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 <cstring>

#define N 50000

using namespace std;

int main(void){
  int p[N+1] = {0};
  int n, ans;
  
  for (int i=2; i<N; i++){
    if (p[i]==-1) continue;
    p[i]=1;
    for (int j=i*2; j<N; j+=i){
      p[j]=-1;
    }
  }
  while (scanf("%d",&n), n){
    ans = 0;
    for (int i=2; i<=n/2; i++){
      if (p[i]==1 && p[n-i]==1){
        ans++;
      }
    }
    printf("%d\n",ans);
  }
  return 0;
}
