Task

Pac-Man got lucky today! Due to minor performance issue all his enemies have frozen. Too bad Pac-Man is not brave enough to face them right now, so he doesn't want any enemy to see him.

Given a gamefield of size N x N, Pac-Man's position(PM) and his enemies' positions(enemies), your task is to count the number of coins he can collect without being seen.

An enemy can see a Pac-Man if they are standing on the same row or column.

It is guaranteed that no enemy can see Pac-Man on the starting position. There is a coin on each empty square (i.e. where there is no Pac-Man or enemy).

Example

For N = 4, PM = [3, 0], enemies = [[1, 2]], the result should be 3.

Let O represent coins, P - Pac-Man and E - enemy.
OOOO
OOEO
OOOO
POOO

Pac-Man cannot cross row 1 and column 2.

He can only collect coins from points (2, 0), (2, 1) and (3, 1), like this:

x is the points that Pac-Man can collect the coins.
OOOO
OOEO
xxOO
PxOO

Input/Output

• [input] integer N

The field size.

• [input] integer array PM

Pac-Man's position (pair of integers)

• [input] 2D integer array enemies

Enemies' positions (array of pairs)

• [output] an integer

Number of coins Pac-Man can collect.

More PacMan Katas

• Play PacMan: Devour all

• Play PacMan 2: The way home