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>

const int MAX = 50001;
using namespace std;

int main(void){
	int i = 3;
	int n = 0;
	int ps[MAX];
	
	for(int i = 0; i < MAX; i++){
		ps[i] = 1;
	}
	for(int i = 2; i < MAX; i++){
		if( ps[i] ){
			for(int j = 2; i * j < MAX; j++){
				ps[i * j] = 0;
			}
		}
	}

	while( 1 ){
		int n;
		int cnt = 0;
		
		cin >> n;
		if( n == 0 ) break;

		if( n % 2 == 1 ){
			if( ps[n - 2] ) cnt++;
		}else{
			for(int i = 2; i <= n / 2; i++){
				if( ps[i] && ps[n - i] ) cnt++;
			}
		}

		cout << cnt << endl;
	}
	return 0;
}