Given an integer N, find two permutations:

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

AND-permutations

Examples