

from __future__ import annotations

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






class _UpperCamelCase				:
			'''simple docstring'''







			def __init__(      self				:			int   ,   a				:			Collection[float] | None = None						)				->							None:

				"""simple docstring"""

				if components is None:
					SCREAMING_SNAKE_CASE :   str					  =							[]
				SCREAMING_SNAKE_CASE :   Tuple					  =							list(a						)
			def __len__(      self				:			Optional[int]						)				->							int:

				"""simple docstring"""

				return len(self.__components						)
			def __str__(      self				:			str						)				->							str:

				"""simple docstring"""

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

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   Any					  =							len(self						)
				if size == len(a						):
					SCREAMING_SNAKE_CASE :   int					  =							[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				:			List[str]   ,   a				:			Vector						)				->							Vector:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   Optional[Any]					  =							len(self						)
				if size == len(a						):
					SCREAMING_SNAKE_CASE :   str					  =							[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				:			List[str]   ,   a				:			float						)				->							Vector:

				"""simple docstring"""

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

				"""simple docstring"""

				...
			def __mul__(      self				:			Optional[int]   ,   a				:			float | Vector						)				->							float | Vector:

				"""simple docstring"""

				if isinstance(a   ,   (float, int)						):
					SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							[c * other for c in self.__components]
					return Vector(a						)
				elif isinstance(a   ,   a						) and len(self						) == len(a						):
					SCREAMING_SNAKE_CASE :   List[Any]					  =							len(self						)
					SCREAMING_SNAKE_CASE :   str					  =							[self.__components[i] * other.component(a						) for i in range(a						)]
					return sum(a						)
				else:  # error case
					raise Exception("invalid operand!"						)
			def 				__UpperCamelCase			(      self				:			Tuple						)				->							Vector:

				"""simple docstring"""

				return Vector(self.__components						)
			def 				__UpperCamelCase			(      self				:			Union[str, Any]   ,   a				:			int						)				->							float:

				"""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 				__UpperCamelCase			(      self				:			str   ,   a				:			int   ,   a				:			float						)				->							None:

				"""simple docstring"""

				assert -len(self.__components						) <= pos < len(self.__components						)
				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							value
			def 				__UpperCamelCase			(      self				:			str						)				->							float:

				"""simple docstring"""

				if len(self.__components						) == 0:
					raise Exception("Vector is empty"						)
				SCREAMING_SNAKE_CASE :   Optional[int]					  =							[c**2 for c in self.__components]
				return math.sqrt(sum(a						)						)






			def 				__UpperCamelCase			(      self				:			int   ,   a				:			Vector   ,   a				:			bool = False						)				->							float:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							self * other
				SCREAMING_SNAKE_CASE :   Tuple					  =							self.euclidean_length() * other.euclidean_length()
				if deg:
					return math.degrees(math.acos(num / den						)						)
				else:
					return math.acos(num / den						)

def 			lowerCamelCase__			(       _a):
	assert isinstance(_a				,      _a)
	return Vector([0] * dimension)

def 			lowerCamelCase__			(       _a				,      _a):
	assert isinstance(_a				,      _a) and (isinstance(_a				,      _a))
	SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							[0] * dimension
	SCREAMING_SNAKE_CASE :   Any					  =							1
	return Vector(_a)

def 			lowerCamelCase__			(       _a				,      _a				,      _a):
	assert (
	    isinstance(_a				,      _a)
	    and isinstance(_a				,      _a)
	    and (isinstance(_a				,      (int, float)))
	)
	return x * scalar + y

def 			lowerCamelCase__			(       _a				,      _a				,      _a):
	random.seed(_a)
	SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							[random.randint(_a				,      _a) for _ in range(_a)]
	return Vector(_a)






class _UpperCamelCase				:
			'''simple docstring'''







			def __init__(      self				:			int   ,   a				:			list[list[float]]   ,   a				:			int   ,   a				:			int						)				->							None:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   List[str]					  =							matrix
				SCREAMING_SNAKE_CASE :   Optional[int]					  =							w
				SCREAMING_SNAKE_CASE :   Optional[Any]					  =							h
			def __str__(      self				:			Any						)				->							str:

				"""simple docstring"""

				SCREAMING_SNAKE_CASE :   Dict					  =							""
				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				:			List[Any]   ,   a				:			Matrix						)				->							Matrix:

				"""simple docstring"""

				if self.__width == other.width() and self.__height == other.height():
					SCREAMING_SNAKE_CASE :   Dict					  =							[]
					for i in range(self.__height						):
						SCREAMING_SNAKE_CASE :   Any					  =							[
						    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				:			Optional[Any]   ,   a				:			Matrix						)				->							Matrix:

				"""simple docstring"""

				if self.__width == other.width() and self.__height == other.height():
					SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							[]
					for i in range(self.__height						):
						SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							[
						    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				:			List[str]   ,   a				:			float						)				->							Matrix:

				"""simple docstring"""

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

				"""simple docstring"""

				...
			def __mul__(      self				:			str   ,   a				:			float | Vector						)				->							Vector | Matrix:

				"""simple docstring"""

				if isinstance(a   ,   a						):  # matrix-vector
					if len(a						) == self.__width:
						SCREAMING_SNAKE_CASE :   Union[str, Any]					  =							zero_vector(self.__height						)
						for i in range(self.__height						):
							SCREAMING_SNAKE_CASE :   Optional[int]					  =							[
							    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
					SCREAMING_SNAKE_CASE :   str					  =							[
					    [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 				__UpperCamelCase			(      self				:			Optional[int]						)				->							int:

				"""simple docstring"""

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

				"""simple docstring"""

				return self.__width
			def 				__UpperCamelCase			(      self				:			Any   ,   a				:			int   ,   a				:			int						)				->							float:

				"""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 				__UpperCamelCase			(      self				:			Tuple   ,   a				:			int   ,   a				:			int   ,   a				:			float						)				->							None:

				"""simple docstring"""

				if 0 <= x < self.__height and 0 <= y < self.__width:
					SCREAMING_SNAKE_CASE :   str					  =							value
				else:
					raise Exception("change_component: indices out of bounds"						)
			def 				__UpperCamelCase			(      self				:			int   ,   a				:			int   ,   a				:			int						)				->							float:

				"""simple docstring"""

				if self.__height != self.__width:
					raise Exception("Matrix is not square"						)
				SCREAMING_SNAKE_CASE :   List[str]					  =							self.__matrix[:x] + self.__matrix[x + 1 :]
				for i in range(len(a						)						):
					SCREAMING_SNAKE_CASE :   Optional[int]					  =							minor[i][:y] + minor[i][y + 1 :]
				return Matrix(a   ,   self.__width - 1   ,   self.__height - 1						).determinant()
			def 				__UpperCamelCase			(      self				:			int   ,   a				:			int   ,   a				:			int						)				->							float:

				"""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 				__UpperCamelCase			(      self				:			Dict						)				->							float:

				"""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:
					SCREAMING_SNAKE_CASE :   List[Any]					  =							[
					    self.__matrix[0][y] * self.cofactor(0   ,   a						) for y in range(self.__width						)
					]
					return sum(a						)

def 			lowerCamelCase__			(       _a):
	SCREAMING_SNAKE_CASE :   list[list[float]]					  =							[[0] * n for _ in range(_a)]
	return Matrix(_a				,      _a				,      _a)


def 			lowerCamelCase__			(       _a				,      _a				,      _a				,      _a):
	random.seed(_a)
	SCREAMING_SNAKE_CASE :   list[list[float]]					  =							[
	    [random.randint(_a				,      _a) for _ in range(_a)] for _ in range(_a)
	]
	return Matrix(_a				,      _a				,      _a)


'''simple docstring'''







from ...configuration_utils import PretrainedConfig


class        A__   (   _snake_case      ):
    lowercase						       =		"bert-generation"



    def __init__(       self		,					UpperCamelCase__=50358		,					UpperCamelCase__=1024		,					UpperCamelCase__=24		,					UpperCamelCase__=16		,					UpperCamelCase__=4096		,					UpperCamelCase__="gelu"		,					UpperCamelCase__=0.1		,					UpperCamelCase__=0.1		,					UpperCamelCase__=512		,					UpperCamelCase__=0.02		,					UpperCamelCase__=1e-1_2		,					UpperCamelCase__=0		,					UpperCamelCase__=2		,					UpperCamelCase__=1		,					UpperCamelCase__="absolute"		,					UpperCamelCase__=True		,					**UpperCamelCase__		,					)    ->   Any:





           '''simple docstring'''
           super().__init__(pad_token_id=UpperCamelCase__		,					bos_token_id=UpperCamelCase__		,					eos_token_id=UpperCamelCase__		,					**UpperCamelCase__							)

           A_						       =   vocab_size
           A_						       =   hidden_size
           A_						       =   num_hidden_layers
           A_						       =   num_attention_heads
           A_						       =   hidden_act
           A_						       =   intermediate_size
           A_						       =   hidden_dropout_prob
           A_						       =   attention_probs_dropout_prob
           A_						       =   max_position_embeddings
           A_						       =   initializer_range
           A_						       =   layer_norm_eps
           A_						       =   position_embedding_type
           A_						       =   use_cache
