





def 	UpperCamelCase__(       UpperCamelCase__			:       Tuple  )->Any:
       A__											=						0
       A__											=						len(UpperCamelCase__  )

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

       return num_inversions


def 	UpperCamelCase__(       UpperCamelCase__			:       Dict  )->List[Any]:
       if len(UpperCamelCase__  ) <= 1:
              return arr, 0
       A__											=						len(UpperCamelCase__  ) // 2
       A__											=						arr[0:mid]
       A__											=						arr[mid:]

       A__					,	A__											=						count_inversions_recursive(UpperCamelCase__  )
       A__					,	A__											=						count_inversions_recursive(UpperCamelCase__  )
       A__					,	A__											=						_count_cross_inversions(UpperCamelCase__ ,     UpperCamelCase__  )

       A__											=						inversion_p + inversions_q + cross_inversions
       return c, num_inversions


def 	UpperCamelCase__(       UpperCamelCase__			:       Dict ,     UpperCamelCase__			:       Any  )->Union[str, Any]:
       A__											=						[]
       A__											=						A__											=						A__											=						0
       while i < len(UpperCamelCase__  ) and j < len(UpperCamelCase__  ):
              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(UpperCamelCase__  ) - i
                     r.append(q[j]  )
                     j += 1
              else:
                     r.append(p[i]  )
                     i += 1

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

       return r, num_inversion


def 	UpperCamelCase__(       )->Dict:
       A__											=						[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)

       A__											=						count_inversions_bf(UpperCamelCase__  )
       A__					,	A__											=						count_inversions_recursive(UpperCamelCase__  )

       assert num_inversions_bf == num_inversions_recursive == 8

       print('''number of inversions = ''' ,     UpperCamelCase__  )

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

       arr_a.sort()
       A__											=						count_inversions_bf(UpperCamelCase__  )
       A__					,	A__											=						count_inversions_recursive(UpperCamelCase__  )

       assert num_inversions_bf == num_inversions_recursive == 0
       print('''number of inversions = ''' ,     UpperCamelCase__  )

       # an empty list should also have zero inversions
       A__											=						[]
       A__											=						count_inversions_bf(UpperCamelCase__  )
       A__					,	A__											=						count_inversions_recursive(UpperCamelCase__  )

       assert num_inversions_bf == num_inversions_recursive == 0
       print('''number of inversions = ''' ,     UpperCamelCase__  )


if __name__ == "__main__":
       main()












from ..utils import DummyObject, requires_backends




class     SCREAMING_SNAKE_CASE__ (						metaclass=UpperCamelCase__      ):
 __SCREAMING_SNAKE_CASE							       =	['''keras_nlp''']



 def __init__(							self,*__lowerCamelCase,**__lowerCamelCase ):
        requires_backends(self,['''keras_nlp'''] )





