Super Paintball

Bessie is playing a paintball game on a square field. The field is divided into an $N \times N$ grid of unit cells ($1 \le N \le 100$). There are $K$ opponents ($1 \le K \le 100{,}000$); opponent $i$ stands in the cell at row $R_i$ and column $C_i$ ($1 \le R_i \le N$, $1 \le C_i \le N$). Several opponents may stand in the same cell.

Bessie's paintball gun fires in any of eight directions: up, down, left, right, and the four diagonals (up-left, up-right, down-left, down-right). She hits an opponent if that opponent lies in the same row, the same column, or on one of the two diagonals through her cell. She can also hit an opponent that shares her own cell.

Bessie will stand in exactly one cell. Count how many of the $N \times N$ cells she may choose so that, from that cell, she can hit every one of the $K$ opponents.

• Line 1: two space-separated integers $N$ and $K$.
• Lines 2 to $K+1$: line $i+1$ contains two space-separated integers $R_i$ and $C_i$, the row and column of opponent $i$.

• Line 1: a single integer — the number of distinct cells Bessie may occupy so that she can hit every opponent.

Consider a field with $4$ rows and $4$ columns and opponents at $(2,1)$, $(2,3)$, and $(4,1)$ (C marks an opponent):

. . . .
C . C .
. . . .
C . . .

From each of the cells $(2,1)$, $(2,3)$, $(3,2)$, $(4,1)$, and $(4,3)$ Bessie can hit all three opponents, so the answer is $5$. Below, B marks a valid cell for Bessie and * marks a cell that is valid and also shared with an opponent:

. . . .        . . . .
B . B .        * . * .
. B . .   =>   . B . .
B . B .        * . B .