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;

bool flag[50001];
int prime[50001];

int main(){
  int n = 0;
  int i, j;

  flag[0] = flag[1] = true;
  for (i = 2; i * i <= 50000; i++){
    if(flag[i] != true){
      for(j = i * i; j <= 50000; j += i){
        flag[j] = true;
      }
    }
  }
  j = 0;
  for (i = 0; i <= 50000; i++){
    if (!flag[i]){
      prime[j++] = i;
    }
  }
  while(cin >> n, n){
    int cnt = 0;
    for(i = 0; prime[i] <= n / 2; i++){
      if (flag[n - prime[i]] == false){
        cnt++;
      }
    }
    cout << cnt << endl;
  }

  return (0);
}