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.util.*;class Main{public static void main(String[]z){int m=50001,i,j,n,v,x=5133,c=0;int[]b=new int[m+1],r=b.clone(),p=b.clone();for(i=1;i++<m;)if(b[i]<1)for(p[c++]=j=i;j<=m;j+=i)b[j]=1;for(i=0;i<x;++i)for(j=i;j<x;++j)if((v=p[i]+p[j])<m)++r[v];else break;for(Scanner s=new Scanner(System.in);(n=s.nextInt())>0;)System.out.println(r[n]);}}