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, m, d;
int a[1200000];
int ws(int n) {
  int ans = 0;
  while (n) {
    ans++;
    n >>= 1;
  }
  return ans;
}
int main() {
  while (cin >> n) {
    for (int i = 0; i <= n; i++) a[i] = 0;
    int newl = n, nn;
    while (newl > 0) {
      int l = ws(newl);
      int g = 1 << (l - 1);
      nn = g - (newl - g + 1);
      for (int i = nn; i <= newl; i++) {
        a[i] = newl - (i - nn);
      }
      newl = nn - 1;
    }
    long long ans = 0;
    for (int i = 0; i <= n; i++) ans += i ^ a[i];
    cout << ans << endl;
    for (int i = 0; i <= n; i++) cout << a[i] << " ";
    cout << endl;
  }
  return 0;
}
