2;i++){
	if(binary_search(p+i,p+min(n,q),n-p[i])) a++;
      }
    }
    cout<<a<<endl;
  }
  return 0;
}