





def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							list[list[int]]   ,				UpperCamelCase__:							list[list[int]]      ):
		SCREAMING_SNAKE_CASE__								= []
		SCREAMING_SNAKE_CASE__								= len(UpperCamelCase__      )
		for i in range(UpperCamelCase__      ):
				SCREAMING_SNAKE_CASE__								= []
				for j in range(UpperCamelCase__      ):
						SCREAMING_SNAKE_CASE__								= 0
						for k in range(UpperCamelCase__      ):
								SCREAMING_SNAKE_CASE__								= val + matrix_a[i][k] * matrix_b[k][j]
						list_a.append(UpperCamelCase__      )
				matrix_c.append(UpperCamelCase__      )
		return matrix_c






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int      ):
		return [[int(row == column      ) for column in range(UpperCamelCase__      )] for row in range(UpperCamelCase__      )]






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






def 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							int      ):
		if n <= 1:
				return n
		SCREAMING_SNAKE_CASE__								= 0
		SCREAMING_SNAKE_CASE__								= 1
		for _ in range(2   ,				n + 1      ):
				SCREAMING_SNAKE_CASE__		,  SCREAMING_SNAKE_CASE__								= fiba, fiba + fiba
		return fiba






def 			SCREAMING_SNAKE_CASE__							(    ):
		for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
				SCREAMING_SNAKE_CASE__								= 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(UpperCamelCase__      )} and using bruteforce is '''
				    f'''{nth_fibonacci_bruteforce(UpperCamelCase__      )}\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 			SCREAMING_SNAKE_CASE__							(    UpperCamelCase__:							list[int | float]      ):
		if len(UpperCamelCase__      ) == 0:
				raise ValueError("""find_min() arg is an empty sequence"""      )
		SCREAMING_SNAKE_CASE__								= nums[0]
		for num in nums:
				SCREAMING_SNAKE_CASE__								= min(UpperCamelCase__   ,				UpperCamelCase__      )
		return min_num


if __name__ == "__main__":
	import doctest

	doctest.testmod(verbose=True)