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 ans[1000005];
int main() {
  int i;
  long long x, sum;
  while (~scanf("%d", &n)) {
    x = 1;
    while (x <= n) x <<= 1;
    x--;
    memset(ans, -1, sizeof(ans));
    for (i = n; i >= 0; i--) {
      if (ans[i] != -1) continue;
      while ((x ^ i) > n || ans[x ^ i] != -1) x >>= 1;
      ans[x ^ i] = i, ans[i] = x ^ i;
    }
    sum = 0;
    for (i = 0; i <= n; i++) sum += i ^ ans[i];
    printf("%I64d\n", sum);
    for (i = 0; i <= n; i++) printf("%I64d ", ans[i]);
    printf("\n");
  }
  return 0;
}
