SPACE PRISON

In the Cosmos, the dark side has made a space prison which has $K$ cells and each cell has a power $P$ that represents the area of the cell. A cell is a closed area where no one can enter or leave. You are given a matrix $A$ with $N$ rows and $M$ columns, where $A[i][j]$ is a $4$ bit binary string that represent the direction of walls. $A[i][j]$ is represented as $North, East, South, West$. For