




'''simple docstring'''







import itertools



def 					lowerCamelCase__							(			__lowercase = 1_000_000							):
     snake_case :			Dict					   = [1]

     for i in itertools.count(len(__lowercase							)							):
          snake_case :			Optional[int]					   = 0
          for j in itertools.count(1							):
               snake_case :			Dict					   = -1 if j % 2 == 0 else +1
               snake_case :			Dict					   = (j * j * 3 - j) // 2
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number
               index += j
               if index > i:
                    break
               item += partitions[i - index] * sign
               item %= number

          if item == 0:
               return i
          partitions.append(__lowercase							)

     return 0


if __name__ == "__main__":
      import doctest

      doctest.testmod()

      print(F"""{solution() = }""")









'''simple docstring'''







from .balanced_parentheses import balanced_parentheses
from .stack import Stack



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



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


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

      testmod()
      lowercase			:      Tuple			=					"""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))



