def is_diagonal(width, tile):
    """
     Check if the given tile is along the diagonal of
     the square grid.
     Assuming the tile number starts from 1,2, ..., width*height

    :param width:
    :param tile:
    :return: True if the given tile is along the diagonal of
            the grid. False otherwise
    """

    row = (tile - 1) // width
    col = (tile - 1) % width
    if row == col:
        return True
    return False


def is_edge(width, height, tile):
    """
     Check if the given tile is along the edge of
     the given grid.
     Assuming the tile number starts from 1,2, ..., width*height

    :param width:
    :param height:
    :param tile:
    :return:
    """

    row = (tile - 1) // width    # row = 0,1,...,height-1
    col = (tile - 1) % width     # col = 0,1,...,width-1
    if row == 0 or row == height-1:
        return True
    if col == 0 or col == width-1:
        return True
    return False