Problem K
Minesweeper Squared
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If you are unfamiliar with the rules of Minesweeper, here is a description:
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Each of the red-labelled cells is either empty or contains a mine. All other cells are empty.
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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 $1 \leq n \leq 1\, 000$, 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.
| Sample Input 1 | Sample Output 1 |
|---|---|
3 |
8 1 3 5 7 9 11 13 15 |
| Sample Input 2 | Sample Output 2 |
|---|---|
1 |
0 |
