

def  UpperCAmelCase_   (_lowerCAmelCase :		list[list[int]]     ,			_lowerCAmelCase :		list[list[int]]		):
			__UpperCamelCase    :    Optional[Any]								=      []
			__UpperCamelCase    :    Dict								=      len(_lowerCAmelCase		)
			for i in range(_lowerCAmelCase		):
						__UpperCamelCase    :    int								=      []
						for j in range(_lowerCAmelCase		):
									__UpperCamelCase    :    Dict								=      0
									for k in range(_lowerCAmelCase		):
												__UpperCamelCase    :    Tuple								=      val + matrix_a[i][k] * matrix_b[k][j]
									list_a.append(_lowerCAmelCase		)
						matrix_c.append(_lowerCAmelCase		)
			return matrix_c







def  UpperCAmelCase_   (_lowerCAmelCase :		int		):
			return [[int(row == column		) for column in range(_lowerCAmelCase		)] for row in range(_lowerCAmelCase		)]







def  UpperCAmelCase_   (_lowerCAmelCase :		int		):
			if n <= 1:
						return n
			__UpperCamelCase    :    int								=      identity(2		)
			__UpperCamelCase    :    str								=      [[1, 1], [1, 0]]
			__UpperCamelCase    :    Optional[Any]								=      n - 1
			while n > 0:
						if n % 2 == 1:
									__UpperCamelCase    :    Union[str, Any]								=      multiply(_lowerCAmelCase     ,			_lowerCAmelCase		)
						__UpperCamelCase    :    Union[str, Any]								=      multiply(_lowerCAmelCase     ,			_lowerCAmelCase		)
						__UpperCamelCase    :    Dict								=      int(n / 2		)
			return res_matrix[0][0]







def  UpperCAmelCase_   (_lowerCAmelCase :		int		):
			if n <= 1:
						return n
			__UpperCamelCase    :    Tuple								=      0
			__UpperCamelCase    :    str								=      1
			for _ in range(2     ,			n + 1		):
						__UpperCamelCase							,				__UpperCamelCase    :    Optional[int]								=      fiba, fiba + fiba
			return fiba







def  UpperCAmelCase_   ():
			for ordinal in "0th 1st 2nd 3rd 10th 100th 1000th".split():
						__UpperCamelCase    :    int								=      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(_lowerCAmelCase		)} and using bruteforce is '''
						    F'''{nth_fibonacci_bruteforce(_lowerCAmelCase		)}\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 .balanced_parentheses import balanced_parentheses
from .stack import Stack







def  UpperCAmelCase_   (_lowerCAmelCase :		str		):
			return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(_lowerCAmelCase     ,			-1		)







def  UpperCAmelCase_   (_lowerCAmelCase :		str		):
			if not balanced_parentheses(_lowerCAmelCase		):
						raise ValueError("Mismatched parentheses"		)
			__UpperCamelCase    :    Stack[str]								=      Stack()
			__UpperCamelCase    :    int								=      []
			for char in expression_str:
						if char.isalpha() or char.isdigit():
									postfix.append(_lowerCAmelCase		)
						elif char == "(":
									stack.push(_lowerCAmelCase		)
						elif char == ")":
									while not stack.is_empty() and stack.peek() != "(":
												postfix.append(stack.pop()		)
									stack.pop()
						else:
									while not stack.is_empty() and precedence(_lowerCAmelCase		) <= precedence(stack.peek()		):
												postfix.append(stack.pop()		)
									stack.push(_lowerCAmelCase		)
			while not stack.is_empty():
						postfix.append(stack.pop()		)
			return " ".join(_lowerCAmelCase		)


if __name__ == "__main__":
					from doctest import testmod

					testmod()
					lowercase     :       int        =       "a+b*(c^d-e)^(f+g*h)-i"

					print("Infix to Postfix Notation demonstration:\n")
					print("Infix notation: " + expression)
					print("Postfix notation: " + infix_to_postfix(expression))