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(){
  const int NUM = 50000;
  bool prime[NUM];
  prime[0] = false;
  prime[1] = false;
  for(int i=2;i<NUM;i++)
    prime[i] = true;
  for(int i=2;i*i<NUM;i++)
    for(int k=2;i*k<NUM;k++)
      prime[i*k]=false;

  int n,c;
  while(true){
    cin>>n;
    if(!n)break;
    c = 0;
    for(int i=2;i<=n/2;i++)
      if(prime[i]&&prime[n-i])
	c++;
    cout << c << endl;
  }
  return 0;
}