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() {
  int list[50000];
  int i,j,c;
  for(i=2;i<50002;i++)list[i-2]=i;
  for(j=2;j*j<50003;j++)
    if(list[j-2]!=0)
      for(i=1;j-2+list[j-2]*i<50001;i++)
	list[j-2+list[j-2]*i]=0;

  while(1){
    cin>>i,c=0;
    if(i==0)break;
    for(j=2;j<=(i/2);j++)
      if((list[j-2]!=0)&&(list[i-j-2]!=0))c++;
    cout<<c<<endl;
  }
}