



def 		lowerCAmelCase__    (					UpperCamelCase_				:       List[str]	)->  int:
    A__		 =					0
    A__		 =					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 		lowerCAmelCase__    (					UpperCamelCase_				:       Optional[int]	)->  List[str]:
    if len(_lowerCAmelCase	) <= 1:
        return arr, 0
    A__		 =					len(_lowerCAmelCase	) // 2
    A__		 =					arr[0:mid]
    A__		 =					arr[mid:]

    A__ ,	A__		 =					count_inversions_recursive(_lowerCAmelCase	)
    A__ ,	A__		 =					count_inversions_recursive(_lowerCAmelCase	)
    A__ ,	A__		 =					_count_cross_inversions(_lowerCAmelCase ,       _lowerCAmelCase	)

    A__		 =					inversion_p + inversions_q + cross_inversions
    return c, num_inversions



def 		lowerCAmelCase__    (					UpperCamelCase_				:       Any ,       UpperCamelCase_				:       Optional[Any]	)->  Optional[Any]:
    A__		 =					[]
    A__		 =					A__		 =					A__		 =					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 		lowerCAmelCase__    (					)->  Optional[int]:
    A__		 =					[1_0, 2, 1, 5, 5, 2, 1_1]

    # 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(_lowerCAmelCase	)
    A__ ,	A__		 =					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()
    A__		 =					count_inversions_bf(_lowerCAmelCase	)
    A__ ,	A__		 =					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
    A__		 =					[]
    A__		 =					count_inversions_bf(_lowerCAmelCase	)
    A__ ,	A__		 =					count_inversions_recursive(_lowerCAmelCase	)

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


if __name__ == "__main__":
   main()





def 		lowerCAmelCase__    (					UpperCamelCase_				:       float ,       UpperCamelCase_				:       int	)->  float:
    if digit_amount > 0:
        return round(number - int(UpperCamelCase_	) ,       UpperCamelCase_	)
    return number - int(UpperCamelCase_	)


if __name__ == "__main__":
   print(decimal_isolate(1.53, 0))
   print(decimal_isolate(35.345, 1))
   print(decimal_isolate(35.345, 2))
   print(decimal_isolate(35.345, 3))
   print(decimal_isolate(-14.789, 3))
   print(decimal_isolate(0, 2))
   print(decimal_isolate(-14.123, 1))
   print(decimal_isolate(-14.123, 2))
   print(decimal_isolate(-14.123, 3))
