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, x;
int a[1000047];
long long b;
int main() {
  scanf("%d", &n);
  int m = n + 1;
  while (n > 0) {
    int x = 1;
    while (x <= n) x *= 2;
    x--;
    int y = n;
    while (y > x - y) {
      a[y] = x - y;
      a[x - y] = y;
      y--;
    }
    n = x - n - 1;
  }
  b = 0;
  for (int i = 0; i < (m); ++i) b += a[i] ^ i;
  cout << b << endl;
  for (int i = 0; i < (m); ++i) cout << a[i] << endl;
}
