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;

int main() {
  int data[50000] = {};
  int size = sizeof(data) / sizeof(int);

  for (int i = 2; i < size; ++i)
    for (int j = i*2; j < size; j+=i)
      data[j] = 1;

  while (true) {
    int n;
    cin >> n;
    if (n == 0)
      break;

    int cnt = 0;
    for (int i = 2, i2 = n - 2; i <= i2; ++i, --i2)
      if ((data[i] == 0) && (data[i2] == 0))
        ++cnt;
    cout << cnt << endl;
  }
}
