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 <algorithm>
#include <cstring>
using namespace std;

const int MAX_N = 100000;
bool sieve[MAX_N];
int n;

void solve() {
	int res = 0;

	for (int i = 2; i < n/2 + 1; i++) {
		if (sieve[i] && sieve[n-i]) {
			res++;
		}
	}
	cout<<res<<endl;
}

int main(int argc, const char *argv[]) {
	// make sieve
	//fill(sieve, sieve+MAX_N-1, true);
	memset(sieve, true, sizeof sieve);
	for (int i = 2; i < MAX_N; i++) {
		if (sieve[i]) {
			for (int j = i+i; j < MAX_N; j+=i) {
				sieve[j] = false;
			}
		}
	}

	// solve
	while (cin>>n, n) {
		solve();
	}	
	
	return 0;
}