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 a[1000010];
int find(int k) {
  int sit = 0, tem = 1;
  while (k >= tem) {
    sit++;
    tem *= 2;
  }
  for (int i = k; i >= tem - 1 - k; i--) a[i] = tem - 1 - i;
  return tem - 1 - k - 1;
}
int main() {
  int n;
  while (scanf("%d", &n) != EOF) {
    memset(a, 0, sizeof(a));
    int t = n;
    while (find(t) != -1) {
      t = find(t);
    }
    long long ans = 0;
    for (int i = 0; i <= n; i++) ans += i ^ a[i];
    printf("%I64d\n", ans);
    for (int i = 0; i <= n; i++) printf("%d ", a[i]);
    printf("\n");
  }
  return 0;
}
