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;
const long long INF = 1e18;
const long long MAXN = 1e6 + 100;
long long n, ans[MAXN];
bool mark[MAXN];
bool val(long long x) { return (!x ? false : true); }
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n;
  cout << n * (n + 1) << endl;
  long long i = n;
  long long k = 0;
  while (k < n) {
    mark[k] = true;
    k *= 2, k++;
  }
  while (val(i)) {
    long long tmp = 0;
    for (long long j = i; j >= k - i; j--) {
      ans[j] = k - j;
      if (mark[j]) tmp = j;
    }
    i = k - i - 1;
    if (mark[i])
      k = i;
    else
      k = tmp;
  }
  for (long long i = 0; i <= n; i++) cout << ans[i] << " ";
}
