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>
#include<string>
#include<vector>
#include<cstdio>
#include<sstream>
#include<algorithm>
#include<cmath>
#include<map>
#include<functional>
#include<queue>
#include<stack>
#include<set>
using namespace std;
const int MA=50000;
int p[100000],tcnt,ans[100000];
int main(){
	for(int i=2;i<=60000;i++){
		bool f=1;
		for(int j=2;j*j<=i;j++)if(i%j==0)f=0;
		if(f)p[tcnt]=i,tcnt++;
	}
	for(int i=0;i<MA;i++){
		if(p[i]>MA)break;
		for(int j=0;j<MA;j++){
			if(p[i]+p[j]>MA)break;
			if(i>j)continue;
			ans[p[i]+p[j]]++;
		}
	}
	
	int n;
	while(cin>>n,n)cout<<ans[n]<<endl;
	
}