



from __future__ import annotations

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


class 	__snake_case   :
		def __init__(							self    ,a_ = None						):







						"""simple docstring"""
						if components is None:
										lowerCAmelCase__		  =  []
						lowerCAmelCase__		  =  list(a_						)
		def __len__(							self						):







						"""simple docstring"""
						return len(self.__components						)
		def __str__(							self						):







						"""simple docstring"""
						return "(" + ",".join(map(a_    ,self.__components						)						) + ")"
		def __add__(							self    ,a_						):







						"""simple docstring"""
						lowerCAmelCase__		  =  len(self						)
						if size == len(a_						):
										lowerCAmelCase__		  =  [self.__components[i] + other.component(a_						) for i in range(a_						)]
										return Vector(a_						)
						else:
										raise Exception('must have the same size'						)
		def __sub__(							self    ,a_						):







						"""simple docstring"""
						lowerCAmelCase__		  =  len(self						)
						if size == len(a_						):
										lowerCAmelCase__		  =  [self.__components[i] - other.component(a_						) for i in range(a_						)]
										return Vector(a_						)
						else:  # error case
										raise Exception('must have the same size'						)
		@overload
		def __mul__(							self    ,a_						):







						"""simple docstring"""
						...
		@overload
		def __mul__(							self    ,a_						):







						"""simple docstring"""
						...
		def __mul__(							self    ,a_						):







						"""simple docstring"""
						if isinstance(a_    ,(float, int)						):
										lowerCAmelCase__		  =  [c * other for c in self.__components]
										return Vector(a_						)
						elif isinstance(a_    ,a_						) and len(self						) == len(a_						):
										lowerCAmelCase__		  =  len(self						)
										lowerCAmelCase__		  =  [self.__components[i] * other.component(a_						) for i in range(a_						)]
										return sum(a_						)
						else:  # error case
										raise Exception('invalid operand!'						)
		def 						SCREAMING_SNAKE_CASE_					(							self						):







						"""simple docstring"""
						return Vector(self.__components						)
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_						):







						"""simple docstring"""
						if isinstance(a_    ,a_						) and -len(self.__components						) <= i < len(self.__components						):
										return self.__components[i]
						else:
										raise Exception('index out of range'						)
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_						):







						"""simple docstring"""
						assert -len(self.__components						) <= pos < len(self.__components						)
						lowerCAmelCase__		  =  value
		def 						SCREAMING_SNAKE_CASE_					(							self						):







						"""simple docstring"""
						if len(self.__components						) == 0:
										raise Exception('Vector is empty'						)
						lowerCAmelCase__		  =  [c**2 for c in self.__components]
						return math.sqrt(sum(a_						)						)



		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_ = False						):







						"""simple docstring"""
						lowerCAmelCase__		  =  self * other
						lowerCAmelCase__		  =  self.euclidean_length() * other.euclidean_length()
						if deg:
										return math.degrees(math.acos(num / den						)						)
						else:
										return math.acos(num / den						)







def     UpperCAmelCase_		(					snake_case__					)	->     Vector:



				"""simple docstring"""





				assert isinstance(snake_case__    ,			snake_case__					)
				return Vector([0] * dimension					)







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__					)	->     Vector:



				"""simple docstring"""





				assert isinstance(snake_case__    ,			snake_case__					) and (isinstance(snake_case__    ,			snake_case__					))
				lowerCAmelCase__		  =  [0] * dimension
				lowerCAmelCase__		  =  1
				return Vector(snake_case__					)







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     Vector:



				"""simple docstring"""





				assert (
				    isinstance(snake_case__    ,			snake_case__					)
				    and isinstance(snake_case__    ,			snake_case__					)
				    and (isinstance(snake_case__    ,			(int, float)					))
				)
				return x * scalar + y







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     Vector:



				"""simple docstring"""





				random.seed(snake_case__					)
				lowerCAmelCase__		  =  [random.randint(snake_case__    ,			snake_case__					) for _ in range(snake_case__					)]
				return Vector(snake_case__					)


class 	__snake_case   :
		def __init__(							self    ,a_    ,a_    ,a_						):







						"""simple docstring"""
						lowerCAmelCase__		  =  matrix
						lowerCAmelCase__		  =  w
						lowerCAmelCase__		  =  h
		def __str__(							self						):







						"""simple docstring"""
						lowerCAmelCase__		  =  ''
						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    ,a_						):







						"""simple docstring"""
						if self.__width == other.width() and self.__height == other.height():
										lowerCAmelCase__		  =  []
										for i in range(self.__height						):
														lowerCAmelCase__		  =  [
														    self.__matrix[i][j] + other.component(a_    ,a_						)
														    for j in range(self.__width						)
														]
														matrix.append(a_						)
										return Matrix(a_    ,self.__width    ,self.__height						)
						else:
										raise Exception('matrix must have the same dimension!'						)
		def __sub__(							self    ,a_						):







						"""simple docstring"""
						if self.__width == other.width() and self.__height == other.height():
										lowerCAmelCase__		  =  []
										for i in range(self.__height						):
														lowerCAmelCase__		  =  [
														    self.__matrix[i][j] - other.component(a_    ,a_						)
														    for j in range(self.__width						)
														]
														matrix.append(a_						)
										return Matrix(a_    ,self.__width    ,self.__height						)
						else:
										raise Exception('matrices must have the same dimension!'						)
		@overload
		def __mul__(							self    ,a_						):







						"""simple docstring"""
						...
		@overload
		def __mul__(							self    ,a_						):







						"""simple docstring"""
						...
		def __mul__(							self    ,a_						):







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







						"""simple docstring"""
						return self.__height
		def 						SCREAMING_SNAKE_CASE_					(							self						):







						"""simple docstring"""
						return self.__width
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_						):







						"""simple docstring"""
						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 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_    ,a_						):







						"""simple docstring"""
						if 0 <= x < self.__height and 0 <= y < self.__width:
										lowerCAmelCase__		  =  value
						else:
										raise Exception('change_component: indices out of bounds'						)
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_						):







						"""simple docstring"""
						if self.__height != self.__width:
										raise Exception('Matrix is not square'						)
						lowerCAmelCase__		  =  self.__matrix[:x] + self.__matrix[x + 1 :]
						for i in range(len(a_						)						):
										lowerCAmelCase__		  =  minor[i][:y] + minor[i][y + 1 :]
						return Matrix(a_    ,self.__width - 1    ,self.__height - 1						).determinant()
		def 						SCREAMING_SNAKE_CASE_					(							self    ,a_    ,a_						):







						"""simple docstring"""
						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(a_    ,a_						)
						else:
										raise Exception('Indices out of bounds'						)



		def 						SCREAMING_SNAKE_CASE_					(							self						):







						"""simple docstring"""
						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__		  =  [
										    self.__matrix[0][y] * self.cofactor(0    ,a_						) for y in range(self.__width						)
										]
										return sum(a_						)







def     UpperCAmelCase_		(					snake_case__					)	->     Matrix:



				"""simple docstring"""





				lowerCAmelCase__		  =  [[0] * n for _ in range(snake_case__					)]
				return Matrix(snake_case__    ,			snake_case__    ,			snake_case__					)







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__    ,			snake_case__					)	->     Matrix:



				"""simple docstring"""





				random.seed(snake_case__					)
				lowerCAmelCase__		  =  [
				    [random.randint(snake_case__    ,			snake_case__					) for _ in range(snake_case__					)] for _ in range(snake_case__					)
				]
				return Matrix(snake_case__    ,			snake_case__    ,			snake_case__					)





import os
from collections import deque

import torch
from torch.utils.data import Dataset


class 	__snake_case   ( SCREAMING_SNAKE_CASE ):
		def __init__(							self    ,a_=""    ,a_="train"						):







						"""simple docstring"""
						assert os.path.isdir(a_						)

						lowerCAmelCase__		  =  []
						lowerCAmelCase__		  =  os.listdir(a_						)
						for story_filename in story_filenames_list:
										if "summary" in story_filename:
														continue
										lowerCAmelCase__		  =  os.path.join(a_    ,a_						)
										if not os.path.isfile(a_						):
														continue
										self.documents.append(a_						)
		def __len__(							self						):







						"""simple docstring"""
						return len(self.documents						)



		def __getitem__(							self    ,a_						):







						"""simple docstring"""
						lowerCAmelCase__		  =  self.documents[idx]
						lowerCAmelCase__		  =  document_path.split('/'						)[-1]
						with open(a_    ,encoding='utf-8'						) as source:
										lowerCAmelCase__		  =  source.read()
										lowerCAmelCase__  ,   lowerCAmelCase__		  =  process_story(a_						)
						return document_name, story_lines, summary_lines







def     UpperCAmelCase_		(					snake_case__					)	->     str:



				"""simple docstring"""





				lowerCAmelCase__		  =  list(filter(lambda snake_case__					: len(snake_case__					) != 0    ,			[line.strip() for line in raw_story.split('\n'					)]					)					)

				# for some unknown reason some lines miss a period, add it
				lowerCAmelCase__		  =  [_add_missing_period(snake_case__					) for line in nonempty_lines]

				# gather article lines
				lowerCAmelCase__		  =  []
				lowerCAmelCase__		  =  deque(snake_case__					)
				while True:
								try:
												lowerCAmelCase__		  =  lines.popleft()
												if element.startswith('@highlight'					):
																break
												story_lines.append(snake_case__					)
								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__		  =  list(filter(lambda snake_case__					: not t.startswith('@highlight'					)    ,			snake_case__					)					)

				return story_lines, summary_lines







def     UpperCAmelCase_		(					snake_case__					)	->     Optional[Any]:



				"""simple docstring"""





				lowerCAmelCase__		  =  ['.', '!', '?', '...', '\'', '`', '"', '\u2019', '\u2019', ')']
				if line.startswith('@highlight'					):
								return line
				if line[-1] in END_TOKENS:
								return line
				return line + "."







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     str:



				"""simple docstring"""





				if len(snake_case__					) > block_size:
								return sequence[:block_size]
				else:
								sequence.extend([pad_token_id] * (block_size - len(snake_case__					))					)
								return sequence







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__					)	->     Optional[int]:



				"""simple docstring"""





				lowerCAmelCase__		  =  torch.ones_like(snake_case__					)
				lowerCAmelCase__		  =  sequence == pad_token_id
				lowerCAmelCase__		  =  0
				return mask







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__    ,			snake_case__					)	->     Dict:



				"""simple docstring"""





				lowerCAmelCase__		  =  [tokenizer.encode(snake_case__					) for line in story_lines]
				lowerCAmelCase__		  =  [token for sentence in story_lines_token_ids for token in sentence]
				lowerCAmelCase__		  =  [tokenizer.encode(snake_case__					) for line in summary_lines]
				lowerCAmelCase__		  =  [token for sentence in summary_lines_token_ids for token in sentence]

				return story_token_ids, summary_token_ids







def     UpperCAmelCase_		(					snake_case__    ,			snake_case__					)	->     Union[str, Any]:



				"""simple docstring"""





				lowerCAmelCase__		  =  []
				for sequence in batch:
								lowerCAmelCase__		  =  -1
								lowerCAmelCase__		  =  []
								for s in sequence:
												if s == separator_token_id:
																sentence_num += 1
												embeddings.append(sentence_num % 2					)
								batch_embeddings.append(snake_case__					)
				return torch.tensor(snake_case__					)
