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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 _gen_prov(self):
 """ Extracts provenance information from the pipeline into a PipelineProv object Returns ------- prov : dict[str, *] A dictionary containing the provenance information to record for the pipeline """

        # Export worfklow graph to node-link data format
        wf_dict = nx_json.node_link_data(self.workflow._graph)
        # Replace references to Node objects with the node's provenance
        # information and convert to a dict organised by node name to allow it
        # to be compared more easily. Also change link node-references from
        # node index to node ID so it is not dependent on the order the nodes
        # are written to the dictionary (which for Python < 3.7 is guaranteed
        # to be the same between identical runs)
        for link in wf_dict['links']:
            if int(networkx_version.split('.')[0]) < 2:  # @UndefinedVariable
                link['source'] = wf_dict['nodes'][link['source']]['id'].name
                link['target'] = wf_dict['nodes'][link['target']]['id'].name
            else:
                link['source'] = link['source'].name
                link['target'] = link['target'].name
        wf_dict['nodes'] = {n['id'].name: n['id'].prov
                            for n in wf_dict['nodes']}
        # Roundtrip to JSON to convert any tuples into lists so dictionaries
        # can be compared directly
        wf_dict = json.loads(json.dumps(wf_dict))
        dependency_versions = {d: extract_package_version(d)
                               for d in ARCANA_DEPENDENCIES}
        pkg_versions = {'arcana': __version__}
        pkg_versions.update((k, v) for k, v in dependency_versions.items()
                            if v is not None)
        prov = {
            '__prov_version__': PROVENANCE_VERSION,
            'name': self.name,
            'workflow': wf_dict,
            'study': self.study.prov,
            'pkg_versions': pkg_versions,
            'python_version': sys.version,
            'joined_ids': self._joined_ids()}
        return prov