


"""simple docstring"""




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





def 			a_   (  lowercase__   :int    ):
			return [[int(row == column    ) for column in range(lowercase__    )] for row in range(lowercase__    )]





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





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





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




import numpy as np





def 			a_   (  lowercase__   :List[str]    ):
			__lowerCamelCase        =			np.exp(lowercase__    )

			# Add up the all the exponentials
			__lowerCamelCase        =			np.sum(lowercase__    )

			# Divide every exponent by the sum of all exponents
			__lowerCamelCase        =			exponent_vector / sum_of_exponents

			return softmax_vector


if __name__ == "__main__":
					print(softmax((0,)))




