During a game of Minesweeper you have arrived in the situation shown in the image, with an $n\times n$ square surrounded by $1$s, themselves surrounded by unknown cells. Your task is to determine which of the $4n+4$ surrounding $1$-cells is guaranteed to not contain a mine. 

If you are unfamiliar with the rules of Minesweeper, here is a description:
 - Each of the red-labelled cells is either empty or contains a mine. All other cells are empty.
 - Each cell with a blue $1$ is adjacent to exactly one mine. Two cells are said to be adjacent if they share an edge or a corner. Thus, except at the border, every cell is adjacent to $8$ other cells.

Determine which of the red-labelled cells are safe, i.e., guaranteed to not contain a mine.

-----Input-----
An integer $n$ with $1 \leq n \leq 1000$, the side length of the square. The image corresponds to $n = 6$.

It can be shown that there exists at least one valid placement of mines for each $n$.

-----Output-----
First print the number $m$ of safe cells. Then print a line with $m$ integers, the indices of the safe cells in increasing order. The cells are indexed clockwise from $1$ to $4n+4$, starting at the bottom left corner, as shown in the image.

-----Examples-----
Sample Input:
3
Sample Output:
8
1 3 5 7 9 11 13 15

Source: kattis | Difficulty: HARD


Solutions: