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;
template <class T, class V>
ostream &operator<<(ostream &s, pair<T, V> a) {
  s << a.first << ' ' << a.second;
  return s;
}
void solve(long long int n, vector<long long int> &ans) {
  if (n <= 0) return;
  int a = log2(n);
  a = (1 << a) - 1;
  long long int l = a, r = a + 1;
  while (r <= n) ans[l] = r, ans[r] = l, l--, r++;
  solve(l, ans);
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  long long int T = 1;
  for (long long int qq = 1; qq <= T; qq++) {
    long long int n;
    cin >> n;
    vector<long long int> ans(n + 1);
    solve(n, ans);
    cout << n * (n + 1) << endl;
    for (auto x : ans) cout << x << ' ';
    cout << endl;
  }
}
