Little penguin Polo likes permutations. But most of all he likes permutations of integers from 0 to n, inclusive.

For permutation p = p0, p1, ..., pn, Polo has defined its beauty — number <image>.

Expression <image> means applying the operation of bitwise excluding "OR" to numbers x and y. This operation exists in all modern programming languages, for example, in language C++ and Java it is represented as "^" and in Pascal — as "xor".

Help him find among all permutations of integers from 0 to n the permutation with the maximum beauty.

Input

The single line contains a positive integer n (1 ≤ n ≤ 106).

Output

In the first line print integer m the maximum possible beauty. In the second line print any permutation of integers from 0 to n with the beauty equal to m.

If there are several suitable permutations, you are allowed to print any of them.

Examples

Input

4


Output

20
0 2 1 4 3
#include <bits/stdc++.h>
using namespace std;
const int maxn = 1000 * 1000 + 100;
int n;
int p[maxn];
int ln[maxn];
void solve(int x) {
  if (x == -1) return;
  if (x == 0) {
    p[0] = 0;
    return;
  }
  assert(x > 0);
  int beg = ln[x];
  for (int i = beg; i < x + 1; ++i) {
    p[i] = beg - 1 - (i - beg);
    p[beg - 1 - (i - beg)] = i;
  }
  solve((beg - 1 - (x - beg)) - 1);
}
int main() {
  ios::sync_with_stdio(false);
  ln[1] = 1;
  for (int i = 2; i < maxn; ++i) ln[i] = ln[i / 2] * 2;
  cin >> n;
  cout << n * (n + 1ll) << endl;
  solve(n);
  for (int i = 0; i < n + 1; ++i) cout << p[i] << " ";
  cout << endl;
  return 0;
}
