Forced Particles

You are given a grid with n rows and m columns. Each cell of this grid can either be empty or it contains one particle. It can never contain more than one particle. Let's denote the cell in the i-th row and j-th column by (i,j), with the top left corner being (0,0). From a cell (i,j), a particle could move in one of the following four directions: - to the left, i.e. to the cell (i,j−1) - to the