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 <vector>
using namespace std;

vector<int> sieve(int n) {
  vector<int> prime(n);
  for(int i=2; i<n; i++) prime[i]=i;
  for(int i=2; i*i<n; i++) {
    if(prime[i]) {
      for(int j=i*i; j<n; j+=i) prime[j]=0;
    }
  }
  return prime;
}

int main() {
  vector<int> prime=sieve(50001);
  int n;
  while(cin >> n && n!=0) {
    int cnt=0;
    for(int i=2; i<=n/2; i++) {
      if(prime[n-i] && prime[i]) cnt++;
    }
    cout << cnt << endl;
  }
  return 0;
}
