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 prime[50001];

void make(){

  for(int i = 0; i < 50001; i++) prime[i] = 1;

  prime[0] = 0;
  prime[1] = 0;

  for(int i = 2; i*i < 50001; i++){
    if(prime[i] == 1){
      for(int j = i*2; j < 50001; j+=i) prime[j] = 0;
    }
  }
}


int main(){

  make();

  int n;

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

    int sum = 0;

    for(int i = 2; i <= n/2; i++){
      if(prime[i] == 1 && prime[n-i] == 1) sum++;
    }
    cout << sum << endl;
  }

  return 0;     
}
  