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 so[50001]={};

int main(){
  so[0] = 1;
  so[1] = 1;
  for(int i=2;i*i<=50000;i++)
    if(so[i]==0)
      for(int j=2;j*i<=50000;j++)
	so[i*j] = 1;
  int n;
  while(cin>>n && n){
    int co=0;
    for(int i=2;i<=n/2;i++)
      if(so[i]==0 && so[n-i]==0) co++;
    cout <<co<<endl;
  }
  return 0;
}