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 int INF = 1e9 + 7;
const int MAXN = 1e6 + 7;
const double EPS = 1e-8;
const int LOGN = 30;
vector<int> res;
bool solve1(int n) {
  if (n == 1) {
    return false;
  }
  if (!n) {
    return true;
  }
  int x = 1;
  while (x <= n) {
    x *= 2;
  }
  x--;
  for (int k = n;; k--) {
    int l = x - k;
    if (!l) {
      return false;
    }
    if (l >= k) {
      break;
    }
    swap(res[k], res[l]);
  }
  solve1(x - n - 1);
}
void solve2(int n) {
  if (n < 6) {
    cout << "NO\n";
    return;
  }
  int k = n;
  while (k % 2 == 0) {
    k /= 2;
  }
  if (k == 1) {
    cout << "NO\n";
    return;
  }
  vector<bool> used(n + 1, 0);
  vector<int> a(n + 1);
  for (int i = 1; i <= n; i++) {
    a[i] = i;
  }
  swap(a[1], a[5]);
  used[1] = 1;
  used[5] = 1;
  for (int bit = LOGN; bit > 0; bit--) {
    if ((1 << bit) > n) continue;
    vector<int> b;
    for (int i = 1; i <= n; i++) {
      if (((i >> bit) & 1) == 0 || used[i]) continue;
      if (!used[i]) {
        b.push_back(i);
        used[i] = 1;
      }
    }
    int x = b.back();
    for (int i = 1; i < (int)b.size(); i++) {
      a[b[i]] = b[i - 1];
    }
    a[b[0]] = x;
  }
  cout << "YES\n";
  for (int i = 1; i <= n; i++) {
    cout << a[i] << " ";
  }
  cout << "\n";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n;
  cin >> n;
  res.resize(n + 1);
  for (int i = 1; i <= n; i++) {
    res[i] = i;
  }
  if (!solve1(n)) {
    cout << "NO\n";
  } else {
    cout << "YES\n";
    for (int i = 1; i <= n; i++) {
      cout << res[i] << " ";
    }
    cout << "\n";
  }
  solve2(n);
}