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 <cmath>
using namespace std;

int main(){
	int n,prime[50000] = {0},c;
	bool f = true;
	prime[2] = 1;
	for(int i = 3;i < 50000;++i){
		for(int j = 2;j <= sqrt(i);++j){
			if(i % j == 0) f = false;
		}
		if(f) prime[i] = 1;
		f = true;
	}
	while(cin >> n,n){
		c = 0;
		for(int i = 0;i <= n/2;++i){
			if(prime[i] == 1 && prime[n-i] == 1) ++c;
		}
		cout << c << endl;
	}
	return 0;
}