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 long long N = 1e6 + 10;
long long ans[N];
int main() {
  long long n;
  cin >> n;
  long long cur = 1;
  while (cur <= n) {
    cur <<= 1;
    cur |= 1;
  }
  memset(ans, -1, sizeof ans);
  long long tot = 0;
  for (long long i = n; i >= 0; --i) {
    if (ans[i] != -1) continue;
    while ((cur ^ i) > i) cur >>= 1;
    tot += cur;
    ans[i] = (cur ^ i);
    ans[(cur ^ i)] = i;
  }
  cout << 2 * tot << '\n';
  for (long long i = 0; i <= n; ++i) cout << ans[i] << ' ';
  cout << '\n';
  return 0;
}
