#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;
template <typename...>
static inline int getchar_unlocked(void) {
  return getchar();
}
template <typename...>
static inline void putchar_unlocked(int c) {
  putchar(c);
}
void reader(int& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
void reader(ll& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
int reader(char c[]) {
  int i, s = 0;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c[s++] = i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c[s++] = i;
  }
  c[s] = '\0';
  return s;
}
int reader(string& c) {
  int i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c.push_back(i);
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c.push_back(i);
  };
  return ((int)c.size());
}
template <class T, class S>
void reader(T& x, S& y) {
  reader(x);
  reader(y);
}
template <class T, class S, class U>
void reader(T& x, S& y, U& z) {
  reader(x);
  reader(y);
  reader(z);
}
template <class T, class S, class U, class V>
void reader(T& x, S& y, U& z, V& w) {
  reader(x);
  reader(y);
  reader(z);
  reader(w);
}
void writer(int x, char c) {
  int s = 0, m = 0;
  char f[10];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(ll x, char c) {
  int s = 0, m = 0;
  char f[20];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(const char c[]) {
  int i;
  for (i = 0; c[i] != '\0'; i++) putchar_unlocked(c[i]);
}
void writer(const string& x, char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
void writer(const char x[], char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
template <class T>
void writerLn(T x) {
  writer(x, '\n');
}
template <class T, class S>
void writerLn(T x, S y) {
  writer(x, ' ');
  writer(y, '\n');
}
template <class T, class S, class U>
void writerLn(T x, S y, U z) {
  writer(x, ' ');
  writer(y, ' ');
  writer(z, '\n');
}
template <class T>
void writerArr(T x[], int n) {
  if (!n) {
    putchar_unlocked('\n');
    return;
  }
  for (int i = 0; i < (n - 1); i++) writer(x[i], ' ');
  writer(x[n - 1], '\n');
}
template <class T>
void writerArr(vector<T>& x) {
  writerArr(x.data(), (int)x.size());
}
template <class T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
ll mod_pow(ll a, ll n, ll mod) {
  ll ret = 1;
  ll p = a % mod;
  while (n) {
    if (n & 1) ret = ret * p % mod;
    p = p * p % mod;
    n >>= 1;
  }
  return ret;
}
template <class T>
T extgcd(T a, T b, T& x, T& y) {
  for (T u = y = 1, v = x = 0; a;) {
    T q = b / a;
    swap(x -= q * u, u);
    swap(y -= q * v, v);
    swap(b -= q * a, a);
  }
  return b;
}
template <class T>
T mod_inv(T a, T m) {
  T x, y;
  extgcd(a, m, x, y);
  return (m + x % m) % m;
}
bool solve1(int n, vector<int>& ret) {
  if (n % 2 != 0) {
    return false;
  }
  if (n == 0) return true;
  int top = 0;
  for (int j = 0; j < (25); j++)
    if (n & (1 << j)) {
      top = 1 << j;
    }
  int cur = top * 2 - 2;
  for (int i = 0; i < (n); i++) {
    ret[i % n] = top * 2 - 2 - i;
  }
  int rem = cur - n;
  solve1(rem, ret);
  bool ok = true;
  for (int i = 0; i < (n); i++)
    if (ret[i] == i + 1 || (ret[i] & (i + 1)) != 0) ok = false;
  if (!ok) {
    cout << "?";
  }
  return true;
}
bool solve2(int n, vector<int>& ret) {
  if (n <= 5) {
    return false;
  }
  if ((n & -n) == n) {
    return false;
  }
  if (n == 6) {
    ret = {3, 6, 1, 5, 4, 2};
    return true;
  } else if (n == 7) {
    ret = {3, 6, 1, 5, 4, 7, 2};
    return true;
  }
  ret = {3, 6, 1, 5, 4, 7, 2};
  ret.resize(n);
  for (int start = 8; start < n; start *= 2) {
    int len = min(n - start + 1, start);
    for (int i = 0; i < (len); i++) {
      if (i == 0) {
        ret[start - 1 + len - 1] = start + i;
      } else {
        ret[start - 1 + i - 1] = start + i;
      }
    }
  }
  bool ok = true;
  for (int i = 0; i < (n); i++)
    if (ret[i] == i + 1 || (ret[i] & (i + 1)) == 0) ok = false;
  if (!ok) {
    cout << "?";
  }
  return true;
}
int main() {
  int n;
  reader(n);
  {
    vector<int> ret(n);
    auto ans = solve1(n, ret);
    if (ans) {
      puts("YES");
      writerArr(ret);
    } else {
      puts("NO");
    }
  }
  {
    vector<int> ret;
    auto ans = solve2(n, ret);
    if (ans) {
      puts("YES");
      writerArr(ret);
    } else {
      puts("NO");
    }
  }
  return 0;
}

### Prompt

Please formulate a Cpp solution to the following 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

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using Pii = pair<int, int>;
using Pll = pair<ll, ll>;
template <typename...>
static inline int getchar_unlocked(void) {
  return getchar();
}
template <typename...>
static inline void putchar_unlocked(int c) {
  putchar(c);
}
void reader(int& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
void reader(ll& x) {
  int k, m = 0;
  x = 0;
  for (;;) {
    (k) = getchar_unlocked();
    if (k == '-') {
      m = 1;
      break;
    }
    if ('0' <= k && k <= '9') {
      x = k - '0';
      break;
    }
  }
  for (;;) {
    (k) = getchar_unlocked();
    if (k < '0' || k > '9') break;
    x = x * 10 + k - '0';
  }
  if (m) x = -x;
}
int reader(char c[]) {
  int i, s = 0;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c[s++] = i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c[s++] = i;
  }
  c[s] = '\0';
  return s;
}
int reader(string& c) {
  int i;
  for (;;) {
    (i) = getchar_unlocked();
    if (i != ' ' && i != '\n' && i != '\r' && i != '\t' && i != EOF) break;
  }
  c.push_back(i);
  for (;;) {
    (i) = getchar_unlocked();
    if (i == ' ' || i == '\n' || i == '\r' || i == '\t' || i == EOF) break;
    c.push_back(i);
  };
  return ((int)c.size());
}
template <class T, class S>
void reader(T& x, S& y) {
  reader(x);
  reader(y);
}
template <class T, class S, class U>
void reader(T& x, S& y, U& z) {
  reader(x);
  reader(y);
  reader(z);
}
template <class T, class S, class U, class V>
void reader(T& x, S& y, U& z, V& w) {
  reader(x);
  reader(y);
  reader(z);
  reader(w);
}
void writer(int x, char c) {
  int s = 0, m = 0;
  char f[10];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(ll x, char c) {
  int s = 0, m = 0;
  char f[20];
  if (x < 0) m = 1, x = -x;
  while (x) f[s++] = x % 10, x /= 10;
  if (!s) f[s++] = 0;
  if (m) putchar_unlocked('-');
  while (s--) putchar_unlocked(f[s] + '0');
  putchar_unlocked(c);
}
void writer(const char c[]) {
  int i;
  for (i = 0; c[i] != '\0'; i++) putchar_unlocked(c[i]);
}
void writer(const string& x, char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
void writer(const char x[], char c) {
  int i;
  for (i = 0; x[i] != '\0'; i++) putchar_unlocked(x[i]);
  putchar_unlocked(c);
}
template <class T>
void writerLn(T x) {
  writer(x, '\n');
}
template <class T, class S>
void writerLn(T x, S y) {
  writer(x, ' ');
  writer(y, '\n');
}
template <class T, class S, class U>
void writerLn(T x, S y, U z) {
  writer(x, ' ');
  writer(y, ' ');
  writer(z, '\n');
}
template <class T>
void writerArr(T x[], int n) {
  if (!n) {
    putchar_unlocked('\n');
    return;
  }
  for (int i = 0; i < (n - 1); i++) writer(x[i], ' ');
  writer(x[n - 1], '\n');
}
template <class T>
void writerArr(vector<T>& x) {
  writerArr(x.data(), (int)x.size());
}
template <class T>
void chmin(T& a, const T& b) {
  if (a > b) a = b;
}
template <class T>
void chmax(T& a, const T& b) {
  if (a < b) a = b;
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <class T>
T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
ll mod_pow(ll a, ll n, ll mod) {
  ll ret = 1;
  ll p = a % mod;
  while (n) {
    if (n & 1) ret = ret * p % mod;
    p = p * p % mod;
    n >>= 1;
  }
  return ret;
}
template <class T>
T extgcd(T a, T b, T& x, T& y) {
  for (T u = y = 1, v = x = 0; a;) {
    T q = b / a;
    swap(x -= q * u, u);
    swap(y -= q * v, v);
    swap(b -= q * a, a);
  }
  return b;
}
template <class T>
T mod_inv(T a, T m) {
  T x, y;
  extgcd(a, m, x, y);
  return (m + x % m) % m;
}
bool solve1(int n, vector<int>& ret) {
  if (n % 2 != 0) {
    return false;
  }
  if (n == 0) return true;
  int top = 0;
  for (int j = 0; j < (25); j++)
    if (n & (1 << j)) {
      top = 1 << j;
    }
  int cur = top * 2 - 2;
  for (int i = 0; i < (n); i++) {
    ret[i % n] = top * 2 - 2 - i;
  }
  int rem = cur - n;
  solve1(rem, ret);
  bool ok = true;
  for (int i = 0; i < (n); i++)
    if (ret[i] == i + 1 || (ret[i] & (i + 1)) != 0) ok = false;
  if (!ok) {
    cout << "?";
  }
  return true;
}
bool solve2(int n, vector<int>& ret) {
  if (n <= 5) {
    return false;
  }
  if ((n & -n) == n) {
    return false;
  }
  if (n == 6) {
    ret = {3, 6, 1, 5, 4, 2};
    return true;
  } else if (n == 7) {
    ret = {3, 6, 1, 5, 4, 7, 2};
    return true;
  }
  ret = {3, 6, 1, 5, 4, 7, 2};
  ret.resize(n);
  for (int start = 8; start < n; start *= 2) {
    int len = min(n - start + 1, start);
    for (int i = 0; i < (len); i++) {
      if (i == 0) {
        ret[start - 1 + len - 1] = start + i;
      } else {
        ret[start - 1 + i - 1] = start + i;
      }
    }
  }
  bool ok = true;
  for (int i = 0; i < (n); i++)
    if (ret[i] == i + 1 || (ret[i] & (i + 1)) == 0) ok = false;
  if (!ok) {
    cout << "?";
  }
  return true;
}
int main() {
  int n;
  reader(n);
  {
    vector<int> ret(n);
    auto ans = solve1(n, ret);
    if (ans) {
      puts("YES");
      writerArr(ret);
    } else {
      puts("NO");
    }
  }
  {
    vector<int> ret;
    auto ans = solve2(n, ret);
    if (ans) {
      puts("YES");
      writerArr(ret);
    } else {
      puts("NO");
    }
  }
  return 0;
}

```