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 <bits/stdc++.h>
using namespace std;

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);

  vector<bool> prime(50100, true);
  prime[0] = prime[1] = false;
  for(int i = 2; i * i < 50100; ++i) {
    if(prime[i]) {
      for(int j = i * i; j < 50100; j += i) {
        prime[j] = false;
      }
    }
  }

  vector<int> vec;
  for(int i = 2; i <= 50000; ++i) {
    if(prime[i]) vec.push_back(i);
  }

  int n;
  while(cin >> n, n != 0) {
    int ans = 0;
    for(int i = 0; vec[i] <= n / 2; ++i) {
      if(prime[n - vec[i]]) ans++;
    }
    cout << ans << endl;
  }
}
