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>
#include<cstring>
#include<vector>
using namespace std;
int main()
{
  int p[60000];
  memset(p,0,sizeof(p));
  for(int i=2;i<30000;i++)
    if(p[i]==0)
	for(int j=i+i;j<60000;j+=i)
	  p[j]=1;
  int n;
  for(;cin>>n,n;)
    {
      int count=0;
	  for(int i=2;i<=n/2;i++)
	    if(p[i]==0 && p[n-i]==0)
	      count++;
      cout<<count<<endl;
    }
}