Problem: Given an integer N, find two permutations:

  1. Permutation p of numbers from 1 to N such that pi ≠ i and pi & i = 0 for all i = 1, 2, ..., N. 
  2. Permutation q of numbers from 1 to N such that qi ≠ i and qi & i ≠ 0 for all i = 1, 2, ..., N. 



& is the [bitwise AND operation](https://en.wikipedia.org/wiki/Bitwise_operation#AND).

Input

The input consists of one line containing a single integer N (1 ≤ N ≤ 105).

Output

For each subtask, if the required permutation doesn't exist, output a single line containing the word "NO"; otherwise output the word "YES" in the first line and N elements of the permutation, separated by spaces, in the second line. If there are several possible permutations in a subtask, output any of them.

Examples

Input

3


Output

NO
NO


Input

6


Output

YES
6 5 4 3 2 1 
YES
3 6 2 5 1 4

Solution (in PYTHON3):

Solution:
from math import log
from sys import exit
n = int(input())
a = [i for i in range(n + 1)]

def ans(n):
    if n <= 0 or n % 2:
        return
    j, cr = (1 << int(log(n, 2))), 1
    while j + cr - 1 <= n:
        a[j - cr], a[j + cr - 1] = a[j + cr - 1], a[j - cr]
        cr += 1
    ans(j - cr)
    
if n % 2 == 0:
    ans(n)
    print("YES")
    print(*a[1:])
else:
    print("NO")

if n <= 5 or (1 << int(log(n, 2))) == n:
    print("NO")
    exit(0)
    
print("YES")
print("3 6 1 5 4 2" if n <= 6 else "3 6 1 5 4 7 2", end=' ')
cr = 8
v = (1 << int(log(n, 2)))
for i in range(8, n + 1):
    if i >= v:
        print(n if i == v else i - 1, end=' ')
        continue
    if i == cr:
        cr *= 2
        print(cr - 1, end=' ')
    else:
        print(i - 1, end=' ')