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 <stdio.h>
#include <cmath>
#include <algorithm>

#define NUM 51000

int main(){
	int table[NUM],limit;

	for(int i=0; i < NUM;i++)table[i] = 1;
	table[0] = 0;
	table[1] = 0;

	limit = sqrt(NUM);

	for(int i=2;i<=limit;i++){
		if(table[i] == 1){
			for(int k=2*i;k < NUM; k += i){
				table[k] = 0;
			}
		}
	}

	int n,count;

	while(true){
		scanf("%d",&n);
		if(n == 0)break;

		count = 0;
		for(int i=2; i<= (n+1)/2; i++){
			if(i <= n-i &&  table[i] == 1 && table[n-i] == 1)count++;
		}
		printf("%d\n",count);
	}
	return 0;
}