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 <bits/stdc++.h>

using namespace std;

const int MAX = 1000100;
bool prime[MAX];

void sieve(){
	fill(prime, prime+MAX, true);
	prime[0] = prime[1] = false;

	for(int i=2; i*i < MAX; i++){
		if(!prime[i]) continue;
		for(int j=i*i; j < MAX; j += i) prime[j] = false;
	}
}


int main(){
	sieve();
	int n;
	while(cin >> n, n){
		int ret = 0;
		for(int i=0; i<= n/2; i++){
			if(prime[i] && prime[n-i]) ret++;
		}
		cout << ret << endl;
	}
}