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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;

public class Main {

	static Main main = new Main();

	public static void main(String[] args) throws IOException {

		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String line = "";

		Prime prime = main.new Prime(50000);

		while (!(line = br.readLine()).equals("0")) {

			int n = Integer.parseInt(line);
			int c = 0;

			for (int v : prime.values) {
				if (v * 2 > n) {
					break;
				}
				if (prime.indexes[v] && prime.indexes[n - v]) {
					c++;
				}
			}
			System.out.println(c);
		}

	}

	class Prime {

		int max;
		int count = 0;
		boolean[] indexes;
		int[] values;

		Prime(int max) {
			this.max = max;
			setIndexes();
			setValues();
		}

		void setIndexes() {

			indexes = new boolean[max + 1];
			Arrays.fill(indexes, true);

			for (int i = 2; i < max + 1; i++) {
				if (indexes[i]) {
					count++;
					for (int j = 2; j <= max / i; j++) {
						indexes[i * j] = false;
					}
				}
			}

		}

		void setValues() {

			values = new int[count];
			int j = 0;
			for (int i = 2; i < max + 1; i++) {
				if (indexes[i]) {
					values[j] = i;
					j++;
				}
			}

		}

	}

}