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 ans[1000010];
int main() {
  memset(ans, -1, sizeof(ans));
  int n, i, j, cnt;
  long long sum = 0;
  scanf("%d", &n);
  for (i = n; i >= 0; --i) {
    if (ans[i] != -1) continue;
    cnt = 0;
    j = i;
    while (j) {
      ++cnt;
      j >>= 1;
    }
    j = (1 << cnt) - 1 - i;
    ans[i] = j, ans[j] = i;
    sum += (j ^ i) * 2;
  }
  cout << sum << endl;
  for (i = 0; i < n; ++i) printf("%d ", ans[i]);
  printf("%d\n", ans[n]);
  return 0;
}
