Given an integer $*N*$, find two permutations:

1. Permutation $*p*$ of numbers from 1 to $*N*$ such that $*p*_{*i*} ≠ *i*$ and $*p*_{*i*} & *i* = 0$ for all $*i* = 1, 2, ..., *N*$.
2. Permutation $*q*$ of numbers from 1 to $*N*$ such that $*q*_{*i*} ≠ *i*$ and $*q*_{*i*} & *i* ≠ 0$ for all $*i* = 1, 2, ..., *N*$.

$&$ is the bitwise AND operation.

Input

The input consists of one line containing a single integer $*N*$ ($1 ≤ *N* ≤ 10^{5}$).

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.