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;
void solve() {
  long long n;
  cin >> n;
  long long st = 0;
  vector<long long> ans(n + 1, -1);
  cout << n * (n + 1) << endl;
  for (long long i = n; i > 0; i--) {
    if (ans[i] == -1) {
      ans[i] = (1 << ((long long)log2(i) + 1)) - 1 - i;
      ans[(1 << ((long long)log2(i) + 1)) - 1 - i] = i;
    }
  }
  if (ans[0] == -1) ans[0] = 0;
  for (long long i = 0; i <= n; i++) cout << ans[i] << " ";
}
int32_t main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long t = 1;
  while (t--) {
    solve();
  }
  return 0;
}
