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>
#pragma warning(disable : 4996)
using namespace std;
int n, k;
int ans[1000005];
int main() {
  int n;
  while (scanf("%d", &n) == 1) {
    memset(ans, 0, sizeof ans);
    long long sum = 0;
    int max = 1;
    while (max <= n) max <<= 1;
    max--;
    for (int i = n; i >= 0; i--) {
      if (ans[i]) continue;
      while ((i ^ max) > n || ans[i ^ max] != 0) max >>= 1;
      ans[i] = i ^ max;
      ans[i ^ max] = i;
    }
    for (int i = 0; i <= n; i++) sum += i ^ ans[i];
    printf("%lld\n", sum);
    for (int i = 0; i <= n - 1; i++) printf("%d ", ans[i]);
    printf("%d\n", ans[n]);
  }
  return 0;
}
