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;

bool p[50050];

void erato(){
	fill(p, p+50050, true);
	p[0] = p[1] = false;

	for(int i=0; i *i < 50050; i++){
		if(!p[i]) continue;
		for(int j = i+i; j < 50050; j += i){
			p[j] = false;
		}
	}
}

int main(){
	erato();
	int input;
	int ans;
	while(cin >> input, input){
		ans = 0;
		for(int i=0; i <= input/2; i++){
			if(p[i] && p[input-i]){
				if(i + input-i == input) ans++;
			}
		}

		cout << ans << endl;
	}
}