code: 
  
  
  """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()
  
  
  
  
  
style_context: 
  
  
  """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,)))
  
  
  
  
  