from __future__ import annotations
def 		snake_case__  (		lowercase       ,							lowercase       ,							lowercase				):
   if len(lowercase				) == 0:
      raise ValueError("find_min() arg is an empty sequence"				)
   if (
       left >= len(lowercase				)
       or left < -len(lowercase				)
       or right >= len(lowercase				)
       or right < -len(lowercase				)
   ):
      raise IndexError("list index out of range"				)
   if left == right:
      return nums[left]
   lowerCAmelCase_:       str         =  (left + right) >> 1  # the middle
   lowerCAmelCase_:       List[Any]         =  find_min(lowercase       ,							lowercase       ,							lowercase				)  # find min in range[left, mid]
   lowerCAmelCase_:       Dict         =  find_min(lowercase       ,							mid + 1       ,							lowercase				)  # find min in range[mid + 1, right]

   return left_min if left_min <= right_min else right_min


if __name__ == "__main__":
     import doctest

     doctest.testmod(verbose=True)
from .balanced_parentheses import balanced_parentheses
from .stack import Stack
def 		snake_case__  (		lowercase				):
   return {"+": 1, "-": 1, "*": 2, "/": 2, "^": 3}.get(lowercase       ,							-1				)
def 		snake_case__  (		lowercase				):
   if not balanced_parentheses(lowercase				):
      raise ValueError("Mismatched parentheses"				)
   lowerCAmelCase_:       Stack[str]         =  Stack()
   lowerCAmelCase_:       Union[str, 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()
 a     :			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))