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;
int n;
bool was[2000000];
int step[30];
int Ans[2000000];
int main() {
  cin >> n;
  long long ans = n;
  int len = 0;
  while (ans > 0) {
    ans >>= 1;
    len++;
  }
  step[0] = 1;
  for (int i = 1; i <= len; i++) step[i] = step[i - 1] * 2;
  for (int i = n; i >= 0; i--) {
    if (was[i]) continue;
    int x = i;
    for (int j = 0; j < len; j++) {
      int p = (x >> j) & 1;
      if (p == 0) p = -1;
      x = x - p * (1 << j);
    }
    for (int j = len; was[x] || x > n; j--) x = x & (step[j] - 1);
    int MAX = -1;
    if (was[x])
      for (int j = 0; j <= n; j++)
        if (!was[j] && (MAX == -1 || (MAX ^ i) < (j ^ i))) MAX = j;
    if (was[x]) x = MAX;
    Ans[i] = x;
    was[i] = true;
    Ans[x] = i;
    was[x] = true;
  }
  ans = 0;
  for (int i = 0; i <= n; i++) ans += (i ^ Ans[i]);
  cout << ans << endl;
  for (int i = 0; i <= n; i++) cout << Ans[i] << " ";
  return 0;
}
