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;
const int mod = 1e9 + 7;
int a[N], b[N];
int work(int x) {
  int ret = 0;
  while (x) {
    ret++;
    x >>= 1;
  }
  return ret;
}
int main() {
  int n;
  long long m = 0;
  scanf("%d", &n);
  for (int i = n; i >= 0; i--)
    if (!a[i]) a[i] = ((1 << work(i)) - 1) ^ i, a[((1 << work(i)) - 1) ^ i] = i;
  for (int i = 0; i <= n; i++) m += a[i] ^ i;
  cout << m << endl;
  for (int i = 0; i <= n; i++) cout << a[i] << " ";
  cout << endl;
  return 0;
}
