


import itertools
import json
import linecache
import os
import pickle
import re
import socket
import string
from collections import Counter
from logging import getLogger
from pathlib import Path
from typing import Callable, Dict, Iterable, List

import git
import torch
from torch.utils.data import Dataset

from transformers import BartTokenizer, RagTokenizer, TaTokenizer



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase=True  ,  __UpperCamelCase="pt" ):
     a_    :     int										=    {"""add_prefix_space""": True} if isinstance(__UpperCamelCase  ,  __UpperCamelCase ) and not line.startswith(""" """ ) else {}
     a_    :     Optional[Any]										=    padding_side
     return tokenizer(
         [line]  ,  max_length=__UpperCamelCase  ,  padding="""max_length""" if pad_to_max_length else None  ,  truncation=__UpperCamelCase  ,  return_tensors=__UpperCamelCase  ,  add_special_tokens=__UpperCamelCase  ,  **__UpperCamelCase  ,  )



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase=None  ,  ):
     a_    :     List[str]										=    input_ids.ne(__UpperCamelCase ).any(dim=0 )
     if attention_mask is None:
          return input_ids[:, keep_column_mask]
     else:
          return (input_ids[:, keep_column_mask], attention_mask[:, keep_column_mask])


class   a__	(						_UpperCAmelCase    ):

       def __init__(   self      :     List[Any]      ,							lowerCamelCase_      :     Optional[int]      ,							lowerCamelCase_      :     int      ,							lowerCamelCase_      :     int      ,							lowerCamelCase_      :     Any      ,							lowerCamelCase_      :     str="train"      ,							lowerCamelCase_      :     Tuple=None      ,							lowerCamelCase_      :     int=None      ,							lowerCamelCase_      :     Union[str, Any]=None      ,							lowerCamelCase_      :     Union[str, Any]=""      ,							):
            super().__init__()
            a_    :     Any										=    Path(A_    ).joinpath(type_path + """.source"""    )
            a_    :     Tuple										=    Path(A_    ).joinpath(type_path + """.target"""    )
            a_    :     Tuple										=    self.get_char_lens(self.src_file    )
            a_    :     Optional[int]										=    max_source_length
            a_    :     List[str]										=    max_target_length
            assert min(self.src_lens    ) > 0, F'''found empty line in {self.src_file}'''
            a_    :     Tuple										=    tokenizer
            a_    :     str										=    prefix
            if n_obs is not None:
                 a_    :     Tuple										=    self.src_lens[:n_obs]
            a_    :     Dict										=    src_lang
            a_    :     Any										=    tgt_lang

       def __len__(   self      :     Any    ):
            return len(self.src_lens    )

       def __getitem__(   self      :     List[str]      ,							lowerCamelCase_      :     Tuple    ):
            a_    :     List[str]										=    index + 1  # linecache starts at 1
            a_    :     Union[str, Any]										=    self.prefix + linecache.getline(str(self.src_file    )      ,							A_    ).rstrip("""\n"""    )
            a_    :     Dict										=    linecache.getline(str(self.tgt_file    )      ,							A_    ).rstrip("""\n"""    )
            assert source_line, F'''empty source line for index {index}'''
            assert tgt_line, F'''empty tgt line for index {index}'''

            # Need to add eos token manually for T5
            if isinstance(self.tokenizer      ,							A_    ):
                 source_line += self.tokenizer.eos_token
                 tgt_line += self.tokenizer.eos_token

            # Pad source and target to the right
            a_    :     Union[str, Any]										=    (
                self.tokenizer.question_encoder if isinstance(self.tokenizer      ,							A_    ) else self.tokenizer
            )
            a_    :     Tuple										=    self.tokenizer.generator if isinstance(self.tokenizer      ,							A_    ) else self.tokenizer

            a_    :     Optional[Any]										=    encode_line(A_      ,							A_      ,							self.max_source_length      ,							"""right"""    )
            a_    :     Tuple										=    encode_line(A_      ,							A_      ,							self.max_target_length      ,							"""right"""    )

            a_    :     Union[str, Any]										=    source_inputs["""input_ids"""].squeeze()
            a_    :     str										=    target_inputs["""input_ids"""].squeeze()
            a_    :     List[str]										=    source_inputs["""attention_mask"""].squeeze()
            return {
                "input_ids": source_ids,
                "attention_mask": src_mask,
                "decoder_input_ids": target_ids,
            }

       @staticmethod
       def 						UpperCAmelCase(   lowerCamelCase_      :     str    ):
            return [len(A_    ) for x in Path(A_    ).open().readlines()]

       def 						UpperCAmelCase(   self      :     int      ,							lowerCamelCase_      :     int    ):
            a_    :     Optional[Any]										=    torch.stack([x["""input_ids"""] for x in batch]    )
            a_    :     Any										=    torch.stack([x["""attention_mask"""] for x in batch]    )
            a_    :     Tuple										=    torch.stack([x["""decoder_input_ids"""] for x in batch]    )
            a_    :     Dict										=    (
                self.tokenizer.generator.pad_token_id
                if isinstance(self.tokenizer      ,							A_    )
                else self.tokenizer.pad_token_id
            )
            a_    :     Dict										=    (
                self.tokenizer.question_encoder.pad_token_id
                if isinstance(self.tokenizer      ,							A_    )
                else self.tokenizer.pad_token_id
            )
            a_    :     Dict										=    trim_batch(A_      ,							A_    )
            a_			,			a_    :     Optional[Any]										=    trim_batch(A_      ,							A_      ,							attention_mask=A_    )
            a_    :     Union[str, Any]										=    {
                """input_ids""": source_ids,
                """attention_mask""": source_mask,
                """decoder_input_ids""": y,
            }
            return batch

__lowerCamelCase        =     getLogger(__name__)



def  _a			(						__UpperCamelCase ):
     return list(itertools.chain.from_iterable(__UpperCamelCase ) )



def  _a			(						__UpperCamelCase ):
     a_    :     List[str]										=    get_git_info()
     save_json(__UpperCamelCase  ,  os.path.join(__UpperCamelCase  ,  """git_log.json""" ) )



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase=4  ,  **__UpperCamelCase ):
     with open(__UpperCamelCase  ,  """w""" ) as f:
          json.dump(__UpperCamelCase  ,  __UpperCamelCase  ,  indent=__UpperCamelCase  ,  **__UpperCamelCase )



def  _a			(						__UpperCamelCase ):
     with open(__UpperCamelCase ) as f:
          return json.load(__UpperCamelCase )



def  _a			(						):
     a_    :     List[Any]										=    git.Repo(search_parent_directories=__UpperCamelCase )
     a_    :     List[str]										=    {
         """repo_id""": str(__UpperCamelCase ),
         """repo_sha""": str(repo.head.object.hexsha ),
         """repo_branch""": str(repo.active_branch ),
         """hostname""": str(socket.gethostname() ),
     }
     return repo_infos



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase ):
     return list(map(__UpperCamelCase  ,  __UpperCamelCase ) )



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase ):
     with open(__UpperCamelCase  ,  """wb""" ) as f:
          return pickle.dump(__UpperCamelCase  ,  __UpperCamelCase )



def  _a			(						__UpperCamelCase ):

     def remove_articles(__UpperCamelCase ):
          return re.sub(r"""\b(a|an|the)\b"""  ,  """ """  ,  __UpperCamelCase )

     def white_space_fix(__UpperCamelCase ):
          return " ".join(text.split() )

     def remove_punc(__UpperCamelCase ):
          a_    :     Optional[Any]										=    set(string.punctuation )
          return "".join(ch for ch in text if ch not in exclude )

     def lower(__UpperCamelCase ):
          return text.lower()

     return white_space_fix(remove_articles(remove_punc(lower(__UpperCamelCase ) ) ) )



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase ):
     a_    :     Optional[int]										=    normalize_answer(__UpperCamelCase ).split()
     a_    :     Tuple										=    normalize_answer(__UpperCamelCase ).split()
     a_    :     Any										=    Counter(__UpperCamelCase ) & Counter(__UpperCamelCase )
     a_    :     Optional[int]										=    sum(common.values() )
     if num_same == 0:
          return 0
     a_    :     Union[str, Any]										=    1.0 * num_same / len(__UpperCamelCase )
     a_    :     Union[str, Any]										=    1.0 * num_same / len(__UpperCamelCase )
     a_    :     int										=    (2 * precision * recall) / (precision + recall)
     return fa



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase ):
     return normalize_answer(__UpperCamelCase ) == normalize_answer(__UpperCamelCase )



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase ):
     assert len(__UpperCamelCase ) == len(__UpperCamelCase )
     a_    :     List[str]										=    0
     for hypo, pred in zip(__UpperCamelCase  ,  __UpperCamelCase ):
          em += exact_match_score(__UpperCamelCase  ,  __UpperCamelCase )
     if len(__UpperCamelCase ) > 0:
          em /= len(__UpperCamelCase )
     return {"em": em}



def  _a			(						__UpperCamelCase ):
     return model_prefix.startswith("""rag""" )



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase ):
     a_    :     Optional[Any]										=    {p: p for p in extra_params}
     # T5 models don't have `dropout` param, they have `dropout_rate` instead
     a_    :     Tuple										=    """dropout_rate"""
     for p in extra_params:
          if getattr(__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase ):
               if not hasattr(__UpperCamelCase  ,  __UpperCamelCase ) and not hasattr(__UpperCamelCase  ,  equivalent_param[p] ):
                    logger.info("""config doesn\'t have a `{}` attribute""".format(__UpperCamelCase ) )
                    delattr(__UpperCamelCase  ,  __UpperCamelCase )
                    continue
               a_    :     Tuple										=    p if hasattr(__UpperCamelCase  ,  __UpperCamelCase ) else equivalent_param[p]
               setattr(__UpperCamelCase  ,  __UpperCamelCase  ,  getattr(__UpperCamelCase  ,  __UpperCamelCase ) )
               delattr(__UpperCamelCase  ,  __UpperCamelCase )
     return hparams, config







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt



def  _a			(						__UpperCamelCase ):
     a_    :     int										=    int(number**0.5 )
     return number == sq * sq



def  _a			(						__UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase ):
     a_    :     int										=    x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
     a_    :     int										=    x_den * y_den * z_den
     a_    :     int										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
     top //= hcf
     bottom //= hcf
     return top, bottom



def  _a			(						__UpperCamelCase = 3_5 ):
     a_    :     set										=    set()
     a_    :     int
     a_    :     Fraction										=    Fraction(0 )
     a_    :     tuple[int, int]

     for x_num in range(1  ,  order + 1 ):
          for x_den in range(x_num + 1  ,  order + 1 ):
               for y_num in range(1  ,  order + 1 ):
                    for y_den in range(y_num + 1  ,  order + 1 ):
                         # n=1
                         a_    :     int										=    x_num * y_den + x_den * y_num
                         a_    :     Optional[int]										=    x_den * y_den
                         a_    :     Optional[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              a_    :     Optional[int]										=    add_three(
                                  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                              unique_s.add(__UpperCamelCase )

                         # n=2
                         a_    :     List[Any]										=    (
                             x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
                         )
                         a_    :     str										=    x_den * x_den * y_den * y_den
                         if is_sq(__UpperCamelCase ) and is_sq(__UpperCamelCase ):
                              a_    :     Optional[Any]										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Optional[int]										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Optional[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   a_    :     str										=    add_three(
                                       __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                                   unique_s.add(__UpperCamelCase )

                    # n=-1
                         a_    :     Union[str, Any]										=    x_num * y_num
                         a_    :     Tuple										=    x_den * y_num + x_num * y_den
                         a_    :     List[Any]										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                         z_num //= hcf
                         z_den //= hcf
                         if 0 < z_num < z_den <= order:
                              a_    :     Union[str, Any]										=    add_three(
                                  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                              unique_s.add(__UpperCamelCase )

                         # n=2
                         a_    :     Union[str, Any]										=    x_num * x_num * y_num * y_num
                         a_    :     Dict										=    (
                             x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
                         )
                         if is_sq(__UpperCamelCase ) and is_sq(__UpperCamelCase ):
                              a_    :     Dict										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Union[str, Any]										=    int(sqrt(__UpperCamelCase ) )
                              a_    :     Dict										=    gcd(__UpperCamelCase  ,  __UpperCamelCase )
                              z_num //= hcf
                              z_den //= hcf
                              if 0 < z_num < z_den <= order:
                                   a_    :     List[Any]										=    add_three(
                                       __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase  ,  __UpperCamelCase )
                                   unique_s.add(__UpperCamelCase )

     for num, den in unique_s:
          total += Fraction(__UpperCamelCase  ,  __UpperCamelCase )

     return total.denominator + total.numerator


if __name__ == "__main__":
       print(f'''{solution() = }''')



