Robot Vacuum Cleaner

Given a robot vacuum cleaner and the state of a room, write a program that counts the cells the robot cleans.

The room is an $N \times M$ rectangle divided into $1 \times 1$ square cells. Each cell is either a wall or an empty cell. The robot faces one of four directions: east, west, south, or north. Each cell of the room is written as a coordinate $(r, c)$. The westmost cell of the northmost row is $(0, 0)$, and the eastmost cell of the southmost row is $(N-1, M-1)$. In other words, $(r, c)$ is the $(c+1)$-th cell from the west in the $(r+1)$-th row from the north. Initially, no empty cell has been cleaned.

The robot works as follows.

1. If the current cell has not been cleaned yet, clean it.

2. If none of the $4$ cells adjacent to the current cell is an uncleaned empty cell:

   1. If the robot can move back one cell while keeping its facing direction, it moves back one cell and returns to step 1.
   2. If the cell behind the robot is a wall so it cannot move back, the robot stops.

3. If at least one of the $4$ cells adjacent to the current cell is an uncleaned empty cell:

   1. Rotate $90^\circ$ counterclockwise.
   2. If the cell in front of the robot is an uncleaned empty cell, move forward one cell.
   3. Return to step 1.

The first line contains the room size $N$ and $M$. $(3 \le N, M \le 50)$

The second line contains the coordinates $(r, c)$ of the robot's starting cell and its initial facing direction $d$. The robot faces north if $d$ is $0$, east if $d$ is $1$, south if $d$ is $2$, and west if $d$ is $3$.

Each of the next $N$ lines contains $M$ values describing the cells. The $j$-th value on the $i$-th of these lines is the state of cell $(i, j)$. A value of $0$ means $(i, j)$ is an uncleaned empty cell, and a value of $1$ means $(i, j)$ is a wall. Every cell in the northmost, southmost, westmost, or eastmost row or column is a wall. The robot's starting cell is always empty.

Print the number of cells the robot cleans from the moment it starts until it stops.