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 is_prime[50001];

void sieve() {
  for(int i=0;i<50001;i++) {
    is_prime[i] = true;
  }

  is_prime[0] = is_prime[1] = false;

  for(int i=2;i<50001;i++) {
    if(is_prime[i]) {
      for(int j=2*i;j<50001;j+=i) {
        is_prime[j] = false;
      }
    }
  }
}

int main() {
  int n;
  sieve();
  while(cin >> n) {
    if(n==0)break;
    int ans = 0;
    for(int i=2;i<=n/2;i++) {
      if(is_prime[i]) {
        if(is_prime[n-i]) {
          ans++;
        }
      }
    }
    cout << ans << endl;
  }
}