'''simple docstring'''






import re

from flax.core.frozen_dict import freeze
from flax.traverse_util import flatten_dict, unflatten_dict
from jax.experimental import PartitionSpec as P


# Sentinels
SCREAMING_SNAKE_CASE_	   =			object()

# For specifying empty leaf dict `{}`
SCREAMING_SNAKE_CASE_	   =			object()






def  UpperCamelCase__					(					_lowercase    :				Dict   ,    _lowercase    :				Dict     )							->	Any:
  __UpperCAmelCase:					Dict		= tuple((re.compile(x + """$"""     ) for x in qs)     )
  for i in range(len(_lowercase     ) - len(_lowercase     ) + 1     ):
    __UpperCAmelCase:					Union[str, Any]		= [x.match(_lowercase     ) for x, y in zip(_lowercase   ,    ks[i:]     )]
    if matches and all(_lowercase     ):
      return True
  return False






def  UpperCamelCase__					(					_lowercase    :				Optional[Any]     )							->	Tuple:
  def replace(_lowercase    :				Dict   ,    _lowercase    :				Union[str, Any]     ):
    for rule, replacement in rules:
      if _match(_lowercase   ,    _lowercase     ):
        return replacement
    return val

  return replace






def  UpperCamelCase__					(					)							->	Optional[Any]:
  return [
      # embeddings
      (("transformer", "wpe", "embedding"), P("""mp"""   ,    _lowercase     )),
      (("transformer", "wte", "embedding"), P("""mp"""   ,    _lowercase     )),
      # atention
      (("attention", "(q_proj|k_proj|v_proj)", "kernel"), P(_lowercase   ,    """mp"""     )),
      (("attention", "out_proj", "kernel"), P("""mp"""   ,    _lowercase     )),
      (("attention", "out_proj", "bias"), None),
      # mlp
      (("mlp", "c_fc", "kernel"), P(_lowercase   ,    """mp"""     )),
      (("mlp", "c_fc", "bias"), P("""mp"""     )),
      (("mlp", "c_proj", "kernel"), P("""mp"""   ,    _lowercase     )),
      (("mlp", "c_proj", "bias"), None),
      # layer norms
      ((r"ln_\d+", "bias"), None),
      ((r"\d+", r"ln_\d+", "scale"), None),
      (("ln_f", "bias"), None),
      (("ln_f", "scale"), None),
  ]







def  UpperCamelCase__					(					_lowercase    :				List[Any]     )							->	int:
  __UpperCAmelCase:					Optional[int]		= _get_partition_rules()
  __UpperCAmelCase:					Union[str, Any]		= _replacement_rules(_lowercase     )
  __UpperCAmelCase:					List[Any]		= {k: _unmatched for k in flatten_dict(_lowercase     )}
  __UpperCAmelCase:					List[Any]		= {k: replace(_lowercase   ,    _lowercase     ) for k, v in initd.items()}
  assert _unmatched not in result.values(), "Incomplete partition spec."
  return freeze(unflatten_dict(_lowercase     )     )
'''simple docstring'''






def  UpperCamelCase__					(					_lowercase    :				List[str]     )							->	Union[str, Any]:
  __UpperCAmelCase:					int		= []
  __UpperCAmelCase:					List[Any]		= []
  __UpperCAmelCase:					List[Any]		= {
      """^""": 3,
      """*""": 2,
      """/""": 2,
      """%""": 2,
      """+""": 1,
      """-""": 1,
  }  # Priority of each operator
  __UpperCAmelCase:					int		= 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  UpperCamelCase__					(					_lowercase    :				str     )							->	Tuple:
  __UpperCAmelCase:					Union[str, Any]		= list(infix[::-1]     )  # reverse the infix equation

  for i in range(len(_lowercase     )     ):
    if infix[i] == "(":
      __UpperCAmelCase:					Tuple		= """)"""  # change "(" to ")"
    elif infix[i] == ")":
      __UpperCAmelCase:					Union[str, Any]		= """("""  # change ")" to "("

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


if __name__ == "__main__":
    SCREAMING_SNAKE_CASE_	   =			input('\nEnter an Infix Equation = ')  # Input an Infix equation
    SCREAMING_SNAKE_CASE_	   =			''.join(Infix.split())  # Remove spaces from the input
    print('\n\t', Infix, '(Infix) -> ', infix_2_prefix(Infix), '(Prefix)')