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<algorithm>
using namespace std;
int main(){
	bool num[50001] = {0};
	for(int i=2; i<50001; i++){
		if(!num[i]){
			for(int j=i*2; j<50001; j+=i){num[j] = true;}
		}
	}
	for(;;){
		int n,sum = 0;
		cin >>n;
		if(n == 0){break;}
		for(int i=2; i<=n/2; i++){
			if(!num[i] && !num[n-i]){sum++;}
		}
		cout <<sum<<endl;
	}
	return 0;
}