for i, inp in zip(remaining_idxs, inputs):
                        if isinstance(inp, Exception):
                            failed_inputs_map[i] = inp
                    inputs = [inp for inp in inputs if not isinstance(inp, Exception)]
                    # If all inputs have failed, stop processing
                    if len(failed_inputs_map) == len(configs):
                        break
                # Reassemble the outputs, inserting Exceptions for failed inputs
                inputs_copy = inputs.copy()
                inputs = []
                for i in range(len(configs)):
                    if i in failed_inputs_map:
                        inputs.append(cast(Input, failed_inputs_map[i]))
                    else:
                        inputs.append(inputs_copy.pop(0))
            else:
                for i, step in enumerate(self.steps):
                    inputs = step.batch(
                        inputs,
                        [
                            # each step a child run of the corresponding root run
                            patch_config(
                                config, callbacks=rm.get_child(f"seq:step:{i+1}")
                            )
                            for rm, config in zip(run_managers, configs)
                        ],
                    )
        # finish the root runs
        except BaseException as e:
            for rm in run_managers:
                rm.on_chain_error(e)
            if return_exceptions:
                return cast(List[Output], [e for _ in inputs])
            else:
                raise
        else:
            first_exception: Optional[Exception] = None
            for run_manager, out in zip(run_managers, inputs):
                if isinstance(out, Exception):
                    first_exception = first_exception or out
                    run_manager.on_chain_error(out)
                else:
                    run_manager.on_chain_end(dumpd(out))
            if return_exceptions or first_exception is None:
                return cast(List[Output], inputs)
            else:
                raise first_exception