



def  UpperCAmelCase__    (    lowercase__   ) ->      Any:
						__lowercase					=				0
						__lowercase					=				len(lowercase__   )

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

						return num_inversions






def  UpperCAmelCase__    (    lowercase__   ) ->      Tuple:
						if len(lowercase__   ) <= 1:
												return arr, 0
						__lowercase					=				len(lowercase__   ) // 2
						__lowercase					=				arr[0:mid]
						__lowercase					=				arr[mid:]

						__lowercase	,			__lowercase					=				count_inversions_recursive(lowercase__   )
						__lowercase	,			__lowercase					=				count_inversions_recursive(lowercase__   )
						__lowercase	,			__lowercase					=				_count_cross_inversions(lowercase__						,       lowercase__   )

						__lowercase					=				inversion_p + inversions_q + cross_inversions
						return c, num_inversions






def  UpperCAmelCase__    (    lowercase__						,       lowercase__   ) ->      Tuple:
						__lowercase					=				[]
						__lowercase					=				__lowercase					=				__lowercase					=				0
						while i < len(lowercase__   ) and j < len(lowercase__   ):
												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(lowercase__   ) - i
																		r.append(q[j]   )
																		j += 1
												else:
																		r.append(p[i]   )
																		i += 1

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

						return r, num_inversion






def  UpperCAmelCase__    (    ) ->      str:
						__lowercase					=				[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)

						__lowercase					=				count_inversions_bf(lowercase__   )
						__lowercase	,			__lowercase					=				count_inversions_recursive(lowercase__   )

						assert num_inversions_bf == num_inversions_recursive == 8

						print("""number of inversions = """						,       lowercase__   )

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

						arr_a.sort()
						__lowercase					=				count_inversions_bf(lowercase__   )
						__lowercase	,			__lowercase					=				count_inversions_recursive(lowercase__   )

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

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

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


if __name__ == "__main__":
			main()










UpperCamelCase__ =						{
    "joule": 1.0,
    "kilojoule": 10_00,
    "megajoule": 1_00_00_00,
    "gigajoule": 10_00_00_00_00,
    "wattsecond": 1.0,
    "watthour": 36_00,
    "kilowatthour": 3_60_00_00,
    "newtonmeter": 1.0,
    "calorie_nutr": 41_86.8,
    "kilocalorie_nutr": 4_18_68_00.00,
    "electronvolt": 1.6_0217_6634e-19,
    "britishthermalunit_it": 10_55.0_55_85,
    "footpound": 1.355_818,
}






def  UpperCAmelCase__    (    lowercase__						,       lowercase__						,       lowercase__   ) ->      float:
						if to_type not in ENERGY_CONVERSION or from_type not in ENERGY_CONVERSION:
												__lowercase					=				(
												    F"Incorrect 'from_type' or 'to_type' value: {from_type!r}, {to_type!r}\n"
												    F"Valid values are: {', '.join(lowercase__   )}"
												)
												raise ValueError(lowercase__   )
						return value * ENERGY_CONVERSION[from_type] / ENERGY_CONVERSION[to_type]


if __name__ == "__main__":
			import doctest

			doctest.testmod()





