You are given integer n. You have to arrange numbers from 1 to 2n, using each of them exactly once, on the circle, so that the following condition would be satisfied:

For every n consecutive numbers on the circle write their sum on the blackboard. Then any two of written on the blackboard 2n numbers differ not more than by 1.

For example, choose n = 3. On the left you can see an example of a valid arrangement: 1 + 4 + 5 = 10, 4 + 5 + 2 = 11, 5 + 2 + 3 = 10, 2 + 3 + 6 = 11, 3 + 6 + 1 = 10, 6 + 1 + 4 = 11, any two numbers differ by at most 1. On the right you can see an invalid arrangement: for example, 5 + 1 + 6 = 12, and 3 + 2 + 4 = 9, 9 and 12 differ more than by 1.

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Input

The first and the only line contain one integer n (1 ≤ n ≤ 10^5).

Output

If there is no solution, output "NO" in the first line. 

If there is a solution, output "YES" in the first line. In the second line output 2n numbers — numbers from 1 to 2n in the order they will stay in the circle. Each number should appear only once. If there are several solutions, you can output any of them.

Examples

Input


3


Output


YES
1 4 5 2 3 6 

Input


4


Output


NO

Note

Example from the statement is shown for the first example. 

It can be proved that there is no solution in the second example.
import java.util.Scanner;

public class C {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int[] nums = new int[2 * n];
		long tmp = 0;
		for (int i = 0, j = n, k = 0; i < n; i++, j++) {
			if (i % 2 == 0) {
				tmp += k + 1;
				nums[i] = ++k;
				nums[j] = ++k;
			} else {
				tmp += k + 2;
				nums[j] = ++k;
				nums[i] = ++k;
			}
		}
		long tmp2 = tmp + 1, tmp3 = tmp + 1;
//		System.out.println(tmp + " " + tmp2);
//		for (int i = 0; i < 2 * n; i++) {
//			System.out.print(nums[i] + " ");
//		}
		for (int i = 1, j = n + 1; i < 2 * n; i++, j++) {
			tmp3 += nums[j % (2 * n)] - nums[i % (2 * n)];
			if (tmp3 == tmp || tmp3 == tmp2) {

			} else {
				System.out.println("NO");
				return;
			}
		}
		System.out.println("YES");
		for (int i = 0; i < 2 * n; i++) {
			System.out.print(nums[i] + " ");
		}

	}

}
