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 <cstdio>
using namespace std;
#define rep2(x,from,to) for(int x = (from); x < (to); ++(x))
#define rep(x,to) rep2(x,0,to)

int main() {
	bool p[50001];
	p[0] = p[1] = 0;
	rep2(i,2,50001) {
		p[i] = 1;
	}
	rep(i,50001) {
		if(p[i]) {
			for(int j = 2; i * j <= 50000; j++) {
				p[i * j] = 0;
			}
		}
	}

	int n;
	while(cin >> n && n) {
		int cnt = 0;
		rep(i,n / 2 + 1) {
			if(p[i] && p[n - i]) cnt++;
		}
		cout << cnt << endl;	
	}
	return 0;
}