Bee House Perimeter

Alice is a queen bee living in Beeland (a honeycomb structure described by $R$, the number of cells of the side of honeycomb). The cells in Beeland are numbered from $1$ to $R^3 - (R-1)^3$ in row major order. For example for $R = 3$, the Beeland that Alice lives in looks like this:

Now Alice lives in a house that occupies $K$ **adjacent**
cells in Beeland. You are Bob, the knight bee. You need to
protect Alice’s house, but first you need to know the length of
its **outer** perimeter (the number of
outermost sides of Alice’s house). The illustration below shows
the visualizations of Sample Inputs/Outputs $2$ and $3$.

The first line of input consists of two integers: $R$ and $K$. ($1 \leq R \leq 50$, $1 \leq K \leq R^3 - (R-1)^3$). The second line contains $K$ unique integers that describe the indices of Alice’s house, where each integer is in the range $[1,R^3-(R-1)^3]$.

Print an integer in one line: The perimeter of Alice’s house.

Sample Input 1 | Sample Output 1 |
---|---|

3 1 7 |
6 |

Sample Input 2 | Sample Output 2 |
---|---|

3 6 5 6 7 11 15 18 |
24 |

Sample Input 3 | Sample Output 3 |
---|---|

3 7 5 6 11 15 18 14 9 |
20 |