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>
using namespace std;

#define MAX 50000

bool is_prime[MAX+1];

void Sieve(){
  fill( is_prime, is_prime + MAX, true );
  is_prime[0] = is_prime[1] = false;
  
  for(int i=0; i<=MAX; i++) {
    if( is_prime[i] ) {
      for(int j=2*i; j<=MAX; j+=i) {
	is_prime[j] = false;
      }
    }
  }
}

int main() {
  int n;

  Sieve();

  while(cin >> n, n) {
    int cnt = 0;
    for(int i=2; i<=n/2; i++) {
      if( is_prime[i] && is_prime[n-i] ) {
	cnt ++;
      }
    }
    cout << cnt << endl;
  }
  return 0;
}