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 size = 1000010;
int ans[size];
bool vis[size];
int main() {
  int n, k, temp;
  cin >> n;
  cout << n * 1LL * (n + 1) << endl;
  k = 2;
  while (k <= n) {
    k <<= 1;
  }
  while (k) {
    temp = k - 1;
    for (int i = 0; i < n; i++) {
      if (temp - i <= n && ans[i] <= temp - i && !vis[temp - i]) {
        ans[i] = temp - i;
        vis[temp - i] = true;
      }
    }
    k >>= 1;
  }
  for (int i = 0; i <= n - 1; i++) cout << ans[i] << " ";
  cout << ans[n] << endl;
  return 0;
}
