




"""simple docstring"""




from __future__ import annotations

import sys







def       __UpperCAmelCase      (				__UpperCamelCase					):
			if n < 0:
						raise ValueError('''Negative arguments are not supported'''					)
			return _fib(__UpperCamelCase					)[0]







def       __UpperCAmelCase      (				__UpperCamelCase					):
			if n == 0:  # (F(0), F(1))
						return (0, 1)

			# F(2n) = F(n)[2F(n+1) − F(n)]
			# F(2n+1) = F(n+1)^2+F(n)^2
			__lowercase	,__lowercase	:       List[Any]				=   _fib(n // 2					)
			__lowercase	:       Any				=   a * (b * 2 - a)
			__lowercase	:       str				=   a * a + b * b
			return (d, c + d) if n % 2 else (c, d)


if __name__ == "__main__":
			a_            =   int(sys.argv[1])
			print(F"fibonacci({n}) is {fibonacci(n)}")









"""simple docstring"""




# A Bipartite Graph is a graph whose vertices can be divided into two independent sets,
# U and V such that every edge (u, v) either connects a vertex from U to V or a vertex
# from V to U. In other words, for every edge (u, v), either u belongs to U and v to V,
# or u belongs to V and v to U. We can also say that there is no edge that connects
# vertices of same set.
from queue import Queue







def       __UpperCAmelCase      (				__UpperCamelCase					):
			__lowercase	:       int				=   Queue()
			__lowercase	:       str				=   [False] * len(__UpperCamelCase					)
			__lowercase	:       str				=   [-1] * len(__UpperCamelCase					)

			def bfs():
						while not queue.empty():
									__lowercase	:       int				=   queue.get()
									__lowercase	:       List[str]				=   True

									for neighbour in graph[u]:
												if neighbour == u:
															return False

												if color[neighbour] == -1:
															__lowercase	:       str				=   1 - color[u]
															queue.put(__UpperCamelCase					)

												elif color[neighbour] == color[u]:
															return False

						return True

			for i in range(len(__UpperCamelCase					)					):
						if not visited[i]:
									queue.put(__UpperCamelCase					)
									__lowercase	:       int				=   0
									if bfs() is False:
												return False

			return True


if __name__ == "__main__":
			# Adjacency List of graph
			print(check_bipartite({0: [1, 3], 1: [0, 2], 2: [1, 3], 3: [0, 2]}))



