


"""simple docstring"""
def 						_a				(      _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				)    ->				bool:
							return not any(
							    neighbour == 1 and colored_vertices[i] == color
							    for i, neighbour in enumerate(_SCREAMING_SNAKE_CASE				)				)







def 						_a				(      _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				)    ->				bool:

							# Base Case
							if index == len(_SCREAMING_SNAKE_CASE				):
														return True

							# Recursive Step
							for i in range(_SCREAMING_SNAKE_CASE				):
														if valid_coloring(graph[index]				, _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				):
																					# Color current vertex
																					snake_case_           =		i
																					# Validate coloring
																					if util_color(_SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				, index + 1				):
																												return True
																					# Backtrack
																					snake_case_           =		-1
							return False







def 						_a				(      _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				)    ->				list[int]:
							snake_case_           =		[-1] * len(_SCREAMING_SNAKE_CASE				)

							if util_color(_SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				, _SCREAMING_SNAKE_CASE				, 0				):
														return colored_vertices

							return []







"""simple docstring"""
from math import factorial







def 						_a				(      _SCREAMING_SNAKE_CASE = 20				)    ->				int:
							snake_case_           =		2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
							# 2, 3,...
							snake_case_           =		n // 2

							return int(factorial(_SCREAMING_SNAKE_CASE				) / (factorial(_SCREAMING_SNAKE_CASE				) * factorial(n - k				))				)


if __name__ == "__main__":
				import sys

				if len(sys.argv) == 1:
								print(solution(20))
				else:
								try:
												__SCREAMING_SNAKE_CASE							:    Optional[int]		=    int(sys.argv[1])
												print(solution(n))
								except ValueError:
												print('Invalid entry - please enter a number.')



