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(){

  long long int a[1000000] = {0};

  a[0] = 1;
  a[1] = 1;

  for(long long int i=2;i*i<1000000;i++){
    if(a[i] == 0){
      for(long long int j=i+i;j<1000000;j+=i) a[j] = 1;
    }
  }

  int n,z = 0;

  while(cin >> n, n){
    z = 0;

    for(int i=2;i<=n/2;i++){
      if(a[i] == 0 && a[n-i] == 0) z++;
    }

    cout << z << endl;

  }
}