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 <string>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <vector>
#include <queue>
#include <set>
#include <utility>
#include <algorithm>
#include <numeric>
#include <iostream>
#include <iterator>
#include <sstream>

using namespace std;

bool b[50000];

int main()
{
	memset(b,1,sizeof(b));
	b[0] = b[1] = false;
	for(int i = 2; i < sizeof(b); i++)
		if(b[i]) for(int j = i*2; j < sizeof(b); j += i) b[j] = false;

	int n;
	while(cin>>n,n){
		int ans = 0;
		for (int i = 2; i <= n/2; i++){
			if(b[i] && b[n-i]) ans++;
		}
		cout << ans << endl;
	}
	return 0;
}