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 func(int n, int &big2) { big2 = 1 << (1 + (int)log2(n)); }
int arr[1000001];
int main() {
  int n, big2;
  cin >> n;
  func(n, big2);
  int v = n;
  while (n > 0) {
    int val = big2 - n - 1;
    for (int i = val; i <= n; ++i) {
      arr[i] = n + val - i;
    }
    n = val - 1;
    func(n, big2);
  }
  cout << (long long)v * (v + 1) << endl;
  for (int i = 0; i <= v; ++i) {
    cout << arr[i] << " ";
  }
  cout << endl;
  return 0;
}
