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>
#define MAX 50000
using namespace std;
int main(){
	int p[MAX+1];
	for(int i=0; i<MAX; i++) p[i] = 1;
	p[0] = p[1] = 0;
	for(int i=2; i*i <= MAX; i++){
		if(p[i] == 1){
			for(int j=i*2; j<=MAX; j+=i){
				p[j]=0;
			}
		}
	}
	
	int n;
	while(cin >> n){
		if(n==0) break;
		int count=0;
		for(int i=2; i<=n/2; i++){
			if(p[i]==1 && p[n-i]==1)
				count++;
		}
		cout << count << endl;
	}
	return 0;
}