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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 mediate_transfer( state: MediatorTransferState, possible_routes: List['RouteState'], payer_channel: NettingChannelState, channelidentifiers_to_channels: ChannelMap, nodeaddresses_to_networkstates: NodeNetworkStateMap, pseudo_random_generator: random.Random, payer_transfer: LockedTransferSignedState, block_number: BlockNumber, ) -> TransitionResult[MediatorTransferState]: """ Try a new route or fail back to a refund. The mediator can safely try a new route knowing that the tokens from payer_transfer will cover the expenses of the mediation. If there is no route available that may be used at the moment of the call the mediator may send a refund back to the payer, allowing the payer to try a different route. """

    reachable_routes = filter_reachable_routes(
        possible_routes,
        nodeaddresses_to_networkstates,
    )
    available_routes = filter_used_routes(
        state.transfers_pair,
        reachable_routes,
    )

    assert payer_channel.partner_state.address == payer_transfer.balance_proof.sender

    transfer_pair, mediated_events = forward_transfer_pair(
        payer_transfer,
        available_routes,
        channelidentifiers_to_channels,
        pseudo_random_generator,
        block_number,
    )

    if transfer_pair is None:
        assert not mediated_events

        if state.transfers_pair:
            original_pair = state.transfers_pair[0]
            original_channel = get_payer_channel(
                channelidentifiers_to_channels,
                original_pair,
            )
        else:
            original_channel = payer_channel

        if original_channel:
            transfer_pair, mediated_events = backward_transfer_pair(
                original_channel,
                payer_transfer,
                pseudo_random_generator,
                block_number,
            )
        else:
            transfer_pair = None
            mediated_events = list()

    if transfer_pair is None:
        assert not mediated_events
        mediated_events = list()
        state.waiting_transfer = WaitingTransferState(payer_transfer)

    else:
        # the list must be ordered from high to low expiration, expiration
        # handling depends on it
        state.transfers_pair.append(transfer_pair)

    return TransitionResult(state, mediated_events)