AND-permutations
Description
Given an integer N, find two permutations:
- Permutation p of numbers from 1 to N such that pi ≠ i and pi & i = 0 for all i = 1, 2, ..., N.
- 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.
The input consists of one line containing a single integer N (1 ≤ N ≤ 105).
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.
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.
Samples
3
NO
NO
6
YES
6 5 4 3 2 1
YES
3 6 2 5 1 4