



def  __lowerCamelCase (       lowerCamelCase__					,			lowerCamelCase__						):

			"""simple docstring"""


			lowercase__					:   str													=					1  # To kept the Calculated Value
			# Since C(n, k) = C(n, n-k)
			if k > (n - k):
						lowercase__					:   Optional[Any]													=					n - k
			# Calculate C(n,k)
			for i in range(lowerCamelCase__						):
						result *= n - i
						result //= i + 1
			return result


def  __lowerCamelCase (       lowerCamelCase__						):

			"""simple docstring"""


			return binomial_coefficient(2 * node_count					,			lowerCamelCase__						) // (node_count + 1)


def  __lowerCamelCase (       lowerCamelCase__						):

			"""simple docstring"""


			if n < 0:
						raise ValueError("factorial() not defined for negative values"						)
			lowercase__					:   Any													=					1
			for i in range(1					,			n + 1						):
						result *= i
			return result


def  __lowerCamelCase (       lowerCamelCase__						):

			"""simple docstring"""


			return catalan_number(lowerCamelCase__						) * factorial(lowerCamelCase__						)


if __name__ == "__main__":
				lowerCAmelCase__					  =  int(input('''Enter the number of nodes: ''').strip() or 0)
				if node_count <= 0:
								raise ValueError('''We need some nodes to work with.''')
				print(
				    f'''Given {node_count} nodes, there are {binary_tree_count(node_count)} '''
				    f'''binary trees and {catalan_number(node_count)} binary search trees.'''
				)









from collections import Counter
from timeit import timeit


def  __lowerCamelCase (       lowerCamelCase__ = ""					,			):

				"""simple docstring"""


				return sum(c % 2 for c in Counter(input_str.replace(" "					,			""						).lower()						).values()						) < 2


def  __lowerCamelCase (       lowerCamelCase__ = ""						):

				"""simple docstring"""


				if len(lowerCamelCase__						) == 0:
								return True
				lowercase__					:   str													=					input_str.replace(" "					,			""						).lower()
				# character_freq_dict: Stores the frequency of every character in the input string
				lowercase__					:   dict[str, int]													=					{}

				for character in lower_case_input_str:
								lowercase__					:   List[Any]													=					character_freq_dict.get(lowerCamelCase__					,			0						) + 1
				lowercase__					:   List[Any]													=					0

				for character_count in character_freq_dict.values():
								if character_count % 2:
												odd_char += 1
				if odd_char > 1:
								return False
				return True


def  __lowerCamelCase (       lowerCamelCase__ = ""						):

				"""simple docstring"""


				print("\nFor string = "					,			lowerCamelCase__					,			":"						)
				print(
				    "> can_string_be_rearranged_as_palindrome_counter()"					,			"\tans ="					,			can_string_be_rearranged_as_palindrome_counter(lowerCamelCase__						)					,			"\ttime ="					,			timeit(
				        "z.can_string_be_rearranged_as_palindrome_counter(z.check_str)"					,			setup="import __main__ as z"					,			)					,			"seconds"					,			)
				print(
				    "> can_string_be_rearranged_as_palindrome()"					,			"\tans ="					,			can_string_be_rearranged_as_palindrome(lowerCamelCase__						)					,			"\ttime ="					,			timeit(
				        "z.can_string_be_rearranged_as_palindrome(z.check_str)"					,			setup="import __main__ as z"					,			)					,			"seconds"					,			)


if __name__ == "__main__":
				lowerCAmelCase__					  =  input(
				    '''Enter string to determine if it can be rearranged as a palindrome or not: '''
				).strip()
				benchmark(check_str)
				lowerCAmelCase__					  =  can_string_be_rearranged_as_palindrome_counter(check_str)
				print(f'''{check_str} can {"" if status else "not "}be rearranged as a palindrome''')




