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>

using namespace std;

int main(){
	int prime[10000],p = 3,n;
	bool isprime[50001];
	prime[1] = 2,prime[2] = 3;
	isprime[1] = isprime[4] = false;
	isprime[2] = isprime[3] = true;
	for(int i=5;i < 50001;i++){
		int f = 0;
		for(int j=1;prime[j]*prime[j] <= i;j++) if(i % prime[j] == 0) {f = 1;break;}
		if(!f) prime[p++] = i,isprime[i] = true;
		else isprime[i] = false;
	}
	
	while(1){
		int out = 0;
		cin >> n;
		if(!n) break;
		for(int i = 1;n >= 2 * prime[i];i++) if(isprime[n-prime[i]]) out++;
		cout << out << endl;
	}
		
	return 0;
}