\item \lect  Complete the following snippet of the python script with the necessary constraint statements.

  The script reads a file that represents a \texttt{size\_x} $\times$ \texttt{size\_y} grid, which includes walkable cells denoted by '$\_$'.

Write constraints for the variables \texttt{coords\_x} and \texttt{coords\_y} such that the variables can only take values that are within the boundaries of the grid and can only represent walkable cells.


  \begin{pythonSourceCode}
    from z3 import *

    ...
    size_y = len(grid)
    size_x = len(grid[0])

    coords_x = Int("coords_x")
    coords_y = Int("coords_y")

    # Enforce that the position is in the grid, use size_x and size_y
    solver.add(coords_x >= 0)
    solver.add(coords_x < size_x)
    solver.add(coords_y >= 0)
    solver.add(coords_y < size_y)


    # Enforce that the coordinates can only be a valid cell
    for i in range(size_y):
        for j in range(size_x):
            if grid[i][j] != "_":
              solver.add(Not(And(coords_y == i, coords_x == j)))

  \end{pythonSourceCode}