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 <cstdio>
#include <vector>
using namespace std;

int main()
{
  const int MAX_P = 50000;
  bool p[MAX_P];
  for (int i = 0; i < MAX_P; ++i)
    p[i] = true;
  p[0] = p[1] = false;

  for (int i = 2; i*i <= MAX_P; ++i) {
    if (p[i]) {
      for (int j = i+i; j < MAX_P; j += i)
	p[j] = false;
    }
  }

  int n;
  while (~scanf("%d", &n)) {
    if (n == 0)
      break;
    
    int ans = 0;
    for (int i = 0; 2*i <= n; ++i) {
      if (p[i] && p[n-i])
	++ans;
    }
    printf("%d\n", ans);
  }
  return 0;
}