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 <cstring>
using namespace std;

int main() {
  bool p[50001];
  int n, c;

  memset(p, 0, sizeof(bool)*50001);
  for (int i=2; i*i<=50000; i++) {
    if (!p[i]) {
      for (int j=i*i; j<=50000; j+=i) {
        p[j] = true;
      }
    }
  }

  while ((cin >> n) && n) {
    c = 0;
    if (!p[n-2]) ++c;
    if (!(n%2)) {
      for (int i=3; (i<<1)<=n; i+=2) {
        if (!p[i] && !p[n-i]) ++c;
      }
    }
    cout << c << endl;
  }

  return 0;
}