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;
using ll = long long;
int main() {
  int n;
  cin >> n;
  int i = n;
  int j = n;
  vector<int> ans(n + 1);
  while (j >= 0) {
    int v = 0;
    for (int jj = 30; jj >= 0; jj--) {
      if ((1 << jj) & i) {
        v = (1 << (jj + 1)) - 1;
        break;
      }
    }
    while ((j ^ i) != v) {
      j--;
    }
    int x = j;
    int y = i;
    while (j <= y) {
      ans[j] = i;
      j++;
      i--;
    }
    i = x - 1, j = x - 1;
  }
  ll u = 0;
  for (int i = 0; i <= n; i++) {
    u += (ll)(ans[i] ^ i);
  }
  cout << u << endl;
  for (auto& x : ans) cout << x << ' ';
  cout << endl;
}
