409752: GYM103729 F Angel

Fluttershy is a Pegasus pony who has the reputation of kindness and has unique skill to take care of animals. However, she has a spoiled rabbit pet called Angel, who sometimes makes fun of Fluttershy.

One day, Angel tells Fluttershy that he is hiding in one of the $$$n$$$ special holes in Everfree Forest and Fluttershy should find him out, before the midnight!!

To make the game more fair, Angel set some rules.

The $$$n$$$ holes straightly lie in one line and Angel gives them indices $$$1,2,3,\dots,n$$$ from left to right.

Angel couldn't stay in one hole for more than one minute, and he must move to a hole adjacent to the hole that he currently stays every one minute. That means, if Angel is currently in the $$$i$$$-th hole, he should move to the $$$i-1$$$-th hole or $$$i+1$$$-th hole in the next minute. Of course, he couldn't move beyond the borders.

Every time before Angel moves, Fluttershy could check one of the $$$n$$$ holes, and if Angel is in the checked hole at this time, he will be caught.

Help Fluttershy finding a way to catch Angel in minimum number of checks in the worst case, or tell her that is impossible.

Attention that we only consider the worst case, that means, after those checks, Angel is bound to be caught no matter how he moves.

Only a single integer $$$n\ (1\le n\le 10^3)$$$ - the number of holes.

If Fluttershy could never catch Angel, print a single integer: $$$-1$$$.

Otherwise, print two lines:

The first line contains a single integer $$$m$$$ - the minimal number of checks Fluttershy has to make to catch Angel in the worst case.

The second line contains $$$m$$$ integers $$$a_1,a_2,\dots,a_m$$$ - the index of the hole in $$$i$$$-th check.

3

2
2 2 

If Angel was initially in hole $$$2$$$, Fluttershy would catch him in check $$$1$$$.

Otherwise, Fluttershy would catch him in check $$$2$$$, Angel would be in hole $$$2$$$ at that time since he had to move from hole $$$1$$$ or hole $$$3$$$.

It can be proved that Fluttershy has no way to catch Angel in only one check, in the worst case.