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>
#include<cmath>
#define N 50000

using namespace std;

int main(){

  int prime[N+1], n;

  fill(prime, prime+N+1, 1);
  prime[0] = 0;
  prime[1] = 0;
  for(int i=2; i<=N; i++){
    if(prime[i] == 1){
      for(int j=2; i*j<=N; j++){
        prime[i*j] = 0;
      }
    }
  }

  int cnt, m;
  while(cin >> n){
    if(n == 0) break;
    cnt = 0;
    m = ceil((double)n / 2);
    for(int i=n-2; i>=m; i--){
      if(prime[i] == 1 && prime[n-i] == 1) cnt++;
    }
    
    cout << cnt << endl;

  }

  return 0;

}