transformers的beam_search_transformers beamsearch

"""
transformer的generation_beam_search.py中beam_search过程
当decoder的输入是[N,1],N为batch_size,设置beams=k,将输入转化为[N*k,1]
输入放入到decoder中生成了logits,形状为[N*k,T]，T为总的token数
logits和历史beam_score相加成为新的beam_score,进行topk排序，获取next_beam_scores、next_beam_index、next_beam_tokens
beam_hyps存储过程：通过上述next_beam_*,判断next_token是否是<eos>,是则存，不是则仍然挑选出beams=k个next_beam进行下一次decoder
 
代码实现基于一个数，生成一组连续的数，遇到末尾数为9则终止。
"""
 

import torch
from typing import *
from abc import ABC, abstractmethod
from collections import UserDict
import torch
#from .file_utils import add_start_docstrings
 
class BeamScorer(ABC):
    """
    Abstract base class for all beam scorers that are used for :meth:`~transformers.PretrainedModel.beam_search` and
    :meth:`~transformers.PretrainedModel.beam_sample`.
    """
 
    @abstractmethod
    #@add_start_docstrings(PROCESS_INPUTS_DOCSTRING)
    def process(
        self,
        input_ids: torch.LongTensor,
        next_scores: torch.FloatTensor,
        next_tokens: torch.LongTensor,
        next_indices: torch.LongTensor,
        **kwargs
    ) -> Tuple[torch.Tensor]:
        raise NotImplementedError("This is an abstract method.")
 
    @abstractmethod
    #@add_start_docstrings(FINALIZE_INPUTS_DOCSTRING)
    def finalize(
        self,
        input_ids: torch.LongTensor,
        next_scores: torch.FloatTensor,
        next_tokens: torch.LongTensor,
        next_indices: torch.LongTensor,
        **kwargs
    ) -> torch.LongTensor:
        raise NotImplementedError("This is an abstract method.")
 
class BeamSearchScorer(BeamScorer):
    def __init__(
            self,
            batch_size: int,
            max_length: int,
            num_beams: int,
            device: torch.device,
            length_penalty: Optional[float] = 1.0,
            do_early_stopping: Optional[bool] = False,
            num_beam_hyps_to_keep: Optional[int] = 1,
            num_beam_groups: Optional[int] = 1
    ):
        self.max_length = max_length
        self.num_beams = num_beams
        self.device = device
        self.length_penalty = length_penalty
        self.do_early_stopping = do_early_stopping
        self.num_beam_hyps_to_keep = num_beam_hyps_to_keep
        self.num_beam_groups = num_beam_groups
        self.group_size = self.num_beams // self.num_beam_groups
 
        self._is_init = False
        self._beam_hyps = [
            BeamHypotheses(
                num_beams=self.num_beams,
                max_length=self.max_length,
                length_penalty=self.length_penalty,
                early_stopping=self.do_early_stopping,
            )
            for _ in range(batch_size)
        ]
        self._done = torch.tensor([False for _ in range(batch_size)], dtype=torch.bool, device=self.device)
 
        if not isinstance(num_beams, int) or num_beams <= 1:
            raise ValueError(
                f"`num_beams` has to be an integer strictly greater than 1, but is {num_beams}. For `num_beams` == 1, one should make use of `greedy_search` instead."
            )
 
        if not isinstance(num_beam_groups, int) or (num_beam_groups > num_beams) or (num_beams % num_beam_groups != 0):
            raise ValueError(
                f"`num_beam_groups` has to be an integer smaller or equal than `num_beams` and `num_beams` "
                f"has to be divisible by `num_beam_groups`, but is {num_beam_groups} with `num_beams` being {num_beams}."
            )
    @property
    def is_done(self) -> bool:
        return self._done.all()
 
    def process(self,
        input_ids: torch.LongTensor,
        next_scores: torch.FloatTensor,
        next_tokens: torch.LongTensor,
        next_indices: torch.LongTensor,
        pad_token_id: Optional[int] = None,
        eos_token_id: Optional[int] = None,
    ) -> Tuple[torch.Tensor]:
        cur_len = input_ids.shape[-1]
        batch_size = len(self._beam_hyps)
        assert batch_size == (input_ids.shape[0] // self.group_size)
 
        device = input_ids.device
        next_beam_scores = torch.zeros((batch_size, self.group_size), dtype=next_scores.dtype, device=device)
        next_beam_tokens = torch.zeros((batch_size, self.group_size), dtype=next_tokens.dtype, device=device)
        next_beam_indices = torch.zeros((batch_size, self.group_size), dtype=next_indices.dtype, device=device)
        for batch_idx, beam_hyp in enumerate(self._beam_hyps):
            if self._done[batch_idx]:#生成的序列彻底完成情况下，依然设置next_beam_*
                assert (
                    len(beam_hyp) >= self.num_beams
                ), "Batch can only be done if at least {} beams have been generated".format(self.num_beams)
                assert (
                    eos_token_id is not None and pad_token_id is not None
                ), "generated beams >= num_beams -> eos_token_id and pad_token have to be defined"
                # pad the batch
                next_beam_scores[batch_idx, :] = 0
                next_beam_tokens[batch_idx, :] = pad_token_id
                next_beam_indices[batch_idx, :] = 0
                continue
 
            # next tokens for this sentence
            beam_idx = 0
            for beam_token_rank, (next_token, next_score, next_index) in enumerate(
                zip(next_tokens[batch_idx], next_scores[batch_idx], next_indices[batch_idx])
            ):
                batch_beam_idx = batch_idx * self.group_size + next_index
                # add to generated hypotheses if end of sentence
                if (eos_token_id is not None) and (next_token.item() == eos_token_id):
                    # if beam_token does not belong to top num_beams tokens, it should not be added
                    is_beam_token_worse_than_top_num_beams = beam_token_rank >= self.group_size
                    if is_beam_token_worse_than_top_num_beams:
                        continue
                    beam_hyp.add(
                        input_ids[batch_beam_idx].clone(),
                        next_score.item(),
                    )
                else:
                    # add next predicted token since it is not eos_token
                    next_beam_scores[batch_idx, beam_idx] = next_score
                    next_beam_tokens[batch_idx, beam_idx] = next_token
                    next_beam_indices[batch_idx, beam_idx] = batch_beam_idx
                    beam_idx += 1
 
                # once the beam for next step is full, don't add more tokens to it.
                if beam_idx == self.group_size:
                    break
 
            if beam_idx < self.group_size:
                raise ValueError(
                    f"At most {self.group_size} tokens in {next_tokens[batch_idx]} can be equal to `eos_token_id: {eos_token_id}`. Make sure {next_tokens[batch_idx]} are corrected."
                )
 
            # Check if we are done so that we can save a pad step if all(done)
            self._done[batch_idx] = self._done[batch_idx] or beam_hyp.is_done(
                next_scores[batch_idx].max().item(), cur_len
            )
 
        return UserDict(
            {
                "next_beam_scores": next_beam_scores.view(-1),
                "next_beam_tokens": next_beam_tokens.view(-1),
                "next_beam_indices": next_beam_indices.view(-1),
            }
        )
 
    def finalize(
        self,
        input_ids: torch.LongTensor,
        final_beam_scores: torch.FloatTensor,
        final_beam_tokens: torch.LongTensor,
        final_beam_indices: torch.LongTensor,
        pad_token_id: Optional[int] = None,
        eos_token_id: Optional[int] = None,
    ) -> Tuple[torch.LongTensor]:
        batch_size = len(self._beam_hyps)
 
        # finalize all open beam hypotheses and add to generated hypotheses
        for batch_idx, beam_hyp in enumerate(self._beam_hyps):
            if self._done[batch_idx]:
                continue
 
            # all open beam hypotheses are added to the beam hypothesis
            # beam hypothesis class automatically keeps the best beams
            for beam_id in range(self.num_beams):
                batch_beam_idx = batch_idx * self.num_beams + beam_id
                final_score = final_beam_scores[batch_beam_idx].item()
                final_tokens = input_ids[batch_beam_idx]
                beam_hyp.add(final_tokens, final_score)
 
        # select the best hypotheses
        sent_lengths = input_ids.new(batch_size * self.num_beam_hyps_to_keep)
        best = []
        best_scores = torch.zeros(batch_size * self.num_beam_hyps_to_keep, device=self.device, dtype=torch.float32)
 
        # retrieve best hypotheses
        for i, beam_hyp in enumerate(self._beam_hyps):
            sorted_hyps = sorted(beam_hyp.beams, key=lambda x: x[0])
            for j in range(self.num_beam_hyps_to_keep):
                best_hyp_tuple = sorted_hyps.pop()
                best_score = best_hyp_tuple[0]
                best_hyp = best_hyp_tuple[1]
                sent_lengths[self.num_beam_hyps_to_keep * i + j] = len(best_hyp)
 
                # append to lists
                best.append(best_hyp)
                best_scores[i * self.num_beam_hyps_to_keep + j] = best_score
 
        # prepare for adding eos
        sent_max_len = min(sent_lengths.max().item() + 1, self.max_length)
        decoded: torch.LongTensor = input_ids.new(batch_size * self.num_beam_hyps_to_keep, sent_max_len)
        # shorter batches are padded if needed
        if sent_lengths.min().item() != sent_lengths.max().item():
            assert pad_token_id is not None, "`pad_token_id` has to be defined"
            decoded.fill_(pad_token_id)
 
        # fill with hypotheses and eos_token_id if the latter fits in
        for i, hypo in enumerate(best):
            decoded[i, : sent_lengths[i]] = hypo
            if sent_lengths[i] < self.max_length:
                decoded[i, sent_lengths[i]] = eos_token_id
        return UserDict(
            {
                "sequences": decoded,
                "sequence_scores": best_scores,
            }
        )
 
 
class BeamHypotheses:
    def __init__(self, num_beams: int, max_length: int, length_penalty: float, early_stopping: bool):
        """
        Initialize n-best list of hypotheses.
        """
        self.max_length = max_length - 1  # ignoring bos_token
        self.length_penalty = length_penalty
        self.early_stopping = early_stopping
        self.num_beams = num_beams
        self.beams = []
        self.worst_score = 1e9
 
    def __len__(self):
        """
        Number of hypotheses in the list.
        """
        return len(self.beams)
 
    def add(self, hyp: torch.LongTensor, sum_logprobs: float):
        """
        Add a new hypothesis to the list.
        """
        score = sum_logprobs / (hyp.shape[-1] ** self.length_penalty)
        if len(self) < self.num_beams or score > self.worst_score:
            self.beams.append((score, hyp))
            if len(self) > self.num_beams:
                sorted_next_scores = sorted([(s, idx) for idx, (s, _) in enumerate(self.beams)])
                del self.beams[sorted_next_scores[0][1]]
                self.worst_score = sorted_next_scores[1][0]
            else:
                self.worst_score = min(score, self.worst_score)
 
    def is_done(self, best_sum_logprobs: float, cur_len: int) -> bool:
        """
        If there are enough hypotheses and that none of the hypotheses being generated can become better than the worst
        one in the heap, then we are done with this sentence.
        """
 
        if len(self) < self.num_beams:
            return False
        elif self.early_stopping:
            return True
        else:
            cur_score = best_sum_logprobs / cur_len ** self.length_penalty
            ret = self.worst_score >= cur_score
            return ret
 
class ToyDecoder():
 
    #@torch.no_grad()
    def generate(self,
        input_ids: Optional[torch.LongTensor] = None,
        max_length: Optional[int] = None,
        min_length: Optional[int] = None,
        do_sample: Optional[bool] = None,
        early_stopping: Optional[bool] = None,
        num_beams: Optional[int] = None,
        temperature: Optional[float] = None,
        top_k: Optional[int] = None,
        top_p: Optional[float] = None,
        repetition_penalty: Optional[float] = None,
        bad_words_ids: Optional[Iterable[int]] = None,
        bos_token_id: Optional[int] = None,
        pad_token_id: Optional[int] = None,
        eos_token_id: Optional[int] = None,
        length_penalty: Optional[float] = None,
        no_repeat_ngram_size: Optional[int] = None,
        encoder_no_repeat_ngram_size: Optional[int] = None,
        num_return_sequences: Optional[int] = None,
        decoder_start_token_id: Optional[int] = None,
        use_cache: Optional[bool] = None,
        num_beam_groups: Optional[int] = None,
        diversity_penalty: Optional[float] = None,
        prefix_allowed_tokens_fn: Optional[Callable[[int, torch.Tensor], List[int]]] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        output_scores: Optional[bool] = None,
        return_dict_in_generate: Optional[bool] = None,
        **model_kwargs,
    ) -> Union[torch.LongTensor]:
        model_kwargs["output_attentions"] = output_attentions
        model_kwargs["output_hidden_states"] = output_hidden_states
 
        # set input_ids as decoder_input_ids
        if "decoder_input_ids" in model_kwargs:
            input_ids = model_kwargs.pop("decoder_input_ids")
        else:
            input_ids = self._prepare_decoder_input_ids_for_generation(
                input_ids, decoder_start_token_id=decoder_start_token_id, bos_token_id=bos_token_id
            )
 
        logits_processor = self._get_logits_processor(
            repetition_penalty=repetition_penalty,
            no_repeat_ngram_size=no_repeat_ngram_size,
            encoder_no_repeat_ngram_size=encoder_no_repeat_ngram_size,
            encoder_input_ids=input_ids,#encoder_input_ids
            bad_words_ids=bad_words_ids,
            min_length=min_length,
            eos_token_id=eos_token_id,
            prefix_allowed_tokens_fn=prefix_allowed_tokens_fn,
            num_beams=num_beams,
            num_beam_groups=num_beam_groups,
            diversity_penalty=diversity_penalty,
        )
 
        is_beam_gen_mode = (num_beams > 1) and (num_beam_groups == 1) and do_sample is False
 
        if is_beam_gen_mode:
            batch_size = input_ids.shape[0]
            length_penalty = length_penalty if length_penalty is not None else self.config.length_penalty
            early_stopping = early_stopping if early_stopping is not None else self.config.early_stopping
            if num_return_sequences > num_beams:
                raise ValueError("`num_return_sequences` has to be smaller or equal to `num_beams`.")
 
        self.device = input_ids.device
 
        beam_scorer = BeamSearchScorer(
            batch_size=batch_size,
            max_length=max_length,
            num_beams=num_beams,
            device=self.device,
            length_penalty=length_penalty,
            do_early_stopping=early_stopping,
            num_beam_hyps_to_keep=num_return_sequences,
        )
 
        input_ids, model_kwargs = self._expand_inputs_for_generation(
            input_ids, expand_size=num_beams, is_encoder_decoder=True, **model_kwargs
        )
 
        return self.beam_search(
                input_ids,
                beam_scorer,
                logits_processor=logits_processor,
                max_length=max_length,
                pad_token_id=pad_token_id,
                eos_token_id=eos_token_id,
                output_scores=output_scores,
                return_dict_in_generate=return_dict_in_generate,
                **model_kwargs,
            )
 
 
    def _prepare_decoder_input_ids_for_generation(
        self, input_ids: torch.LongTensor, decoder_start_token_id: int = None, bos_token_id: int = None
    ) -> torch.LongTensor:
        #取输入的最后一个字作为输入
        decoder_input_ids = input_ids[:,-1].unsqueeze(-1)
        return decoder_input_ids
 
    @staticmethod
    def _expand_inputs_for_generation(
        input_ids: torch.LongTensor,
        expand_size: int = 1,
        is_encoder_decoder: bool = False,
        attention_mask: torch.LongTensor = None,
        #encoder_outputs: ModelOutput = None,
        **model_kwargs,
    ) -> Tuple[torch.LongTensor, Dict[str, Any]]:
        expanded_return_idx = (
            torch.arange(input_ids.shape[0]).view(-1, 1).repeat(1, expand_size).view(-1).to(input_ids.device)
        )
        input_ids = input_ids.index_select(0,expanded_return_idx)
 
        if "token_type_ids" in model_kwargs:
            token_type_ids = model_kwargs["token_type_ids"]
            model_kwargs["token_type_ids"] = token_type_ids.index_select(0, expanded_return_idx)
 
        if attention_mask is not None:
            model_kwargs["attention_mask"] = attention_mask.index_select(0, expanded_return_idx)
 
        if is_encoder_decoder:
            pass
            # assert encoder_outputs is not None
            # encoder_outputs["last_hidden_state"] = encoder_outputs.last_hidden_state.index_select(
            #     0, expanded_return_idx.to(encoder_outputs.last_hidden_state.device)
            # )
            # model_kwargs["encoder_outputs"] = encoder_outputs
        return input_ids, model_kwargs
 
    def _get_logits_processor(
        self,
        repetition_penalty: float,
        no_repeat_ngram_size: int,
        encoder_no_repeat_ngram_size: int,
        encoder_input_ids: torch.LongTensor,
        bad_words_ids: List[List[int]],
        min_length: int,
        eos_token_id: int,
        prefix_allowed_tokens_fn: Callable[[int, torch.Tensor], List[int]],
        num_beams: int,
        num_beam_groups: int,
        diversity_penalty: float,
    ) :
        return None
 
 
    def beam_search(
        self,
        input_ids: torch.LongTensor,
        beam_scorer: BeamScorer,
        logits_processor: Optional[List] = None,
        max_length: Optional[int] = None,
        pad_token_id: Optional[int] = None,
        eos_token_id: Optional[int] = None,
        output_attentions: Optional[bool] = None,
        output_hidden_states: Optional[bool] = None,
        output_scores: Optional[bool] = None,
        return_dict_in_generate: Optional[bool] = None,
        **model_kwargs,
    ) -> Union[torch.LongTensor]:
 
        # init attention / hidden states / scores tuples
        scores = () if (return_dict_in_generate and output_scores) else None
        decoder_attentions = () if (return_dict_in_generate and output_attentions) else None
        decoder_hidden_states = () if (return_dict_in_generate and output_hidden_states) else None
 
        # if return_dict_in_generate and self.config.is_encoder_decoder:
        #     encoder_attentions = model_kwargs["encoder_outputs"].get("attentions") if output_attentions else None
        #     encoder_hidden_states = (
        #         model_kwargs["encoder_outputs"].get("hidden_states") if output_hidden_states else None
        #     )
 
        batch_size = len(beam_scorer._beam_hyps)
        num_beams = beam_scorer.num_beams
 
        batch_beam_size, cur_len = input_ids.shape
 
        assert (
            num_beams * batch_size == batch_beam_size
        ), "Batch dimension of `input_ids` should be {num_beams * batch_size}, but is {batch_beam_size}."
 
        beam_scores = torch.zeros((batch_size, num_beams), dtype=torch.float, device=input_ids.device)
        beam_scores[:,1:] = -1e9 #这个是针对起始位置是同一个字符，比如<eos>,<bos>情况设置的，目的是这样避免topk的值是一样的。
        beam_scores = beam_scores.view((batch_size * num_beams,))
        while cur_len < max_length:
            model_inputs = self.prepare_inputs_for_generation(input_ids, **model_kwargs)
 
            outputs = self(
                **model_inputs,
                return_dict=True,
                output_attentions=output_attentions,
                output_hidden_states=output_hidden_states,
            )
            #next_token_logits = outputs.logits[:, -1, :]
            next_token_logits = outputs['logits'][:, -1, :]
            next_token_logits = self.adjust_logits_during_generation(
                next_token_logits, cur_len=cur_len, max_length=max_length
            )
            next_token_scores = next_token_logits/100
            next_token_scores = next_token_scores + beam_scores[:, None].expand_as(next_token_scores)
            vocab_size = next_token_scores.shape[-1]
            next_token_scores = next_token_scores.view(batch_size, num_beams * vocab_size)
            next_token_scores, next_tokens = torch.topk(
                next_token_scores, 2 * num_beams, dim=1, largest=True, sorted=True
            )
            next_indices = next_tokens // vocab_size
            next_tokens = next_tokens % vocab_size
            # stateless
            beam_outputs = beam_scorer.process(
                input_ids,
                next_token_scores,
                next_tokens,
                next_indices,
                pad_token_id=pad_token_id,
                eos_token_id=eos_token_id,
            )
            beam_scores = beam_outputs["next_beam_scores"]
            beam_next_tokens = beam_outputs["next_beam_tokens"]
            beam_idx = beam_outputs["next_beam_indices"]
            input_ids = torch.cat([input_ids[beam_idx, :], beam_next_tokens.unsqueeze(-1)], dim=-1)
            cur_len = cur_len + 1
            # model_kwargs = self._update_model_kwargs_for_generation(
            #     outputs, model_kwargs, is_encoder_decoder=self.config.is_encoder_decoder
            # )
            # if model_kwargs["past"] is not None:
            #     model_kwargs["past"] = self._reorder_cache(model_kwargs["past"], beam_idx)
            #
            # if beam_scorer.is_done:
            #     break
        sequence_outputs = beam_scorer.finalize(
            input_ids, beam_scores, next_tokens, next_indices, pad_token_id=pad_token_id, eos_token_id=eos_token_id
        )
        return sequence_outputs["sequences"]
 
    def prepare_inputs_for_generation(
        self,
        decoder_input_ids,
        past=None,
        attention_mask=None,
        head_mask=None,
        use_cache=None,
        encoder_outputs=None,
        **kwargs
    ):
        # cut decoder_input_ids if past is used
        # if past is not None:
        #     decoder_input_ids = decoder_input_ids[:, -1:] #取一个batch每个序列最后一个token
 
        decoder_input_ids = decoder_input_ids[:, -1:]
        return {
            "input_ids": None,  # encoder_outputs is defined. input_ids not needed
            "encoder_outputs": encoder_outputs,
            "past_key_values": past,
            "decoder_input_ids": decoder_input_ids,
            "attention_mask": attention_mask,
            "head_mask": head_mask,
            "use_cache": use_cache,  # change this to avoid caching (presumably for debugging)
        }
 
 
    def __call__(#其实是forward方法，这里简化decoder计算结果
            self,
            input_ids=None,
            attention_mask=None,
            decoder_input_ids=None,
            decoder_attention_mask=None,
            head_mask=None,
            decoder_head_mask=None,
            encoder_outputs=None,
            past_key_values=None,
            inputs_embeds=None,
            decoder_inputs_embeds=None,
            labels=None,
            use_cache=None,
            output_attentions=None,
            output_hidden_states=None,
            return_dict=None,
                 ):
        input_shape = decoder_input_ids.size()
        decoder_input_ids = decoder_input_ids.view(-1, input_shape[-1])
        shape = tuple(decoder_input_ids.shape)+(100,) #设置0-99个数字的预测
        lm_logits = torch.zeros(shape)
        for ids, num  in enumerate(decoder_input_ids.squeeze()):
            if (num.item()+1)%10 == 0:#当遇到以9结尾的数字就停止继续生成数字了
                num = 1 #num+1=2是<eos>token
            maxnum = min(num+1+10,99)
            lm_logits[ids,:,num+1:maxnum] = torch.arange(99,99-(maxnum-num-1), step=-1)
        return {'logits': lm_logits}
 
 
    def adjust_logits_during_generation(self, logits, cur_len, max_length):
        # if cur_len == 1 and self.config.force_bos_token_to_be_generated:
        #     self._force_token_id_to_be_generated(logits, self.config.bos_token_id)
        # elif cur_len == max_length - 1 and self.config.eos_token_id is not None:
        #     self._force_token_id_to_be_generated(logits, self.config.eos_token_id)
        if cur_len == max_length - 1:
            self._force_token_id_to_be_generated(logits, 2)
 
        return logits
 
 
    @staticmethod
    def _force_token_id_to_be_generated(scores, token_id) -> None:
        """force one of token_ids to be generated by setting prob of all other tokens to 0 (logprob=-float("inf"))"""
        scores[:, [x for x in range(scores.shape[1]) if x != token_id]] = -float("inf")
 
 
 
if __name__ == '__main__':
    input_ids = torch.randint(0,100,(2,5))
    print(input_ids)
 
    decoder = ToyDecoder()
 
    t=decoder._prepare_decoder_input_ids_for_generation(input_ids)
    print(t)
 
    t1=decoder.generate(input_ids,8,num_beams=4, num_beam_groups=1, do_sample=False,
                     length_penalty=1,early_stopping=True, num_return_sequences=4,eos_token_id=2, pad_token_id=1)
    print(t1)

结果：

tensor([[91, 50, 26, 71, 23],
        [25, 22, 31, 20, 71]])
tensor([[23],
        [71]])
tensor([[23, 24, 25, 26, 27, 28, 29,  2],
        [23, 24, 25, 26, 27, 29,  2,  1],
        [23, 24, 25, 26, 28, 29,  2,  1],
        [23, 24, 25, 27, 28, 29,  2,  1],
        [71, 72, 73, 74, 75, 76, 77,  2],
        [71, 72, 73, 74, 75, 77, 78,  2],
        [71, 72, 73, 75, 76, 77, 78,  2],
        [71, 72, 74, 75, 76, 77, 78,  2]])