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>
#define MAX 50001
using namespace std;

int main(){
  
   bool p[MAX];
   p[0] = p[1] = false;
   for(int i=2;i<MAX;i++)p[i] = true;
   for(int i=2;i<MAX;i++){
      if(p[i]){
	 for(int j=i+i;j<MAX;j=j+i){
	    p[j] = false;
	 }
      }
   }
   
   int cnt[MAX];
   for(int i=0;i<MAX;i++) cnt[i] = 0;
   for(int i=0;i<MAX;i++){
      for(int j=i;i+j<MAX;j++){
	 if(p[i] && p[j]) cnt[i + j]++;
      }
   }  
   
   int n;
   while (cin >> n,n){
      cout << cnt[n] << endl;
   }
   return 0;
}