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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long modn = 1000000007;
inline long long mod(long long x) { return x % modn; }
void verify1(vector<int> p) {
  for (int i = 1; i < p.size(); i++) assert(p[i] != i && ((p[i] & i) == 0));
}
vector<int> solve1(int n) {
  if (!(n & (n + 1))) return vector<int>();
  int k = 1;
  while ((1 << (k + 1)) - 1 <= n) k++;
  vector<int> p(n + 1);
  p[(1 << k) - 1] = (1 << k);
  p[(1 << k)] = (1 << k) - 1;
  for (int i = 1; i < (1 << k); i++) {
    int x = i ^ ((1 << k) - 1);
    if ((1 << k) + x <= n)
      p[i] = (1 << k) + x;
    else
      p[i] = x;
  }
  if (n == (1 << k)) {
    verify1(p);
    return p;
  }
  vector<int> q = solve1(n - (1 << k));
  if (q.empty()) return q;
  for (int i = (1 << k) + 1; i <= n; i++) p[i] = q[i - (1 << k)];
  verify1(p);
  return p;
}
void verify2(vector<int> p) {
  for (int i = 1; i < p.size(); i++) assert(p[i] != i && ((p[i] & i) != 0));
}
vector<int> solve2(int n) {
  if (n <= 5) return vector<int>();
  vector<int> p(n + 1);
  p[1] = 5;
  p[5] = 1;
  p[2] = 3;
  p[3] = 2;
  for (int i = 4; i <= n;) {
    vector<int> all;
    int j;
    for (j = i; j <= n && (j & i); j++)
      if (j != 5) all.push_back(j);
    if (all.size() == 1) return vector<int>();
    for (int i = 0; i < all.size(); i++) p[all[i]] = all[(i + 1) % all.size()];
    i = j;
  }
  verify2(p);
  return p;
}
int n;
int main() {
  int i, j;
  scanf("%d", &n);
  vector<int> p = solve1(n);
  if (p.empty())
    puts("NO");
  else {
    puts("YES");
    for (int i = 1; i <= n; i++) printf("%d ", p[i]);
    putchar('\n');
  }
  p = solve2(n);
  if (p.empty())
    puts("NO");
  else {
    puts("YES");
    for (int i = 1; i <= n; i++) printf("%d ", p[i]);
    putchar('\n');
  }
}