





def 		A_				(     _lowerCAmelCase     )						-> Tuple:
 UpperCamelCase	:					Dict       	=   0
 UpperCamelCase	:					Any       	=   len(_lowerCAmelCase     )

 for i in range(n - 1     ):
  for j in range(i + 1							,   _lowerCAmelCase     ):
   if arr[i] > arr[j]:
    num_inversions += 1

 return num_inversions



def 		A_				(     _lowerCAmelCase     )						-> Optional[int]:
 if len(_lowerCAmelCase     ) <= 1:
  return arr, 0
 UpperCamelCase	:					int       	=   len(_lowerCAmelCase     ) // 2
 UpperCamelCase	:					Union[str, Any]       	=   arr[0:mid]
 UpperCamelCase	:					Optional[Any]       	=   arr[mid:]

 UpperCamelCase	,    UpperCamelCase	:					Optional[int]       	=   count_inversions_recursive(_lowerCAmelCase     )
 UpperCamelCase	,    UpperCamelCase	:					Optional[Any]       	=   count_inversions_recursive(_lowerCAmelCase     )
 UpperCamelCase	,    UpperCamelCase	:					List[str]       	=   _count_cross_inversions(_lowerCAmelCase							,   _lowerCAmelCase     )

 UpperCamelCase	:					Optional[int]       	=   inversion_p + inversions_q + cross_inversions
 return c, num_inversions



def 		A_				(     _lowerCAmelCase							,   _lowerCAmelCase     )						-> int:
 UpperCamelCase	:					Dict       	=   []
 UpperCamelCase	:					int       	=   0
 while i < len(_lowerCAmelCase     ) and j < len(_lowerCAmelCase     ):
  if p[i] > q[j]:
   # if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
   # These are all inversions. The claim emerges from the
   # property that P is sorted.
   num_inversion += len(_lowerCAmelCase     ) - i
   r.append(q[j]     )
   j += 1
  else:
   r.append(p[i]     )
   i += 1

 if i < len(_lowerCAmelCase     ):
  r.extend(p[i:]     )
 else:
  r.extend(q[j:]     )

 return r, num_inversion



def 		A_				(     )						-> Dict:
 UpperCamelCase	:					Tuple       	=   [10, 2, 1, 5, 5, 2, 11]

 # this arr has 8 inversions:
 # (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

 UpperCamelCase	:					Optional[int]       	=   count_inversions_bf(_lowerCAmelCase     )
 UpperCamelCase	,    UpperCamelCase	:					str       	=   count_inversions_recursive(_lowerCAmelCase     )

 assert num_inversions_bf == num_inversions_recursive == 8

 print("number of inversions = "							,   _lowerCAmelCase     )

 # testing an array with zero inversion (a sorted arr_1)

 arr_a.sort()
 UpperCamelCase	:					int       	=   count_inversions_bf(_lowerCAmelCase     )
 UpperCamelCase	,    UpperCamelCase	:					List[Any]       	=   count_inversions_recursive(_lowerCAmelCase     )

 assert num_inversions_bf == num_inversions_recursive == 0
 print("number of inversions = "							,   _lowerCAmelCase     )

 # an empty list should also have zero inversions
 UpperCamelCase	:					List[str]       	=   []
 UpperCamelCase	:					Any       	=   count_inversions_bf(_lowerCAmelCase     )
 UpperCamelCase	,    UpperCamelCase	:					Tuple       	=   count_inversions_recursive(_lowerCAmelCase     )

 assert num_inversions_bf == num_inversions_recursive == 0
 print("number of inversions = "							,   _lowerCAmelCase     )


if __name__ == "__main__":
    main()







from typing import TYPE_CHECKING

from ....utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


__lowerCamelCase       :     Optional[int]   =     {"""configuration_mmbt""": ["""MMBTConfig"""]}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    __lowerCamelCase       :     List[Any]   =     ["""MMBTForClassification""", """MMBTModel""", """ModalEmbeddings"""]


if TYPE_CHECKING:
    from .configuration_mmbt import MMBTConfig

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_mmbt import MMBTForClassification, MMBTModel, ModalEmbeddings

else:
    import sys

    __lowerCamelCase       :     int   =     _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)
