



"""simple docstring"""


def 					_lowerCAmelCase (  lowercase_						,      lowercase_		):
						UpperCAmelCase			 =					[]
						UpperCAmelCase			 =					len(lowercase_		)
						for i in range(lowercase_		):
												UpperCAmelCase			 =					[]
												for j in range(lowercase_		):
																		UpperCAmelCase			 =					0
																		for k in range(lowercase_		):
																								UpperCAmelCase			 =					val + matrix_a[i][k] * matrix_b[k][j]
																		list_a.append(lowercase_		)
												matrix_c.append(lowercase_		)
						return matrix_c

def 					_lowerCAmelCase (  lowercase_		):
						return [[int(row == column		) for column in range(lowercase_		)] for row in range(lowercase_		)]

def 					_lowerCAmelCase (  lowercase_		):
						if n <= 1:
												return n
						UpperCAmelCase			 =					identity(2		)
						UpperCAmelCase			 =					[[1, 1], [1, 0]]
						UpperCAmelCase			 =					n - 1
						while n > 0:
												if n % 2 == 1:
																		UpperCAmelCase			 =					multiply(lowercase_						,      lowercase_		)
												UpperCAmelCase			 =					multiply(lowercase_						,      lowercase_		)
												UpperCAmelCase			 =					int(n / 2		)
						return res_matrix[0][0]

def 					_lowerCAmelCase (  lowercase_		):
						if n <= 1:
												return n
						UpperCAmelCase			 =					0
						UpperCAmelCase			 =					1
						for _ in range(2						,      n + 1		):
												UpperCAmelCase ,       UpperCAmelCase			 =					fiba, fiba + fiba
						return fiba

def 					_lowerCAmelCase (  ):
						for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
												UpperCAmelCase			 =					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()










"""simple docstring"""


def 					_lowerCAmelCase (  lowercase_		):
						return " ".join(sorted(set(sentence.split()		)		)		)


if __name__ == "__main__":
				import doctest

				doctest.testmod()





