from __future__ import annotations






def    __lowerCamelCase	(		lowerCAmelCase__			,						lowerCAmelCase__			,						lowerCAmelCase__			):
							if len(lowerCAmelCase__			) == 0:
														raise ValueError('find_min() arg is an empty sequence'			)
							if (
							    left >= len(lowerCAmelCase__			)
							    or left < -len(lowerCAmelCase__			)
							    or right >= len(lowerCAmelCase__			)
							    or right < -len(lowerCAmelCase__			)
							):
														raise IndexError('list index out of range'			)
							if left == right:
														return nums[left]
							lowerCAmelCase__  			=      (left + right) >> 1  # the middle
							lowerCAmelCase__  			=      find_min(lowerCAmelCase__			,						lowerCAmelCase__			,						lowerCAmelCase__			)  # find min in range[left, mid]
							lowerCAmelCase__  			=      find_min(lowerCAmelCase__			,						mid + 1			,						lowerCAmelCase__			)  # find min in range[mid + 1, right]

							return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
				import doctest

				doctest.testmod(verbose=True)

from ..utils import DummyObject, requires_backends
class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						Any    ,					**lowercase__      :						List[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						List[str]    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						Dict    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Dict    ,					*lowercase__      :						int    ,					**lowercase__      :						Dict):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[Any]    ,					*lowercase__      :						Dict    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Any    ,					*lowercase__      :						int    ,					**lowercase__      :						str):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						Dict    ,					**lowercase__      :						int):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						Dict    ,					**lowercase__      :						Dict):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Any    ,					*lowercase__      :						Tuple    ,					**lowercase__      :						Dict):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[Any]    ,					*lowercase__      :						int    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						int    ,					*lowercase__      :						Optional[Any]    ,					**lowercase__      :						Union[str, Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Tuple    ,					*lowercase__      :						Dict    ,					**lowercase__      :						Any):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Tuple    ,					*lowercase__      :						Optional[Any]    ,					**lowercase__      :						Any):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						Union[str, Any]    ,					**lowercase__      :						Dict):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						int    ,					*lowercase__      :						Tuple    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[Any]    ,					*lowercase__      :						List[Any]    ,					**lowercase__      :						Union[str, Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						List[Any]    ,					**lowercase__      :						Any):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						Any    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						int    ,					*lowercase__      :						Union[str, Any]    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						List[str]    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Any    ,					*lowercase__      :						Dict    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						Tuple    ,					**lowercase__      :						List[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						int    ,					*lowercase__      :						Dict    ,					**lowercase__      :						Dict):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						List[Any]    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						Any    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						int    ,					*lowercase__      :						Union[str, Any]    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Tuple    ,					*lowercase__      :						Any    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Dict    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						Dict):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[Any]    ,					*lowercase__      :						str    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[int]    ,					*lowercase__      :						Any    ,					**lowercase__      :						Union[str, Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[int]    ,					*lowercase__      :						List[str]    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Dict    ,					*lowercase__      :						List[Any]    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Any    ,					*lowercase__      :						Union[str, Any]    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[Any]    ,					*lowercase__      :						Tuple    ,					**lowercase__      :						Optional[int]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						int    ,					*lowercase__      :						Any    ,					**lowercase__      :						str):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Dict    ,					*lowercase__      :						Dict    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[Any]    ,					*lowercase__      :						str    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[int]    ,					*lowercase__      :						str    ,					**lowercase__      :						List[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						Any    ,					**lowercase__      :						Union[str, Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[Any]    ,					*lowercase__      :						int    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[Any]    ,					*lowercase__      :						Union[str, Any]    ,					**lowercase__      :						Optional[int]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						Optional[int]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Union[str, Any]    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[int]    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						int):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Any    ,					*lowercase__      :						Dict    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Any    ,					*lowercase__      :						Tuple    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Union[str, Any]    ,					*lowercase__      :						Union[str, Any]    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[Any]    ,					*lowercase__      :						Tuple    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Union[str, Any]    ,					*lowercase__      :						Union[str, Any]    ,					**lowercase__      :						List[str]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[int]    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						str):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Optional[int]    ,					*lowercase__      :						Any    ,					**lowercase__      :						Any):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						str    ,					*lowercase__      :						Dict    ,					**lowercase__      :						Optional[Any]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						List[str]    ,					*lowercase__      :						str    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Any    ,					*lowercase__      :						Dict    ,					**lowercase__      :						Tuple):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Tuple    ,					*lowercase__      :						Any    ,					**lowercase__      :						Dict):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Union[str, Any]    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						Optional[int]):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])






class        a_				(		metaclass=SCREAMING_SNAKE_CASE		):






 '''simple docstring'''






 UpperCAmelCase_							=      ['tokenizers']




 def __init__(    self      :						Dict    ,					*lowercase__      :						Optional[int]    ,					**lowercase__      :						str):







        '''simple docstring'''



        requires_backends(self    ,					['tokenizers'])
