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;
int N, lim;
int Q[1000010];
bool Used[1000010 * 3];
long long Ans1;
int main() {
  int i;
  scanf("%d", &N);
  for (lim = 0; (1 << lim) <= N; ++lim)
    ;
  cout << (long long)N * (long long)(N + 1) << endl;
  for (i = N; i >= 0; --i) {
    int now = (((1 << lim) - 1) ^ i), maxx = lim - 1, now1 = now;
    for (; now > N || Used[now]; now = ((now - 1) & now1))
      ;
    Used[now] = 1;
    Q[i] = now;
  }
  for (i = 0; i <= N; ++i) printf("%d ", Q[i]);
  puts("");
  return 0;
}
