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
import java.io.*;

class Main{
public static void main(String[] args) throws IOException{
BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
String line="";
int count;
boolean[] p=new boolean[50001];
for(int i=0;i<=50000;i++){
p[i]=true;
}
p[0]=false;
p[1]=false;
for(int i=2;i<=Math.sqrt(50000)+1;i++){
if(p[i]){
for(int j=i+i;j<=50000;j+=i){
p[j]=false;
}
}
}
while(!(line=br.readLine()).equals("0")){
count=0;
int n=Integer.parseInt(line);
for(int i=2;i<=n/2;i++){
if(p[i]&&p[n-i]){
count++;
}
}
System.out.println(count);
}
}
}