

def       __lowerCAmelCase      (						A    ):
	UpperCAmelCase_       				=			[[0 for _ in range(__lowerCAmelCase    )] for _ in range(m + 1    )]
	for i in range(m + 1    ):
		UpperCAmelCase_       				=			1

	for n in range(m + 1    ):
		for k in range(1       ,     __lowerCAmelCase    ):
			memo[n][k] += memo[n][k - 1]
			if n - k > 0:
				memo[n][k] += memo[n - k - 1][k]

	return memo[m][m - 1]


if __name__ == "__main__":
				import sys

				if len(sys.argv) == 1:
								try:
												_a:    Optional[int] 							=			int(input("""Enter a number: """).strip())
												print(partition(n))
								except ValueError:
												print("""Please enter a number.""")
				else:
								try:
												_a:    int 							=			int(sys.argv[1])
												print(partition(n))
								except ValueError:
												print("""Please pass a number.""")







def       __lowerCAmelCase      (						A    ):
	UpperCAmelCase_       				=			generate_pascal_triangle(A    )
	for row_idx in range(A    ):
		# Print left spaces
		for _ in range(num_rows - row_idx - 1    ):
			print(end=" "    )
		# Print row values
		for col_idx in range(row_idx + 1    ):
			if col_idx != row_idx:
				print(triangle[row_idx][col_idx]       ,     end=" "    )
			else:
				print(triangle[row_idx][col_idx]       ,     end=""    )
		print()



def       __lowerCAmelCase      (						A    ):

	if not isinstance(A       ,     A    ):
		raise TypeError("The input value of 'num_rows' should be 'int'"    )

	if num_rows == 0:
		return []
	elif num_rows < 0:
		raise ValueError(
		    "The input value of 'num_rows' should be greater than or equal to 0"    )

	UpperCAmelCase_       				=			[]
	for current_row_idx in range(A    ):
		UpperCAmelCase_       				=			populate_current_row(A       ,     A    )
		triangle.append(A    )
	return triangle



def       __lowerCAmelCase      (						A       ,     A    ):
	UpperCAmelCase_       				=			[-1] * (current_row_idx + 1)
	# first and last elements of current row are equal to 1
	UpperCAmelCase_				,   UpperCAmelCase_       				=			1, 1
	for current_col_idx in range(1       ,     A    ):
		calculate_current_element(
		    A       ,     A       ,     A       ,     A    )
	return current_row



def       __lowerCAmelCase      (						A       ,     A       ,     A       ,     A       ,     ):
	UpperCAmelCase_       				=			triangle[current_row_idx - 1][current_col_idx - 1]
	UpperCAmelCase_       				=			triangle[current_row_idx - 1][current_col_idx]
	UpperCAmelCase_       				=			above_to_left_elt + above_to_right_elt



def       __lowerCAmelCase      (						A    ):

	if not isinstance(A       ,     A    ):
		raise TypeError("The input value of 'num_rows' should be 'int'"    )

	if num_rows == 0:
		return []
	elif num_rows < 0:
		raise ValueError(
		    "The input value of 'num_rows' should be greater than or equal to 0"    )

	UpperCAmelCase_       				=			[[1]]

	for row_index in range(1       ,     A    ):
		UpperCAmelCase_       				=			[0] + result[-1] + [0]
		UpperCAmelCase_       				=			row_index + 1
		# Calculate the number of distinct elements in a row
		UpperCAmelCase_       				=			sum(divmod(A       ,     2    )    )
		UpperCAmelCase_       				=			[
		    temp_row[i - 1] + temp_row[i] for i in range(1       ,     distinct_elements + 1    )
		]
		UpperCAmelCase_       				=			row_first_half[: (row_index + 1) // 2]
		row_second_half.reverse()
		UpperCAmelCase_       				=			row_first_half + row_second_half
		result.append(A    )

	return result



def       __lowerCAmelCase      (						):
	from collections.abc import Callable
	from timeit import timeit

	def benchmark_a_function(A       ,     A    ) -> None:
		UpperCAmelCase_       				=			F"{func.__name__}({value})"
		UpperCAmelCase_       				=			timeit(F"__main__.{call}"       ,     setup="import __main__"    )
		# print(f"{call:38} = {func(value)} -- {timing:.4f} seconds")
		print(F"{call:38} -- {timing:.4f} seconds"    )

	for value in range(15    ):  # (1, 7, 14):
		for func in (generate_pascal_triangle, generate_pascal_triangle_optimized):
			benchmark_a_function(A       ,     A    )
		print()


if __name__ == "__main__":
				import doctest

				doctest.testmod()
				benchmark()