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>
int n, m, x, y, l, i, k, a[1000100];
long long r;
int main() {
  scanf("%d", &n);
  m = n;
  for (k = 20; k >= 0; k--) {
    x = 1 << k;
    if (n < x) continue;
    y = x * 4 - 2;
    l = n - x + 1;
    for (i = 0; i < l; i++) {
      a[x + i] = x - 1 - i;
      a[x - 1 - i] = x + i;
      r += y;
    }
    n -= 2 * l;
  }
  printf("%I64d\n", r);
  for (i = 0; i <= m; i++) printf("%d%c", a[i], (i == m) ? '\n' : ' ');
  return 0;
}
