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;
#pragma comment(linker, "/STACK:1000000000")
static int m1[2000000];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  long long n, a, b = 0, c = 0, cu;
  cin >> n;
  cu = n;
  cout << (n * (n + 1)) << '\n';
  while (cu > 0) {
    int a = 0;
    for (int i = 0; (1 << i) <= cu; ++i) a = i;
    for (int i = 0; i <= cu; ++i)
      if (i & (1 << a)) {
        b = i;
        break;
      }
    c = cu - b + 1;
    for (int i = b - c; i <= cu; ++i) m1[i] = i + 2 * (b - i) - 1;
    cu = b - c - 1;
  }
  for (int i = 0; i <= n; ++i) cout << m1[i] << ' ';
  return 0;
}
