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 <vector>
#include <cstdio>
using namespace std;

#define MAX 50000

int main(void)
{
	bool p[MAX + 5];
	int i, j;
	
	for (i = 0; i <= MAX; i++){
		p[i] = true;
	}
	p[0] = p[1] = false;
	for (i = 2; i <= MAX; i++){
		if (p[i]){
			for (j = (i * 2); j <= MAX; j += i){
				p[j] = false;
			}
		}
	}
	
	int n;
	while (scanf("%d", &n)){
		if (n == 0) break;
		int res = 0;
		for (i = 2; i <= (n / 2); i++){
			if (p[i] && p[n - i]) res++;
		}
		printf("%d\n", res);
	}
		
	return (0);
}