Given a collection of DNA fragments from a large DNA sequence. For each fragment, a list of other fragments which are positioned to the right of this fragment are given. A consistent ordering is one that respects these constraints.

E.g., given the fragments (ACA, ATT, GGC, CCA, AAT) and the following constraints:

to the right of ACA are ATT and GGC,
to the right of ATT are GGC and CCA,
to the right of GGC is AAT,
to the right of CCA are GGC and AAT

The constraints can be represented by a directed acyclic graph:

DAG

A consistent ordering is [ACA, ATT, CCA, GGC, AAT]. The corresponding drawing of the graph has all arrows pointing forward:

ordering

Assignment

Write a Python function ordering which takes a collection of DNA fragments as parameter and which returns a list with a consistent ordering of the fragments.

Example

>>> ordering({'ACA': ['ATT', 'GGC'], 'ATT':['GGC', 'CCA'], 'GGC': ['AAT'], 'CCA': ['GGC', 'AAT']})
['ACA', 'ATT', 'CCA', 'GGC', 'AAT']