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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:

def recursively_collect_orders(
        name, ctx, all_inputs, orders=None, blacklist=None
        ):
    '''For each possible recipe ordering, try to add the new recipe name
    to that order. Recursively do the same thing with all the
    dependencies of each recipe.

    '''
    name = name.lower()
    if orders is None:
        orders = []
    if blacklist is None:
        blacklist = set()
    try:
        recipe = Recipe.get_recipe(name, ctx)
        dependencies = get_dependency_tuple_list_for_recipe(
            recipe, blacklist=blacklist
        )

        # handle opt_depends: these impose requirements on the build
        # order only if already present in the list of recipes to build
        dependencies.extend(fix_deplist(
            [[d] for d in recipe.get_opt_depends_in_list(all_inputs)
             if d.lower() not in blacklist]
        ))

        if recipe.conflicts is None:
            conflicts = []
        else:
            conflicts = [dep.lower() for dep in recipe.conflicts]
    except ValueError:
        # The recipe does not exist, so we assume it can be installed
        # via pip with no extra dependencies
        dependencies = []
        conflicts = []

    new_orders = []
    # for each existing recipe order, see if we can add the new recipe name
    for order in orders:
        if name in order:
            new_orders.append(deepcopy(order))
            continue
        if order.conflicts():
            continue
        if any([conflict in order for conflict in conflicts]):
            continue

        for dependency_set in product(*dependencies):
            new_order = deepcopy(order)
            new_order[name] = set(dependency_set)

            dependency_new_orders = [new_order]
            for dependency in dependency_set:
                dependency_new_orders = recursively_collect_orders(
                    dependency, ctx, all_inputs, dependency_new_orders,
                    blacklist=blacklist
                )

            new_orders.extend(dependency_new_orders)

    return new_orders