




from __future__ import annotations

import math







def SCREAMING_SNAKE_CASE    (	lowercase_			,    lowercase_			,    lowercase_			,    lowercase_			,    lowercase_						)       ->	str:



       """simple docstring"""

       if depth < 0:
              raise ValueError('''Depth cannot be less than 0'''						)

       if not scores:
              raise ValueError('''Scores cannot be empty'''						)

       if depth == height:
              return scores[node_index]

       return (
           max(
               minimax(depth + 1			,    node_index * 2			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__						)			,    minimax(depth + 1			,    node_index * 2 + 1			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__						)			,    )
           if is_max
           else min(
               minimax(depth + 1			,    node_index * 2			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__						)			,    minimax(depth + 1			,    node_index * 2 + 1			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__						)			,    )
       )







def SCREAMING_SNAKE_CASE    (	)       ->	Any:



       """simple docstring"""

       A__							=   [90, 23, 6, 33, 21, 65, 123, 34_423]
       A__							=   math.log(len(lowerCAmelCase__						)			,    2						)
       print(f"""Optimal value : {minimax(0			,    0			,    lowerCAmelCase__			,    lowerCAmelCase__			,    lowerCAmelCase__						)}"""						)


if __name__ == "__main__":
  import doctest

  doctest.testmod()
  main()








def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	str:



       """simple docstring"""

       A__							=   []
       A__							=   []
       A__							=   {
           '''^''': 3,
           '''*''': 2,
           '''/''': 2,
           '''%''': 2,
           '''+''': 1,
           '''-''': 1,
       }  # Priority of each operator
       A__							=   len(lowercase_						) if (len(lowercase_						) > 7) else 7

       # Print table header for output
       print(
           '''Symbol'''.center(8						)			,    '''Stack'''.center(lowercase_						)			,    '''Postfix'''.center(lowercase_						)			,    sep=''' | '''			,    )
       print('''-''' * (print_width * 3 + 7)						)

       for x in infix:
              if x.isalpha() or x.isdigit():
                     post_fix.append(lowercase_						)  # if x is Alphabet / Digit, add it to Postfix
              elif x == "(":
                     stack.append(lowercase_						)  # if x is "(" push to Stack
              elif x == ")":  # if x is ")" pop stack until "(" is encountered
                     while stack[-1] != "(":
                            post_fix.append(stack.pop()						)  # Pop stack & add the content to Postfix
                     stack.pop()
              else:
                     if len(lowercase_						) == 0:
                            stack.append(lowercase_						)  # If stack is empty, push x to stack
                     else:  # while priority of x is not > priority of element in the stack
                            while len(lowercase_						) > 0 and priority[x] <= priority[stack[-1]]:
                                   post_fix.append(stack.pop()						)  # pop stack & add to Postfix
                            stack.append(lowercase_						)  # push x to stack

              print(
                  x.center(8						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    sep=''' | '''			,    )  # Output in tabular format

       while len(lowercase_						) > 0:  # while stack is not empty
              post_fix.append(stack.pop()						)  # pop stack & add to Postfix
              print(
                  ''' '''.center(8						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    (''''''.join(lowercase_						)).ljust(lowercase_						)			,    sep=''' | '''			,    )  # Output in tabular format

       return "".join(lowercase_						)  # return Postfix as str







def SCREAMING_SNAKE_CASE    (	lowercase_						)       ->	Optional[Any]:



       """simple docstring"""

       A__							=   list(infix[::-1]						)  # reverse the infix equation

       for i in range(len(lowercase_						)						):
              if infix[i] == "(":
                     A__							=   ''')'''  # change "(" to ")"
              elif infix[i] == ")":
                     A__							=   '''('''  # change ")" to "("

       return (infix_2_postfix(''''''.join(lowercase_						)						))[
           ::-1
       ]  # call infix_2_postfix on Infix, return reverse of Postfix


if __name__ == "__main__":
  _lowerCamelCase     :		List[str]								=       input("""\nEnter an Infix Equation = """)  # Input an Infix equation
  _lowerCamelCase     :		Dict								=       """""".join(Infix.split())  # Remove spaces from the input
  print("""\n\t""", Infix, """(Infix) -> """, infix_2_prefix(Infix), """(Prefix)""")


