

"""simple docstring"""




def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							list[int | list]		,    SCREAMING_SNAKE_CASE_:							int )     -> int:




				'''simple docstring'''





				A__            =     0
				for ele in arr:
								total_sum += product_sum(SCREAMING_SNAKE_CASE_		,    depth + 1 ) if isinstance(SCREAMING_SNAKE_CASE_		,    SCREAMING_SNAKE_CASE_ ) else ele
				return total_sum * depth



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							list[int | list] )     -> int:




				'''simple docstring'''





				return product_sum(SCREAMING_SNAKE_CASE_		,    1 )


if __name__ == "__main__":
	import doctest

	doctest.testmod()




from .balanced_parentheses import balanced_parentheses
from .stack import Stack



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							str )     -> int:




				'''simple docstring'''





				return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(SCREAMING_SNAKE_CASE_		,    -1 )



def    lowerCAmelCase__							(		SCREAMING_SNAKE_CASE_:							str )     -> str:




				'''simple docstring'''





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


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

	testmod()
	lowerCAmelCase__						=	"""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))

