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 N = 1000010;
int ans[N], n;
long long sum = 0;
int getbits(int x) {
  int bits = 0;
  if (x == 0) return 1;
  while (x) bits++, x >>= 1;
  return bits;
}
int main() {
  cin >> n;
  memset(ans, -1, sizeof ans);
  for (int i = n; i; i--) {
    if (ans[i] != -1) continue;
    int x = i ^ ((1 << getbits(i)) - 1);
    ans[i] = x, ans[x] = i;
    sum += (x ^ i) << 1;
  }
  cout << sum << endl;
  for (int i = 0; i <= n; i++)
    printf("%d%c", ans[i] == -1 ? 0 : ans[i], i == n ? '\n' : ' ');
  return 0;
}
