




from __future__ import annotations

import math
import random
from collections.abc import Collection
from typing import overload




class 		UpperCamelCase__	:

    '''simple docstring'''



    def __init__(    self     ,  UpperCamelCase__ = None     )     ->      Optional[int]:






           if components is None:
                  lowerCamelCase   :      int			 =					[]
           lowerCamelCase   :      List[str]			 =					list(UpperCamelCase__     )







    def __len__(    self     )     ->      Optional[int]:
           return len(self.__components     )







    def __str__(    self     )     ->      Union[str, Any]:
           return "(" + ",".join(map(UpperCamelCase__     ,  self.__components     )     ) + ")"







    def __add__(    self     ,  UpperCamelCase__     )     ->      Optional[Any]:
           lowerCamelCase   :      int			 =					len(self     )
           if size == len(UpperCamelCase__     ):
                  lowerCamelCase   :      Union[str, Any]			 =					[self.__components[i] + other.component(UpperCamelCase__     ) for i in range(UpperCamelCase__     )]
                  return Vector(UpperCamelCase__     )
           else:
                  raise Exception("must have the same size"     )







    def __sub__(    self     ,  UpperCamelCase__     )     ->      Dict:
           lowerCamelCase   :      Optional[int]			 =					len(self     )
           if size == len(UpperCamelCase__     ):
                  lowerCamelCase   :      Dict			 =					[self.__components[i] - other.component(UpperCamelCase__     ) for i in range(UpperCamelCase__     )]
                  return Vector(UpperCamelCase__     )
           else:  # error case
                  raise Exception("must have the same size"     )







    @overload
    def __mul__(    self     ,  UpperCamelCase__     )     ->      List[Any]:
           ...







    @overload
    def __mul__(    self     ,  UpperCamelCase__     )     ->      List[str]:
           ...







    def __mul__(    self     ,  UpperCamelCase__     )     ->      Optional[Any]:






           if isinstance(UpperCamelCase__     ,  (float, int)     ):
                  lowerCamelCase   :      Any			 =					[c * other for c in self.__components]
                  return Vector(UpperCamelCase__     )
           elif isinstance(UpperCamelCase__     ,  UpperCamelCase__     ) and len(self     ) == len(UpperCamelCase__     ):
                  lowerCamelCase   :      Dict			 =					len(self     )
                  lowerCamelCase   :      Union[str, Any]			 =					[self.__components[i] * other.component(UpperCamelCase__     ) for i in range(UpperCamelCase__     )]
                  return sum(UpperCamelCase__     )
           else:  # error case
                  raise Exception("invalid operand!"     )







    def     _lowercase     (    self     )     ->      Optional[int]:
           return Vector(self.__components     )







    def     _lowercase     (    self     ,  UpperCamelCase__     )     ->      str:






           if isinstance(UpperCamelCase__     ,  UpperCamelCase__     ) and -len(self.__components     ) <= i < len(self.__components     ):
                  return self.__components[i]
           else:
                  raise Exception("index out of range"     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      Union[str, Any]:
           assert -len(self.__components     ) <= pos < len(self.__components     )
           lowerCamelCase   :      Optional[Any]			 =					value







    def     _lowercase     (    self     )     ->      Any:






           if len(self.__components     ) == 0:
                  raise Exception("Vector is empty"     )
           lowerCamelCase   :      List[Any]			 =					[c**2 for c in self.__components]
           return math.sqrt(sum(UpperCamelCase__     )     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__ = False     )     ->      List[Any]:
           lowerCamelCase   :      List[Any]			 =					self * other
           lowerCamelCase   :      List[Any]			 =					self.euclidean_length() * other.euclidean_length()
           if deg:
                  return math.degrees(math.acos(num / den     )     )
           else:
                  return math.acos(num / den     )




def      A      (      _SCREAMING_SNAKE_CASE    )	-> Vector:
       assert isinstance(__lowerCAmelCase ,__lowerCAmelCase    )
       return Vector([0] * dimension    )

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Vector:
       assert isinstance(__lowerCAmelCase ,__lowerCAmelCase    ) and (isinstance(__lowerCAmelCase ,__lowerCAmelCase    ))
       lowerCamelCase   :      str			 =					[0] * dimension
       lowerCamelCase   :      Union[str, Any]			 =					1
       return Vector(__lowerCAmelCase    )

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Vector:
       assert (
           isinstance(__lowerCAmelCase ,__lowerCAmelCase    )
           and isinstance(__lowerCAmelCase ,__lowerCAmelCase    )
           and (isinstance(__lowerCAmelCase ,(int, float)    ))
       )
       return x * scalar + y

def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Vector:
       random.seed(__lowerCAmelCase    )
       lowerCamelCase   :      int			 =					[random.randint(__lowerCAmelCase ,__lowerCAmelCase    ) for _ in range(__lowerCAmelCase    )]
       return Vector(__lowerCAmelCase    )




class 		UpperCamelCase__	:

    '''simple docstring'''



    def __init__(    self     ,  UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      List[Any]:
           lowerCamelCase   :      Dict			 =					matrix
           lowerCamelCase   :      int			 =					w
           lowerCamelCase   :      Optional[Any]			 =					h







    def __str__(    self     )     ->      Optional[int]:
           lowerCamelCase   :      List[str]			 =					""
           for i in range(self.__height     ):
                  ans += "|"
                  for j in range(self.__width     ):
                         if j < self.__width - 1:
                                ans += str(self.__matrix[i][j]     ) + ","
                         else:
                                ans += str(self.__matrix[i][j]     ) + "|\n"
           return ans







    def __add__(    self     ,  UpperCamelCase__     )     ->      Optional[Any]:






           if self.__width == other.width() and self.__height == other.height():
                  lowerCamelCase   :      Union[str, Any]			 =					[]
                  for i in range(self.__height     ):
                         lowerCamelCase   :      List[str]			 =					[
                             self.__matrix[i][j] + other.component(UpperCamelCase__     ,  UpperCamelCase__     )
                             for j in range(self.__width     )
                         ]
                         matrix.append(UpperCamelCase__     )
                  return Matrix(UpperCamelCase__     ,  self.__width     ,  self.__height     )
           else:
                  raise Exception("matrix must have the same dimension!"     )







    def __sub__(    self     ,  UpperCamelCase__     )     ->      List[str]:






           if self.__width == other.width() and self.__height == other.height():
                  lowerCamelCase   :      Optional[int]			 =					[]
                  for i in range(self.__height     ):
                         lowerCamelCase   :      List[str]			 =					[
                             self.__matrix[i][j] - other.component(UpperCamelCase__     ,  UpperCamelCase__     )
                             for j in range(self.__width     )
                         ]
                         matrix.append(UpperCamelCase__     )
                  return Matrix(UpperCamelCase__     ,  self.__width     ,  self.__height     )
           else:
                  raise Exception("matrices must have the same dimension!"     )







    @overload
    def __mul__(    self     ,  UpperCamelCase__     )     ->      Dict:
           ...







    @overload
    def __mul__(    self     ,  UpperCamelCase__     )     ->      Optional[Any]:
           ...







    def __mul__(    self     ,  UpperCamelCase__     )     ->      Any:






           if isinstance(UpperCamelCase__     ,  UpperCamelCase__     ):  # matrix-vector
                  if len(UpperCamelCase__     ) == self.__width:
                         lowerCamelCase   :      int			 =					zero_vector(self.__height     )
                         for i in range(self.__height     ):
                                lowerCamelCase   :      List[Any]			 =					[
                                    self.__matrix[i][j] * other.component(UpperCamelCase__     )
                                    for j in range(self.__width     )
                                ]
                                ans.change_component(UpperCamelCase__     ,  sum(UpperCamelCase__     )     )
                         return ans
                  else:
                         raise Exception(
                             "vector must have the same size as the "
                             "number of columns of the matrix!"     )
           elif isinstance(UpperCamelCase__     ,  (int, float)     ):  # matrix-scalar
                  lowerCamelCase   :      Any			 =					[
                      [self.__matrix[i][j] * other for j in range(self.__width     )]
                      for i in range(self.__height     )
                  ]
                  return Matrix(UpperCamelCase__     ,  self.__width     ,  self.__height     )
           return None







    def     _lowercase     (    self     )     ->      Union[str, Any]:
           return self.__height







    def     _lowercase     (    self     )     ->      int:
           return self.__width







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      str:






           if 0 <= x < self.__height and 0 <= y < self.__width:
                  return self.__matrix[x][y]
           else:
                  raise Exception("change_component: indices out of bounds"     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      List[str]:






           if 0 <= x < self.__height and 0 <= y < self.__width:
                  lowerCamelCase   :      Tuple			 =					value
           else:
                  raise Exception("change_component: indices out of bounds"     )







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      Tuple:






           if self.__height != self.__width:
                  raise Exception("Matrix is not square"     )
           lowerCamelCase   :      Dict			 =					self.__matrix[:x] + self.__matrix[x + 1 :]
           for i in range(len(UpperCamelCase__     )     ):
                  lowerCamelCase   :      Optional[Any]			 =					minor[i][:y] + minor[i][y + 1 :]
           return Matrix(UpperCamelCase__     ,  self.__width - 1     ,  self.__height - 1     ).determinant()







    def     _lowercase     (    self     ,  UpperCamelCase__     ,  UpperCamelCase__     )     ->      Dict:






           if self.__height != self.__width:
                  raise Exception("Matrix is not square"     )
           if 0 <= x < self.__height and 0 <= y < self.__width:
                  return (-1) ** (x + y) * self.minor(UpperCamelCase__     ,  UpperCamelCase__     )
           else:
                  raise Exception("Indices out of bounds"     )







    def     _lowercase     (    self     )     ->      List[str]:






           if self.__height != self.__width:
                  raise Exception("Matrix is not square"     )
           if self.__height < 1:
                  raise Exception("Matrix has no element"     )
           elif self.__height == 1:
                  return self.__matrix[0][0]
           elif self.__height == 2:
                  return (
                      self.__matrix[0][0] * self.__matrix[1][1]
                      - self.__matrix[0][1] * self.__matrix[1][0]
                  )
           else:
                  lowerCamelCase   :      Tuple			 =					[
                      self.__matrix[0][y] * self.cofactor(0     ,  UpperCamelCase__     ) for y in range(self.__width     )
                  ]
                  return sum(UpperCamelCase__     )




def      A      (      _SCREAMING_SNAKE_CASE    )	-> Matrix:
       lowerCamelCase   :      list[list[float]]			 =					[[0] * n for _ in range(__lowerCAmelCase    )]
       return Matrix(__lowerCAmelCase ,__lowerCAmelCase ,__lowerCAmelCase    )


def      A      (      _SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE ,_SCREAMING_SNAKE_CASE    )	-> Matrix:
       random.seed(__lowerCAmelCase    )
       lowerCamelCase   :      list[list[float]]			 =					[
           [random.randint(__lowerCAmelCase ,__lowerCAmelCase    ) for _ in range(__lowerCAmelCase    )] for _ in range(__lowerCAmelCase    )
       ]
       return Matrix(__lowerCAmelCase ,__lowerCAmelCase ,__lowerCAmelCase    )














from google.protobuf import descriptor as _descriptor
from google.protobuf import descriptor_pool as _descriptor_pool
from google.protobuf import symbol_database as _symbol_database
from google.protobuf.internal import builder as _builder


# @@protoc_insertion_point(imports)

lowerCamelCase	:							Tuple				=_symbol_database.Default()


lowerCamelCase	:							List[str]				=_descriptor_pool.Default().AddSerializedFile(
    b'''\n\x19sentencepiece_model.proto\x12\rsentencepiece"\x80\x0c\n\x0bTrainerSpec\x12\r\n\x05input\x18\x01 \x03(\t\x12\x14\n\x0cinput_format\x18\x07 \x01(\t\x12\x14\n\x0cmodel_prefix\x18\x02 \x01(\t\x12\x41\n\nmodel_type\x18\x03 \x01(\x0e\x32$.sentencepiece.TrainerSpec.ModelType:\x07UNIGRAM\x12\x18\n\nvocab_size\x18\x04 \x01(\x05:\x04\x38\x30\x30\x30\x12\x17\n\x0f\x61\x63\x63\x65pt_language\x18\x05 \x03(\t\x12 \n\x15self_test_sample_size\x18\x06 \x01(\x05:\x01\x30\x12*\n\x1b\x65nable_differential_privacy\x18\x32 \x01(\x08:\x05\x66\x61lse\x12+\n differential_privacy_noise_level\x18\x33 \x01(\x02:\x01\x30\x12\x32\n\'differential_privacy_clipping_threshold\x18\x34 \x01(\x04:\x01\x30\x12"\n\x12\x63haracter_coverage\x18\n \x01(\x02:\x06\x30.9995\x12\x1e\n\x13input_sentence_size\x18\x0b \x01(\x04:\x01\x30\x12$\n\x16shuffle_input_sentence\x18\x13 \x01(\x08:\x04true\x12 \n\x14mining_sentence_size\x18\x0c \x01(\x05\x42\x02\x18\x01\x12"\n\x16training_sentence_size\x18\r \x01(\x05\x42\x02\x18\x01\x12(\n\x17seed_sentencepiece_size\x18\x0e \x01(\x05:\x07\x31\x30\x30\x30\x30\x30\x30\x12\x1e\n\x10shrinking_factor\x18\x0f \x01(\x02:\x04\x30.75\x12!\n\x13max_sentence_length\x18\x12 \x01(\x05:\x04\x34\x31\x39\x32\x12\x17\n\x0bnum_threads\x18\x10 \x01(\x05:\x02\x31\x36\x12\x1d\n\x12num_sub_iterations\x18\x11 \x01(\x05:\x01\x32\x12$\n\x18max_sentencepiece_length\x18\x14 \x01(\x05:\x02\x31\x36\x12%\n\x17split_by_unicode_script\x18\x15 \x01(\x08:\x04true\x12\x1d\n\x0fsplit_by_number\x18\x17 \x01(\x08:\x04true\x12!\n\x13split_by_whitespace\x18\x16 \x01(\x08:\x04true\x12)\n\x1atreat_whitespace_as_suffix\x18\x18 \x01(\x08:\x05\x66\x61lse\x12+\n\x1c\x61llow_whitespace_only_pieces\x18\x1a \x01(\x08:\x05\x66\x61lse\x12\x1b\n\x0csplit_digits\x18\x19 \x01(\x08:\x05\x66\x61lse\x12#\n\x19pretokenization_delimiter\x18\x35 \x01(\t:\x00\x12\x17\n\x0f\x63ontrol_symbols\x18\x1e \x03(\t\x12\x1c\n\x14user_defined_symbols\x18\x1f \x03(\t\x12\x16\n\x0erequired_chars\x18$ \x01(\t\x12\x1c\n\rbyte_fallback\x18# \x01(\x08:\x05\x66\x61lse\x12+\n\x1dvocabulary_output_piece_score\x18  \x01(\x08:\x04true\x12\x1e\n\x10hard_vocab_limit\x18! \x01(\x08:\x04true\x12\x1c\n\ruse_all_vocab\x18" \x01(\x08:\x05\x66\x61lse\x12\x11\n\x06unk_id\x18( \x01(\x05:\x01\x30\x12\x11\n\x06\x62os_id\x18) \x01(\x05:\x01\x31\x12\x11\n\x06\x65os_id\x18* \x01(\x05:\x01\x32\x12\x12\n\x06pad_id\x18+ \x01(\x05:\x02-1\x12\x18\n\tunk_piece\x18- \x01(\t:\x05<unk>\x12\x16\n\tbos_piece\x18. \x01(\t:\x03<s>\x12\x17\n\teos_piece\x18/ \x01(\t:\x04</s>\x12\x18\n\tpad_piece\x18\x30 \x01(\t:\x05<pad>\x12\x1a\n\x0bunk_surface\x18, \x01(\t:\x05 \xe2\x81\x87 \x12+\n\x1ctrain_extremely_large_corpus\x18\x31 \x01(\x08:\x05\x66\x61lse"5\n\tModelType\x12\x0b\n\x07UNIGRAM\x10\x01\x12\x07\n\x03\x42PE\x10\x02\x12\x08\n\x04WORD\x10\x03\x12\x08\n\x04\x43HAR\x10\x04*\t\x08\xc8\x01\x10\x80\x80\x80\x80\x02"\xd1\x01\n\x0eNormalizerSpec\x12\x0c\n\x04name\x18\x01 \x01(\t\x12\x1c\n\x14precompiled_charsmap\x18\x02 \x01(\x0c\x12\x1e\n\x10\x61\x64\x64_dummy_prefix\x18\x03 \x01(\x08:\x04true\x12&\n\x18remove_extra_whitespaces\x18\x04 \x01(\x08:\x04true\x12 \n\x12\x65scape_whitespaces\x18\x05 \x01(\x08:\x04true\x12\x1e\n\x16normalization_rule_tsv\x18\x06 \x01(\t*\t\x08\xc8\x01\x10\x80\x80\x80\x80\x02"y\n\x0cSelfTestData\x12\x33\n\x07samples\x18\x01 \x03(\x0b\x32".sentencepiece.SelfTestData.Sample\x1a)\n\x06Sample\x12\r\n\x05input\x18\x01 \x01(\t\x12\x10\n\x08\x65xpected\x18\x02 \x01(\t*\t\x08\xc8\x01\x10\x80\x80\x80\x80\x02"\xfe\x03\n\nModelProto\x12\x37\n\x06pieces\x18\x01 \x03(\x0b\x32\'.sentencepiece.ModelProto.SentencePiece\x12\x30\n\x0ctrainer_spec\x18\x02 \x01(\x0b\x32\x1a.sentencepiece.TrainerSpec\x12\x36\n\x0fnormalizer_spec\x18\x03 \x01(\x0b\x32\x1d.sentencepiece.NormalizerSpec\x12\x33\n\x0eself_test_data\x18\x04 \x01(\x0b\x32\x1b.sentencepiece.SelfTestData\x12\x38\n\x11\x64\x65normalizer_spec\x18\x05 \x01(\x0b\x32\x1d.sentencepiece.NormalizerSpec\x1a\xd2\x01\n\rSentencePiece\x12\r\n\x05piece\x18\x01 \x01(\t\x12\r\n\x05score\x18\x02 \x01(\x02\x12\x42\n\x04type\x18\x03 \x01(\x0e\x32,.sentencepiece.ModelProto.SentencePiece.Type:\x06NORMAL"T\n\x04Type\x12\n\n\x06NORMAL\x10\x01\x12\x0b\n\x07UNKNOWN\x10\x02\x12\x0b\n\x07\x43ONTROL\x10\x03\x12\x10\n\x0cUSER_DEFINED\x10\x04\x12\x08\n\x04\x42YTE\x10\x06\x12\n\n\x06UNUSED\x10\x05*\t\x08\xc8\x01\x10\x80\x80\x80\x80\x02*\t\x08\xc8\x01\x10\x80\x80\x80\x80\x02\x42\x02H\x03'''
)

lowerCamelCase	:							str				=globals()
_builder.BuildMessageAndEnumDescriptors(DESCRIPTOR, _globals)
_builder.BuildTopDescriptorsAndMessages(DESCRIPTOR, '''sentencepiece_model_pb2''', _globals)
if _descriptor._USE_C_DESCRIPTORS is False:
 lowerCamelCase	:							Optional[int]				=None
 lowerCamelCase	:							Tuple				=b'''H\003'''
 # (generated by protobuf compiler, but `_TRAINERSPEC` is not defined)
 # _TRAINERSPEC.fields_by_name["mining_sentence_size"]._options = None
 # _TRAINERSPEC.fields_by_name["mining_sentence_size"]._serialized_options = b"\030\001"
 # _TRAINERSPEC.fields_by_name["training_sentence_size"]._options = None
 # _TRAINERSPEC.fields_by_name["training_sentence_size"]._serialized_options = b"\030\001"
 lowerCamelCase	:							List[str]				=45
 lowerCamelCase	:							List[Any]				=1581
 lowerCamelCase	:							Optional[int]				=1517
 lowerCamelCase	:							Tuple				=1570
 lowerCamelCase	:							Dict				=1584
 lowerCamelCase	:							Optional[Any]				=1793
 lowerCamelCase	:							Dict				=1795
 lowerCamelCase	:							Any				=1916
 lowerCamelCase	:							Dict				=1864
 lowerCamelCase	:							Dict				=1905
 lowerCamelCase	:							Dict				=1919
 lowerCamelCase	:							Union[str, Any]				=2429
 lowerCamelCase	:							List[Any]				=2208
 lowerCamelCase	:							List[Any]				=2418
 lowerCamelCase	:							List[str]				=2323
 lowerCamelCase	:							Dict				=2407
# @@protoc_insertion_point(module_scope)