
'''simple docstring'''
def      UpperCamelCase_				(      A__						):
	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_				(      A__						):





	if len(UpperCamelCase__						) <= 1:
		return arr, 0
	a_      				=						len(UpperCamelCase__						) // 2
	a_      				=						arr[0:mid]
	a_      				=						arr[mid:]

	a_      				=						count_inversions_recursive(UpperCamelCase__						)
	a_      				=						count_inversions_recursive(UpperCamelCase__						)
	a_      				=						_count_cross_inversions(UpperCamelCase__  ,      UpperCamelCase__						)

	a_      				=						inversion_p + inversions_q + cross_inversions
	return c, num_inversions






def      UpperCamelCase_				(      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_				(      ):
	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_      				=						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_      				=						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_      				=						count_inversions_recursive(UpperCamelCase__						)

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


if __name__ == "__main__":
		main()







def 		lowerCAmelCase  (	UpperCamelCase__   :   List[Any]       ,			UpperCamelCase__   :   Dict					)      ->    List[Any]:

						"""simple docstring"""





						__SCREAMING_SNAKE_CASE:				int           =   [0 for i in range(r + 1					)]
						# nc0 = 1
						__SCREAMING_SNAKE_CASE:				Dict           =   1
						for i in range(1       ,			n + 1					):
												# to compute current row from previous row.
												__SCREAMING_SNAKE_CASE:				Optional[Any]           =   min(UpperCamelCase__       ,			UpperCamelCase__					)
												while j > 0:
																		c[j] += c[j - 1]
																		j -= 1
						return c[r]




print(binomial_coefficient(n=10, r=5))



