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;
long long sum = 0;
int v[1000050];
int ans[1000050];
int main() {
  scanf("%d", &n);
  for (int i = n; i > 0; i--) {
    if (!v[i]) {
      int num = (int)(log2(i)) + 1;
      int x = ((1 << num) - 1) ^ i;
      v[x] = 1, ans[i] = x, ans[x] = i;
      sum += (((1 << num) - 1) << 1);
    }
  }
  printf("%I64d\n", sum);
  for (int i = 0; i < n; i++) printf("%d ", ans[i]);
  printf("%d\n", ans[n]);
  return 0;
}
