def     UpperCAmelCase						(   lowercase							,      lowercase							):







				"""simple docstring"""



				__lowercase			      =							[]
				__lowercase			      =							len(lowercase							)
				for i in range(lowercase							):
								__lowercase			      =							[]
								for j in range(lowercase							):
												__lowercase			      =							0
												for k in range(lowercase							):
																__lowercase			      =							val + matrix_a[i][k] * matrix_b[k][j]
												list_a.append(lowercase							)
								matrix_c.append(lowercase							)
				return matrix_c





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				return [[int(row == column							) for column in range(lowercase							)] for row in range(lowercase							)]





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				if n <= 1:
								return n
				__lowercase			      =							identity(2							)
				__lowercase			      =							[[1, 1], [1, 0]]
				__lowercase			      =							n - 1
				while n > 0:
								if n % 2 == 1:
												__lowercase			      =							multiply(lowercase							,      lowercase							)
								__lowercase			      =							multiply(lowercase							,      lowercase							)
								__lowercase			      =							int(n / 2							)
				return res_matrix[0][0]





def     UpperCAmelCase						(   lowercase							):







				"""simple docstring"""



				if n <= 1:
								return n
				__lowercase			      =							0
				__lowercase			      =							1
				for _ in range(2							,      n + 1							):
								__lowercase      ,					__lowercase			      =							fiba, fiba + fiba
				return fiba





def     UpperCAmelCase						(   ):







				"""simple docstring"""



				for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
								__lowercase			      =							int(''''''.join(c for c in ordinal if c in '''0123456789'''							)							)  # 1000th --> 1000
								print(
								    F"{ordinal} fibonacci number using matrix exponentiation is "
								    F"{nth_fibonacci_matrix(lowercase							)} and using bruteforce is "
								    F"{nth_fibonacci_bruteforce(lowercase							)}\n"							)
				# from timeit import timeit
				# print(timeit("nth_fibonacci_matrix(1000000)",
				#              "from main import nth_fibonacci_matrix", number=5))
				# print(timeit("nth_fibonacci_bruteforce(1000000)",
				#              "from main import nth_fibonacci_bruteforce", number=5))
				# 2.3342058970001744
				# 57.256506615000035


if __name__ == "__main__":
							import doctest

							doctest.testmod()
							main()
__a  :					Union[str, Any]          =  [[0, 1, 1], [0, 0, 1], [1, 0, 0]]




class        _UpperCamelCase				:


			"""simple docstring"""






			def __init__(       self				,       lowerCAmelCase__						)					-> List[str]:

							'''simple docstring'''


							__lowercase			      =							name
							__lowercase			      =							[]
							__lowercase			      =							[]





			def 	_SCREAMING_SNAKE_CASE      (       self				,       lowerCAmelCase__						)					-> Union[str, Any]:

							'''simple docstring'''


							self.inbound.append(lowerCAmelCase__						)





			def 	_SCREAMING_SNAKE_CASE      (       self				,       lowerCAmelCase__						)					-> Union[str, Any]:

							'''simple docstring'''


							self.outbound.append(lowerCAmelCase__						)





			def __repr__(       self						)					-> Tuple:

							'''simple docstring'''


							return F"<node={self.name} inbound={self.inbound} outbound={self.outbound}>"





def     UpperCAmelCase						(   lowercase							,      lowercase=3							,      lowercase=0.85							):







				"""simple docstring"""



				__lowercase			      =							{}
				for node in nodes:
								__lowercase			      =							1

				__lowercase			      =							{}
				for node in nodes:
								__lowercase			      =							len(node.outbound							)

				for i in range(lowercase							):
								print(F"======= Iteration {i + 1} ======="							)
								for _, node in enumerate(lowercase							):
												__lowercase			      =							(1 - d) + d * sum(
												    ranks[ib] / outbounds[ib] for ib in node.inbound							)
								print(lowercase							)





def     UpperCAmelCase						(   ):







				"""simple docstring"""



				__lowercase			      =							list(input('''Enter Names of the Nodes: '''							).split()							)

				__lowercase			      =							[Node(lowercase							) for name in names]

				for ri, row in enumerate(lowercase							):
								for ci, col in enumerate(lowercase							):
												if col == 1:
																nodes[ci].add_inbound(names[ri]							)
																nodes[ri].add_outbound(names[ci]							)

				print('''======= Nodes ======='''							)
				for node in nodes:
								print(lowercase							)

				page_rank(lowercase							)


if __name__ == "__main__":
		main()