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<cstdio>
using namespace std;
int sosu[55555];
int main(){
  int N;

  sosu[0]=1;
  sosu[1]=1;
  for(int j=2;j<224;j++){
    if(sosu[j]==1) continue;
    for(int i=j+j;i<50001;i+=j){
      sosu[i]=1;
    }
  }
  
  while(1){
    scanf("%d",&N);
    if(N==0) break;
    int res=0;
    for(int i=2;i<=N/2;i++){
      int a = N-i;
      if(sosu[a]==0 && sosu[i]==0){
	res++;
      }
    }
    printf("%d\n",res);
  }
}