def    __lowerCamelCase	(		lowerCAmelCase__			,						lowerCAmelCase__			,						lowerCAmelCase__			,						lowerCAmelCase__			):
       if start == end:
              return start if lst[start] > item else start + 1
       if start > end:
              return start

       lowerCAmelCase__  			=      (start + end) // 2
       if lst[mid] < item:
              return binary_search(lowerCAmelCase__			,						lowerCAmelCase__			,						mid + 1			,						lowerCAmelCase__			)
       elif lst[mid] > item:
              return binary_search(lowerCAmelCase__			,						lowerCAmelCase__			,						lowerCAmelCase__			,						mid - 1			)
       else:
              return mid






def    __lowerCamelCase	(		lowerCAmelCase__			):
       lowerCAmelCase__  			=      len(lowerCAmelCase__			)

       for index in range(1			,						lowerCAmelCase__			):
              lowerCAmelCase__  			=      lst[index]
              lowerCAmelCase__  			=      binary_search(lowerCAmelCase__			,						lowerCAmelCase__			,						0			,						index - 1			)
              lowerCAmelCase__  			=      lst[:pos] + [value] + lst[pos:index] + lst[index + 1 :]

       return lst






def    __lowerCamelCase	(		lowerCAmelCase__			,						lowerCAmelCase__			):
       if not left:
              return right

       if not right:
              return left

       if left[0] < right[0]:
              return [left[0], *merge(left[1:]			,						lowerCAmelCase__			)]

       return [right[0], *merge(lowerCAmelCase__			,						right[1:]			)]






def    __lowerCamelCase	(		lowerCAmelCase__			):
       lowerCAmelCase__  			=      len(lowerCAmelCase__			)
       lowerCAmelCase__			,      lowerCAmelCase__  			=      [], []
       lowerCAmelCase__  			=      [lst[0]]
       lowerCAmelCase__  			=      []
       lowerCAmelCase__  			=      1
       while i < length:
              if lst[i] < lst[i - 1]:
                     runs.append(lowerCAmelCase__			)
                     lowerCAmelCase__  			=      [lst[i]]
              else:
                     new_run.append(lst[i]			)
              i += 1
       runs.append(lowerCAmelCase__			)

       for run in runs:
              sorted_runs.append(insertion_sort(lowerCAmelCase__			)			)
       for run in sorted_runs:
              lowerCAmelCase__  			=      merge(lowerCAmelCase__			,						lowerCAmelCase__			)

       return sorted_array






def    __lowerCamelCase	(		):
       lowerCAmelCase__  			=      [5, 9, 1_0, 3, -4, 5, 1_7_8, 9_2, 4_6, -1_8, 0, 7]
       lowerCAmelCase__  			=      tim_sort(lowerCAmelCase__			)
       print(lowerCAmelCase__			)


if __name__ == "__main__":
    main()

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'])
