Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Polo the Penguin and XOR operation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputLittle penguin Polo likes permutations. But most of all he likes permutations of integers from 0 to *n*, inclusive.

For permutation *p* = *p*_{0}, *p*_{1}, ..., *p*_{n}, Polo has defined its beauty — number .

Expression 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* ≤ 10^{6}).

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

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/20/2017 23:07:34 (p1).

Desktop version, switch to mobile version.

User lists

Name |
---|