


'''simple docstring'''




def 				a_							(    lowercase				,    lowercase     )      ->Optional[Any]:






				'''simple docstring'''

				__lowerCamelCase		:   Tuple           =       []
				__lowerCamelCase		:   Any           =       len(SCREAMING_SNAKE_CASE__     )
				for i in range(SCREAMING_SNAKE_CASE__     ):
								__lowerCamelCase		:   Any           =       []
								for j in range(SCREAMING_SNAKE_CASE__     ):
												__lowerCamelCase		:   Union[str, Any]           =       0
												for k in range(SCREAMING_SNAKE_CASE__     ):
																__lowerCamelCase		:   Optional[int]           =       val + matrix_a[i][k] * matrix_b[k][j]
												list_a.append(SCREAMING_SNAKE_CASE__     )
								matrix_c.append(SCREAMING_SNAKE_CASE__     )
				return matrix_c





def 				a_							(    lowercase     )      ->Optional[Any]:






				'''simple docstring'''

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





def 				a_							(    lowercase     )      ->Any:






				'''simple docstring'''

				if n <= 1:
								return n
				__lowerCamelCase		:   Tuple           =       identity(2     )
				__lowerCamelCase		:   List[Any]           =       [[1, 1], [1, 0]]
				__lowerCamelCase		:   Union[str, Any]           =       n - 1
				while n > 0:
								if n % 2 == 1:
												__lowerCamelCase		:   Dict           =       multiply(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__     )
								__lowerCamelCase		:   Optional[Any]           =       multiply(SCREAMING_SNAKE_CASE__				,    SCREAMING_SNAKE_CASE__     )
								__lowerCamelCase		:   Optional[int]           =       int(n / 2     )
				return res_matrix[0][0]





def 				a_							(    lowercase     )      ->Dict:






				'''simple docstring'''

				if n <= 1:
								return n
				__lowerCamelCase		:   Dict           =       0
				__lowerCamelCase		:   List[str]           =       1
				for _ in range(2				,    n + 1     ):
								__lowerCamelCase    ,       __lowerCamelCase		:   Dict           =       fiba, fiba + fiba
				return fiba





def 				a_							(    )      ->List[Any]:






				'''simple docstring'''

				for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
								__lowerCamelCase		:   Optional[Any]           =       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(SCREAMING_SNAKE_CASE__     )} and using bruteforce is '
								    F'{nth_fibonacci_bruteforce(SCREAMING_SNAKE_CASE__     )}\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()









def 		_UpperCAmelCase							(     SCREAMING_SNAKE_CASE__     :   list     ,	SCREAMING_SNAKE_CASE__     :   int     ,	SCREAMING_SNAKE_CASE__     :   int     ,	SCREAMING_SNAKE_CASE__     :   int							):
     __UpperCamelCase       				=int((lower_bound + upper_bound) // 2							)
     if array[r] == value:
          return r
     if lower_bound >= upper_bound:
          return -1
     if array[r] < value:
          return binary_search(SCREAMING_SNAKE_CASE__     ,	r + 1     ,	SCREAMING_SNAKE_CASE__     ,	SCREAMING_SNAKE_CASE__							)
     else:
          return binary_search(SCREAMING_SNAKE_CASE__     ,	SCREAMING_SNAKE_CASE__     ,	r - 1     ,	SCREAMING_SNAKE_CASE__							)

def 		_UpperCAmelCase							(     SCREAMING_SNAKE_CASE__     :   int     ,	SCREAMING_SNAKE_CASE__     :   list							):
     __UpperCamelCase       				=0
     if matrix[index][0] == value:
          return [index, 0]
     while index < len(SCREAMING_SNAKE_CASE__							) and matrix[index][0] < value:
          __UpperCamelCase       				=binary_search(matrix[index]     ,	0     ,	len(matrix[index]							) - 1     ,	SCREAMING_SNAKE_CASE__							)
          if r != -1:
               return [index, r]
          index += 1
     return [-1, -1]


if __name__ == "__main__":
   import doctest

   doctest.testmod()





