Numerical methods for solving partial differential equations typically require that the geometry be subdivided into a mesh of simple shapes such as rectangles. By doing so$,$ a complex problem can be reduced to a collection of simple problems defined on each of the simple shapes. In formulating the solution for a particular simple shape, the algorithms typically need to identify the neighboring shapes. Consider the mesh comprising a grid of $24$ rectangles shown below. The neighbors of rectangle $14$ are rectangles $7,8,9,13,15,19,20,$ and $21.$ Likewise the neighbors of rectangle $6$ are rectangles $5,11,$ and $12.$

Your task is to write a MATLAB function that enumerates the neighbors of a rectangle in an $mn$ mesh of rectangles. Assume that the rectangles are numbered starting at $1in$ the upper left corner and increasing from left to right and top to bottom as shown in the example.

Your function should be called getNeighbors. It should take exactly three input arguments in this order: $m,n,$ and $r.$ Here $m$ is the number of rows in the mesh, $n$ is the number of columns, and $r$ is the rectangle whose neighbors must be identified. The function should return exactly one argument, an array containing the numbers of the neighbors in increasing order. Write your code so that the array is directly generated in the correct order; do not use the sort function. For example, getNeighbors $(4,6,14)$ should return the array $\left[\begin{array}{cccccccc}7& 8& 9& 13& 15& 19& 20& 21\end{array}\right].$

Your program should validate the input arguments and return and empty array $($i$.$e$.,[])$ if any of the inputs are invalid. More specifically, your program must check that $m$ and $n$ are not less than $2,r$ is the number of a rectangle that exists in the mesh, and all input values are integers. For example, the following should return an empty array because there is no rectangle with number $100$ for the given mesh size: getNeighbors $(4,6,100).$

Test your function using the testGetNeighbors test stub.