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 v[1 << 20], n, L = 1048575;
void R(int i) {
  if (~i) {
    int p;
    for (; v[p = L ^ i] || p > n; L /= 2)
      ;
    v[p] = 1;
    R(i - 1);
    printf("%d ", p);
  }
}
int main() {
  scanf("%d", &n);
  printf("%lld\n", 1LL * n * (n + 1));
  R(n);
}
