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.
def int_multiple():
    return  [int(c) for c in input().split()]

def int_single():
    return int(input())

def str_multiple():
    return [c for c in input().split()]

def str_single():
    return input()

# start
n = int_single()

if n % 2 == 0:
    print("NO")
else:
    ls = []
    le = []
    turn_s = True
    small_left_s = True
    small_right_e = True

    res = ""

    for i in range(n):
        if turn_s:
            l = []
            if small_left_s:
                l = [1 + i, 2*n - i]
                small_left_s = False
            else:
                l = [2*n - i, 1 + i]
                small_left_s = True
            turn_s = False
            ls.append(l)
        else:
            l = []
            if small_right_e:
                l = [2*n - i, 1 + i]
                small_right_e = False
            else:
                l = [1 + i, 2*n - i]
                small_right_e = True
            turn_s = True
            le.append(l)

    for i in range(len(ls)):
        res += str(ls[i][0]) + " "
    for i in reversed(range(len(le))):
        res += str(le[i][0]) + " "
    for i in range(len(le)):
        res += str(le[i][1]) + " "
    for i in reversed(range(len(ls))):
        res += str(ls[i][1]) + " "

    print("YES")
    print(res[:-1])
