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 f[1111111], m, dd, dt, g[1111111];
long long ans = 0, tt;
int main() {
  while (cin >> m) {
    ans = 0;
    memset(g, 0, sizeof(g));
    int i, j, k;
    k = 1;
    while (k < m + 1) k *= 2;
    for (i = 0; i <= m; i++) {
      f[i] = k - 1 - i;
      g[k - i - 1] = 1;
    }
    dd = m;
    for (i = m; i >= 0; i--) {
      dt = k / 2;
      while (f[i] < dt) dt /= 2;
      while (f[i] > dd || g[f[i]] > 1) {
        g[f[i]]--;
        f[i] -= dt;
        g[f[i]]++;
        dt /= 2;
      }
      ans += (i ^ f[i]);
    }
    tt = m;
    tt = tt * (tt + 1);
    if (ans != tt)
      while (1)
        ;
    cout << ans << endl;
    for (i = 0; i < m; i++) cout << f[i] << " ";
    cout << f[m] << endl;
  }
  return 0;
}
