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 isPrime(int n){
  for(int i=2;i*i<=n;i++) if(n%i==0) return false;
  return true;
}
int main(){
  bool d[50000]={};
  int i,j,k;
  for(i=2;i<50000;i++) d[i]=isPrime(i);
  int n;
  while(cin>>n,n){
    int o=0;
    for(i=1;i<=n/2;i++) if(d[i]&&d[n-i]) o++;
    cout << o << endl;
  }
  return 0;
}