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 p[1000010];
int n, m;
long long ans;
void dfs(int n) {
  if (n <= 0) return;
  int i;
  for (i = 20; i >= 0; i--)
    if (n >> i & 1) break;
  m = 1 << i;
  for (int j = n - m; j >= 0; j--) {
    p[m + j] = m - 1 - j;
    p[m - 1 - j] = m + j;
    ans += 2 * ((1 << i + 1) - 1);
  }
  dfs(m - 2 - (n - m));
}
int main() {
  cin >> n;
  dfs(n);
  cout << ans << endl;
  for (int i = 0; i <= n; i++) cout << p[i] << ' ';
  cout << endl;
  return 0;
}
