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
/* 0056*/
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;

std::vector<int> p;
bool s[50001];
int main(void){
	for(int i=0;i<50001;i++)s[i]=true;
	s[0]=s[1]=false;
	for(int i=2;i<50001;i++){
		if(s[i]){
			p.push_back(i);
			for(int j=i*2;j<50001;s[j]=false,j+=i);
		}
	}
	int n;
	while(cin>>n,n){
		int c=0;
		for(int i=0;p[i]<=n/2;i++){
			int a=p[i];
			if(binary_search(p.begin(),p.end(),n-a))c++;
		}
		cout<<c<<endl;
	}
	return 0;
}