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>
#include<iostream>

#define NMAX 50000
using namespace std;
   
int main(void){
  
	int hurui[NMAX]={0};
   int prime[NMAX]={0};
   int dp[NMAX*3]={0};
   int cnt=0;

   hurui[0]=1,hurui[1]=1;

   for(int i=2;i<NMAX;i++){
	   if(hurui[i]==0){
		   prime[cnt]=i;
		   cnt++;
		   for(int j=i*2;j<NMAX;j+=i){
			   hurui[j]=1;
		   }
	   }
   }

   for(int i=0;i<cnt;i++){
	   for(int j=i;j<cnt;j++){
		   dp[prime[i]+prime[j]]++;
	   }
   }

   int n;

   while(1){
	   cin>>n;
	   if(n==0) break;
	   cout<<dp[n]<<endl;
   }

    return 0;
}