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>
int n;
int a[1000006];
int b[1000];
long long ans = 0;
bool found[1000006];
int main() {
  scanf("%d", &n);
  for (int i = n; i >= 1; i--) {
    if (found[i]) {
      continue;
    }
    int x = i, bit = 0;
    while (x > 0) {
      b[bit++] = x & 1;
      x >>= 1;
    }
    bit--;
    int sum = 0;
    for (int j = 0; j <= bit; j++) {
      sum += b[j] ? 0 : (1 << j);
    }
    a[sum] = i;
    a[i] = sum;
    found[i] = found[sum] = true;
    ans += (sum ^ i) * 2;
  }
  printf("%I64d\n", ans);
  for (int i = 0; i <= n; i++) {
    printf("%d ", a[i]);
  }
  printf("\n");
}
