






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		:			List[str]       ,				lowerCamelCase		:			List[Any] = None							)						->	List[Any]:


         """simple docstring"""




         if components is None:
                _UpperCAmelCase							=    []
         _UpperCAmelCase							=    list(_lowerCAmelCase							)


  def __len__(      self		:			Any							)						->	List[Any]:


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


  def __str__(      self		:			Union[str, Any]							)						->	Dict:


         """simple docstring"""
         return "(" + ",".join(map(_lowerCAmelCase       ,				self.__components							)							) + ")"


  def __add__(      self		:			Dict       ,				lowerCamelCase		:			Optional[int]							)						->	int:


         """simple docstring"""
         _UpperCAmelCase							=    len(self							)
         if size == len(_lowerCAmelCase							):
                _UpperCAmelCase							=    [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		:			Any       ,				lowerCamelCase		:			Any							)						->	Optional[Any]:


         """simple docstring"""
         _UpperCAmelCase							=    len(self							)
         if size == len(_lowerCAmelCase							):
                _UpperCAmelCase							=    [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		:			Tuple       ,				lowerCamelCase		:			List[str]							)						->	Optional[Any]:


         """simple docstring"""
         ...


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


         """simple docstring"""
         ...


  def __mul__(      self		:			List[Any]       ,				lowerCamelCase		:			Any							)						->	List[str]:


         """simple docstring"""




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


  def  lowerCamelCase       (      self		:			str							)						->	Dict:


         """simple docstring"""
         return Vector(self.__components							)


  def  lowerCamelCase       (      self		:			int       ,				lowerCamelCase		:			Dict							)						->	int:


         """simple docstring"""




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


  def  lowerCamelCase       (      self		:			List[Any]       ,				lowerCamelCase		:			Optional[int]       ,				lowerCamelCase		:			str							)						->	Any:


         """simple docstring"""
         assert -len(self.__components							) <= pos < len(self.__components							)
         _UpperCAmelCase							=    value


  def  lowerCamelCase       (      self		:			int							)						->	Union[str, Any]:


         """simple docstring"""




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





  def  lowerCamelCase       (      self		:			int       ,				lowerCamelCase		:			int       ,				lowerCamelCase		:			int = False							)						->	Optional[Any]:


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




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




def       _SCREAMING_SNAKE_CASE (							__snake_case   ,      __snake_case )				->						Vector:
       assert isinstance(UpperCamelCase__   ,      UpperCamelCase__ ) and (isinstance(UpperCamelCase__   ,      UpperCamelCase__ ))
       _UpperCAmelCase							=    [0] * dimension
       _UpperCAmelCase							=    1
       return Vector(UpperCamelCase__ )




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




def       _SCREAMING_SNAKE_CASE (							__snake_case   ,      __snake_case   ,      __snake_case )				->						Vector:
       random.seed(UpperCamelCase__ )
       _UpperCAmelCase							=    [random.randint(UpperCamelCase__   ,      UpperCamelCase__ ) for _ in range(UpperCamelCase__ )]
       return Vector(UpperCamelCase__ )
class 		SCREAMING_SNAKE_CASE__	:

  '''simple docstring'''







  def __init__(      self		:			Optional[Any]       ,				lowerCamelCase		:			List[str]       ,				lowerCamelCase		:			Union[str, Any]       ,				lowerCamelCase		:			Union[str, Any]							)						->	Union[str, Any]:


         """simple docstring"""
         _UpperCAmelCase							=    matrix
         _UpperCAmelCase							=    w
         _UpperCAmelCase							=    h


  def __str__(      self		:			List[str]							)						->	Union[str, Any]:


         """simple docstring"""
         _UpperCAmelCase							=    ''''''
         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		:			Optional[int]       ,				lowerCamelCase		:			str							)						->	Optional[Any]:


         """simple docstring"""




         if self.__width == other.width() and self.__height == other.height():
                _UpperCAmelCase							=    []
                for i in range(self.__height							):
                       _UpperCAmelCase							=    [
                           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		:			Optional[int]       ,				lowerCamelCase		:			str							)						->	List[str]:


         """simple docstring"""




         if self.__width == other.width() and self.__height == other.height():
                _UpperCAmelCase							=    []
                for i in range(self.__height							):
                       _UpperCAmelCase							=    [
                           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		:			int       ,				lowerCamelCase		:			List[str]							)						->	Dict:


         """simple docstring"""
         ...


  @overload
  def __mul__(      self		:			str       ,				lowerCamelCase		:			Optional[int]							)						->	List[Any]:


         """simple docstring"""
         ...


  def __mul__(      self		:			Union[str, Any]       ,				lowerCamelCase		:			List[str]							)						->	Any:


         """simple docstring"""




         if isinstance(_lowerCAmelCase       ,				_lowerCAmelCase							):  # matrix-vector
                if len(_lowerCAmelCase							) == self.__width:
                       _UpperCAmelCase							=    zero_vector(self.__height							)
                       for i in range(self.__height							):
                              _UpperCAmelCase							=    [
                                  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
                _UpperCAmelCase							=    [
                    [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  lowerCamelCase       (      self		:			str							)						->	Optional[Any]:


         """simple docstring"""
         return self.__height


  def  lowerCamelCase       (      self		:			List[Any]							)						->	str:


         """simple docstring"""
         return self.__width


  def  lowerCamelCase       (      self		:			Optional[Any]       ,				lowerCamelCase		:			Union[str, Any]       ,				lowerCamelCase		:			List[str]							)						->	Optional[Any]:


         """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  lowerCamelCase       (      self		:			List[Any]       ,				lowerCamelCase		:			Optional[Any]       ,				lowerCamelCase		:			List[Any]       ,				lowerCamelCase		:			Optional[int]							)						->	List[Any]:


         """simple docstring"""




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


  def  lowerCamelCase       (      self		:			Dict       ,				lowerCamelCase		:			str       ,				lowerCamelCase		:			List[Any]							)						->	Dict:


         """simple docstring"""




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


  def  lowerCamelCase       (      self		:			Optional[int]       ,				lowerCamelCase		:			str       ,				lowerCamelCase		:			str							)						->	List[Any]:


         """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(_lowerCAmelCase       ,				_lowerCAmelCase							)
         else:
                raise Exception("""Indices out of bounds"""							)





  def  lowerCamelCase       (      self		:			List[Any]							)						->	Tuple:


         """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:
                _UpperCAmelCase							=    [
                    self.__matrix[0][y] * self.cofactor(0       ,				_lowerCAmelCase							) for y in range(self.__width							)
                ]
                return sum(_lowerCAmelCase							)




def       _SCREAMING_SNAKE_CASE (							__snake_case )				->						Matrix:
       _UpperCAmelCase							=    [[0] * n for _ in range(UpperCamelCase__ )]
       return Matrix(UpperCamelCase__   ,      UpperCamelCase__   ,      UpperCamelCase__ )





def       _SCREAMING_SNAKE_CASE (							__snake_case   ,      __snake_case   ,      __snake_case   ,      __snake_case )				->						Matrix:
       random.seed(UpperCamelCase__ )
       _UpperCAmelCase							=    [
           [random.randint(UpperCamelCase__   ,      UpperCamelCase__ ) for _ in range(UpperCamelCase__ )] for _ in range(UpperCamelCase__ )
       ]
       return Matrix(UpperCamelCase__   ,      UpperCamelCase__   ,      UpperCamelCase__ )






import unittest
from dataclasses import dataclass

import pytest

from accelerate.commands.config.config_args import SageMakerConfig
from accelerate.utils import ComputeEnvironment
from accelerate.utils.launch import _convert_nargs_to_dict





@dataclass
class 				a			(      __lowercase			):
				SCREAMING_SNAKE_CASE__     :   Any		      =     ComputeEnvironment.AMAZON_SAGEMAKER
				SCREAMING_SNAKE_CASE__     :   Optional[int]		      =     True
				SCREAMING_SNAKE_CASE__     :   int		      =     '''ml.p3.2xlarge'''
				SCREAMING_SNAKE_CASE__     :   Union[str, Any]		      =     '''accelerate_sagemaker_execution_role'''
				SCREAMING_SNAKE_CASE__     :   List[Any]		      =     '''hf-sm'''
				SCREAMING_SNAKE_CASE__     :   Any		      =     '''us-east-1'''
				SCREAMING_SNAKE_CASE__     :   Any		      =     1
				SCREAMING_SNAKE_CASE__     :   Dict		      =     '''accelerate-sagemaker-1'''
				SCREAMING_SNAKE_CASE__     :   Dict		      =     '''1.6'''
				SCREAMING_SNAKE_CASE__     :   int		      =     '''4.4'''
				SCREAMING_SNAKE_CASE__     :   int		      =     '''train.py'''
				SCREAMING_SNAKE_CASE__     :   Tuple		      =     [
				    '''--model_name_or_path''',
				    '''bert''',
				    '''--do_train''',
				    '''False''',
				    '''--epochs''',
				    '''3''',
				    '''--learning_rate''',
				    '''5e-5''',
				    '''--max_steps''',
				    '''50.5''',
				]
				SCREAMING_SNAKE_CASE__     :   List[str]		      =     [
				    '''--model_name_or_path''',
				    '''bert''',
				    '''--do_train''',
				    '''--do_test''',
				    '''False''',
				    '''--do_predict''',
				    '''--epochs''',
				    '''3''',
				    '''--learning_rate''',
				    '''5e-5''',
				    '''--max_steps''',
				    '''50.5''',
				]





class 				a			(      unittest.TestCase			):






				def 			snake_case_    (  self					):

										"""simple docstring"""




										__SCREAMING_SNAKE_CASE:				Optional[Any]           =   _convert_nargs_to_dict(MockLaunchConfig.success_training_script_args					)
										assert isinstance(converted_args['''model_name_or_path''']			, _lowerCAmelCase					)
										assert isinstance(converted_args['''do_train''']			, _lowerCAmelCase					)
										assert isinstance(converted_args['''epochs''']			, _lowerCAmelCase					)
										assert isinstance(converted_args['''learning_rate''']			, _lowerCAmelCase					)
										assert isinstance(converted_args['''max_steps''']			, _lowerCAmelCase					)

										with pytest.raises(_lowerCAmelCase					):
																_convert_nargs_to_dict(MockLaunchConfig.fail_training_script_args					)



