


def 				UpperCamelCase      (			__magic_name__  :							list[list[int]]					,					__magic_name__  :							list[list[int]]  )     ->						list[list[int]]:
		"""simple docstring"""




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






def 				UpperCamelCase      (			__magic_name__  :							int  )     ->						list[list[int]]:
		"""simple docstring"""




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






def 				UpperCamelCase      (			__magic_name__  :							int  )     ->						int:
		"""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(__magic_name__					,					__magic_name__  )
				lowercase__      =	multiply(__magic_name__					,					__magic_name__  )
				lowercase__      =	int(n / 2  )
		return res_matrix[0][0]






def 				UpperCamelCase      (			__magic_name__  :							int  )     ->						int:
		"""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      (			)     ->						None:
		"""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(__magic_name__  )} and using bruteforce is '''
				    f'''{nth_fibonacci_bruteforce(__magic_name__  )}\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()





from __future__ import annotations






def 				UpperCamelCase      (			__magic_name__  :							list[list[int]]					,					__magic_name__  :							list[list[int]]  )     ->						list[int]:
		"""simple docstring"""




		assert len(__magic_name__  ) == len(__magic_name__  )

		lowercase__      =	len(__magic_name__  )
		lowercase__      =	list(range(__magic_name__  )  )
		lowercase__      =	[-1] * n  # who the donor has donated to
		lowercase__      =	[-1] * n  # who the recipient has received from
		lowercase__      =	[0] * n

		while unmatched_donors:
				lowercase__      =	unmatched_donors[0]
				lowercase__      =	donor_pref[donor]
				lowercase__      =	donor_preference[num_donations[donor]]
				num_donations[donor] += 1
				lowercase__      =	recipient_pref[recipient]
				lowercase__      =	rec_record[recipient]

				if prev_donor != -1:
						if rec_preference.index(__magic_name__  ) > rec_preference.index(__magic_name__  ):
								lowercase__      =	donor
								lowercase__      =	recipient
								unmatched_donors.append(__magic_name__  )
								unmatched_donors.remove(__magic_name__  )
				else:
						lowercase__      =	donor
						lowercase__      =	recipient
						unmatched_donors.remove(__magic_name__  )
		return donor_record

