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<string>
using namespace std;
bool isprime[50000];
int main(){
 for(int i=0;i<50000;i++){
  isprime[i]=true;   
 }
 for(int i=2;i*i<50000;i++){
  for(int j=2;j<50000;j++){
      if(j%i==0&&i!=j){
       isprime[j]=false;   
      }
  }
 }
 int n;
 while(true){
 cin>>n;
 if(n==0)
 break;
 int count=0;
 for(int i=2;i<=n/2;i++){
  if(isprime[i]==true&&isprime[n-i]==true)
  count++;
 }
 cout<<count<<endl;
 }
 return 0;   
}