






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







def   snake_case		(				UpperCAmelCase						:							int ):
				return [[int(row == column ) for column in range(UpperCAmelCase )] for row in range(UpperCAmelCase )]







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







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







def   snake_case		(				):
				for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
								A									=   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   snake_case		(				UpperCAmelCase						:							int,    UpperCAmelCase						:							list[int],    UpperCAmelCase						:							list[int],    UpperCAmelCase						:							int ):

				# Base Case
				if counter == 0 or capacity == 0:
								return 0

				# If weight of the nth item is more than Knapsack of capacity,
				#   then this item cannot be included in the optimal solution,
				# else return the maximum of two cases:
				#   (1) nth item included
				#   (2) not included
				if weights[counter - 1] > capacity:
								return knapsack(UpperCAmelCase,    UpperCAmelCase,    UpperCAmelCase,    counter - 1 )
				else:
								A									=   capacity - weights[counter - 1]
								A									=   values[counter - 1] + knapsack(
								    UpperCAmelCase,    UpperCAmelCase,    UpperCAmelCase,    counter - 1 )
								A									=   knapsack(UpperCAmelCase,    UpperCAmelCase,    UpperCAmelCase,    counter - 1 )
								return max(UpperCAmelCase,    UpperCAmelCase )


if __name__ == "__main__":
					import doctest

					doctest.testmod()





