



"""simple docstring"""






from __future__ import annotations

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

class 	__SCREAMING_SNAKE_CASE     :


					'''simple docstring'''





					def __init__(	self							:  Any,  lowerCamelCase							:  Collection[float] | None = None					)-> None:
								if components is None:
											lowerCamelCase__		:		Optional[Any]		     =[]
								lowerCamelCase__		:		Optional[int]		     =list(lowerCamelCase					)



					def __len__(	self							:  Union[str, Any]					)-> int:
								return len(self.__components					)



					def __str__(	self							:  Dict					)-> str:
								return "(" + ",".join(map(lowerCamelCase,  self.__components					)					) + ")"



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



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



					@overload
					def __mul__(	self							:  Dict,  lowerCamelCase							:  float					)-> Vector:
								...



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



					def __mul__(	self							:  Tuple,  lowerCamelCase							:  float | Vector					)-> float | Vector:
								if isinstance(lowerCamelCase,  (float, int)					):
											lowerCamelCase__		:		Optional[Any]		     =[c * other for c in self.__components]
											return Vector(lowerCamelCase					)
								elif isinstance(lowerCamelCase,  lowerCamelCase					) and len(self					) == len(lowerCamelCase					):
											lowerCamelCase__		:		str		     =len(self					)
											lowerCamelCase__		:		Optional[Any]		     =[self.__components[i] * other.component(lowerCamelCase					) for i in range(lowerCamelCase					)]
											return sum(lowerCamelCase					)
								else:  # error case
											raise Exception('''invalid operand!'''					)



					def 		snake_case	(	self							:  Dict					)-> Vector:
								return Vector(self.__components					)



					def 		snake_case	(	self							:  Optional[int],  lowerCamelCase							:  int					)-> float:
								if isinstance(lowerCamelCase,  lowerCamelCase					) and -len(self.__components					) <= i < len(self.__components					):
											return self.__components[i]
								else:
											raise Exception('''index out of range'''					)



					def 		snake_case	(	self							:  Optional[Any],  lowerCamelCase							:  int,  lowerCamelCase							:  float					)-> None:
								assert -len(self.__components					) <= pos < len(self.__components					)
								lowerCamelCase__		:		Union[str, Any]		     =value



					def 		snake_case	(	self							:  Any					)-> float:
								if len(self.__components					) == 0:
											raise Exception('''Vector is empty'''					)
								lowerCamelCase__		:		Union[str, Any]		     =[c**2 for c in self.__components]
								return math.sqrt(sum(lowerCamelCase					)					)




					def 		snake_case	(	self							:  Dict,  lowerCamelCase							:  Vector,  lowerCamelCase							:  bool = False					)-> float:
								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 					snake_case__       (		__lowerCamelCase    :   int     ) ->    List[Any]:
			"""simple docstring"""
			assert isinstance(__lowerCamelCase							,		__lowerCamelCase     )
			return Vector([0] * dimension     )






def 					snake_case__       (		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int     ) ->    Dict:
			"""simple docstring"""
			assert isinstance(__lowerCamelCase							,		__lowerCamelCase     ) and (isinstance(__lowerCamelCase							,		__lowerCamelCase     ))
			lowerCamelCase__		:		Optional[Any]		     =[0] * dimension
			lowerCamelCase__		:		Optional[Any]		     =1
			return Vector(__lowerCamelCase     )






def 					snake_case__       (		__lowerCamelCase    :   float							,		__lowerCamelCase    :   Vector							,		__lowerCamelCase    :   Vector     ) ->    Optional[Any]:
			"""simple docstring"""
			assert (
			    isinstance(__lowerCamelCase							,		__lowerCamelCase     )
			    and isinstance(__lowerCamelCase							,		__lowerCamelCase     )
			    and (isinstance(__lowerCamelCase							,		(int, float)     ))
			)
			return x * scalar + y






def 					snake_case__       (		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int     ) ->    List[str]:
			"""simple docstring"""
			random.seed(__lowerCamelCase     )
			lowerCamelCase__		:		Union[str, Any]		     =[random.randint(__lowerCamelCase							,		__lowerCamelCase     ) for _ in range(__lowerCamelCase     )]
			return Vector(__lowerCamelCase     )

class 	__SCREAMING_SNAKE_CASE     :


					'''simple docstring'''





					def __init__(	self							:  str,  lowerCamelCase							:  list[list[float]],  lowerCamelCase							:  int,  lowerCamelCase							:  int					)-> None:
								lowerCamelCase__		:		Any		     =matrix
								lowerCamelCase__		:		List[str]		     =w
								lowerCamelCase__		:		Dict		     =h



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



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



					@overload
					def __mul__(	self							:  Dict,  lowerCamelCase							:  float					)-> Matrix:
								...



					@overload
					def __mul__(	self							:  Any,  lowerCamelCase							:  Vector					)-> Vector:
								...



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



					def 		snake_case	(	self							:  Tuple					)-> int:
								return self.__height



					def 		snake_case	(	self							:  List[Any]					)-> int:
								return self.__width



					def 		snake_case	(	self							:  Optional[int],  lowerCamelCase							:  int,  lowerCamelCase							:  int					)-> float:
								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 		snake_case	(	self							:  List[str],  lowerCamelCase							:  int,  lowerCamelCase							:  int,  lowerCamelCase							:  float					)-> None:
								if 0 <= x < self.__height and 0 <= y < self.__width:
											lowerCamelCase__		:		str		     =value
								else:
											raise Exception('''change_component: indices out of bounds'''					)



					def 		snake_case	(	self							:  Optional[int],  lowerCamelCase							:  int,  lowerCamelCase							:  int					)-> float:
								if self.__height != self.__width:
											raise Exception('''Matrix is not square'''					)
								lowerCamelCase__		:		Optional[Any]		     =self.__matrix[:x] + self.__matrix[x + 1 :]
								for i in range(len(lowerCamelCase					)					):
											lowerCamelCase__		:		str		     =minor[i][:y] + minor[i][y + 1 :]
								return Matrix(lowerCamelCase,  self.__width - 1,  self.__height - 1					).determinant()



					def 		snake_case	(	self							:  int,  lowerCamelCase							:  int,  lowerCamelCase							:  int					)-> float:
								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(lowerCamelCase,  lowerCamelCase					)
								else:
											raise Exception('''Indices out of bounds'''					)




					def 		snake_case	(	self							:  str					)-> float:
								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__		:		Dict		     =[
											    self.__matrix[0][y] * self.cofactor(0,  lowerCamelCase					) for y in range(self.__width					)
											]
											return sum(lowerCamelCase					)






def 					snake_case__       (		__lowerCamelCase    :   int     ) ->    int:
			"""simple docstring"""
			lowerCamelCase__		:		list[list[float]]		     =[[0] * n for _ in range(__lowerCamelCase     )]
			return Matrix(__lowerCamelCase							,		__lowerCamelCase							,		__lowerCamelCase     )






def 					snake_case__       (		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int							,		__lowerCamelCase    :   int     ) ->    Optional[Any]:
			"""simple docstring"""
			random.seed(__lowerCamelCase     )
			lowerCamelCase__		:		list[list[float]]		     =[
			    [random.randint(__lowerCamelCase							,		__lowerCamelCase     ) for _ in range(__lowerCamelCase     )] for _ in range(__lowerCamelCase     )
			]
			return Matrix(__lowerCamelCase							,		__lowerCamelCase							,		__lowerCamelCase     )









"""simple docstring"""






import os
from collections import deque

import torch
from torch.utils.data import Dataset

class 	__SCREAMING_SNAKE_CASE     (				lowerCAmelCase_       ):


					'''simple docstring'''





					def __init__(	self							:  List[Any],  lowerCamelCase							:  Dict="",  lowerCamelCase							:  Tuple="train"					)-> Dict:
								assert os.path.isdir(lowerCamelCase					)

								lowerCamelCase__		:		Optional[Any]		     =[]
								lowerCamelCase__		:		Dict		     =os.listdir(lowerCamelCase					)
								for story_filename in story_filenames_list:
											if "summary" in story_filename:
														continue
											lowerCamelCase__		:		Optional[int]		     =os.path.join(lowerCamelCase,  lowerCamelCase					)
											if not os.path.isfile(lowerCamelCase					):
														continue
											self.documents.append(lowerCamelCase					)



					def __len__(	self							:  Optional[Any]					)-> List[str]:
								return len(self.documents					)




					def __getitem__(	self							:  List[str],  lowerCamelCase							:  Dict					)-> str:
								lowerCamelCase__		:		int		     =self.documents[idx]
								lowerCamelCase__		:		List[Any]		     =document_path.split('''/'''					)[-1]
								with open(lowerCamelCase,  encoding='''utf-8'''					) as source:
											lowerCamelCase__		:		Optional[int]		     =source.read()
											lowerCamelCase__     ,       lowerCamelCase__		:		List[Any]		     =process_story(lowerCamelCase					)
								return document_name, story_lines, summary_lines






def 					snake_case__       (		__lowerCamelCase    :   int     ):
			"""simple docstring"""
			lowerCamelCase__		:		List[str]		     =list(filter(lambda __lowerCamelCase     : len(__lowerCamelCase     ) != 0							,		[line.strip() for line in raw_story.split('''\n'''     )]     )     )

			# for some unknown reason some lines miss a period, add it
			lowerCamelCase__		:		Dict		     =[_add_missing_period(__lowerCamelCase     ) for line in nonempty_lines]

			# gather article lines
			lowerCamelCase__		:		Union[str, Any]		     =[]
			lowerCamelCase__		:		Optional[Any]		     =deque(__lowerCamelCase     )
			while True:
						try:
									lowerCamelCase__		:		Tuple		     =lines.popleft()
									if element.startswith('''@highlight'''     ):
												break
									story_lines.append(__lowerCamelCase     )
						except IndexError:
									# if "@highlight" is absent from the file we pop
									# all elements until there is None, raising an exception.
									return story_lines, []

    # gather summary lines
			lowerCamelCase__		:		Dict		     =list(filter(lambda __lowerCamelCase     : not t.startswith('''@highlight'''     )							,		__lowerCamelCase     )     )

			return story_lines, summary_lines






def 					snake_case__       (		__lowerCamelCase    :   str     ):
			"""simple docstring"""
			lowerCamelCase__		:		Any		     =['''.''', '''!''', '''?''', '''...''', '''\'''', '''`''', '''"''', '''\u2019''', '''\u2019''', ''')''']
			if line.startswith('''@highlight'''     ):
						return line
			if line[-1] in END_TOKENS:
						return line
			return line + "."






def 					snake_case__       (		__lowerCamelCase    :   Dict							,		__lowerCamelCase    :   Union[str, Any]							,		__lowerCamelCase    :   List[Any]     ):
			"""simple docstring"""
			if len(__lowerCamelCase     ) > block_size:
						return sequence[:block_size]
			else:
						sequence.extend([pad_token_id] * (block_size - len(__lowerCamelCase     ))     )
						return sequence






def 					snake_case__       (		__lowerCamelCase    :   Tuple							,		__lowerCamelCase    :   str     ):
			"""simple docstring"""
			lowerCamelCase__		:		int		     =torch.ones_like(__lowerCamelCase     )
			lowerCamelCase__		:		Any		     =sequence == pad_token_id
			lowerCamelCase__		:		List[str]		     =0
			return mask






def 					snake_case__       (		__lowerCamelCase    :   str							,		__lowerCamelCase    :   Optional[Any]							,		__lowerCamelCase    :   Optional[Any]     ):
			"""simple docstring"""
			lowerCamelCase__		:		Dict		     =[tokenizer.encode(__lowerCamelCase     ) for line in story_lines]
			lowerCamelCase__		:		List[Any]		     =[token for sentence in story_lines_token_ids for token in sentence]
			lowerCamelCase__		:		List[Any]		     =[tokenizer.encode(__lowerCamelCase     ) for line in summary_lines]
			lowerCamelCase__		:		Optional[int]		     =[token for sentence in summary_lines_token_ids for token in sentence]

			return story_token_ids, summary_token_ids






def 					snake_case__       (		__lowerCamelCase    :   Tuple							,		__lowerCamelCase    :   Optional[int]     ):
			"""simple docstring"""
			lowerCamelCase__		:		Any		     =[]
			for sequence in batch:
						lowerCamelCase__		:		Optional[int]		     =-1
						lowerCamelCase__		:		List[str]		     =[]
						for s in sequence:
									if s == separator_token_id:
												sentence_num += 1
									embeddings.append(sentence_num % 2     )
						batch_embeddings.append(__lowerCamelCase     )
			return torch.tensor(__lowerCamelCase     )




