Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only 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. Slava and tanks

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputSlava plays his favorite game "Peace Lightning". Now he is flying a bomber on a very specific map.

Formally, map is a checkered field of size 1 × *n*, the cells of which are numbered from 1 to *n*, in each cell there can be one or several tanks. Slava doesn't know the number of tanks and their positions, because he flies very high, but he can drop a bomb in any cell. All tanks in this cell will be damaged.

If a tank takes damage for the first time, it instantly moves to one of the neighboring cells (a tank in the cell *n* can only move to the cell *n* - 1, a tank in the cell 1 can only move to the cell 2). If a tank takes damage for the second time, it's counted as destroyed and never moves again. The tanks move only when they are damaged for the first time, they do not move by themselves.

Help Slava to destroy all tanks using as few bombs as possible.

Input

The first line contains a single integer *n* (2 ≤ *n* ≤ 100 000) — the size of the map.

Output

In the first line print *m* — the minimum number of bombs Slava needs to destroy all tanks.

In the second line print *m* integers *k*_{1}, *k*_{2}, ..., *k*_{m}. The number *k*_{i} means that the *i*-th bomb should be dropped at the cell *k*_{i}.

If there are multiple answers, you can print any of them.

Examples

Input

2

Output

3

2 1 2

Input

3

Output

4

2 1 3 2

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jan/20/2020 10:56:34 (e1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|