



"""simple docstring"""







import dataclasses
import json
import sys
import types
from argparse import ArgumentDefaultsHelpFormatter, ArgumentParser, ArgumentTypeError
from copy import copy
from enum import Enum
from inspect import isclass
from pathlib import Path
from typing import Any, Callable, Dict, Iterable, List, Literal, NewType, Optional, Tuple, Union, get_type_hints

import yaml


lowercase__		:    Dict				   =			NewType("""DataClass""", Any)
lowercase__		:    int				   =			NewType("""DataClassType""", Any)

def     UpperCamelCase_   (   lowerCAmelCase__				:    int						)						->       int:

  """simple docstring"""




  if isinstance(__lowerCamelCase   ,       __lowerCamelCase						):
    return v
  if v.lower() in ("yes", "true", "t", "y", "1"):
    return True
  elif v.lower() in ("no", "false", "f", "n", "0"):
    return False
  else:
    raise ArgumentTypeError(
        f"Truthy value expected: got {v} but expected one of yes/no, true/false, t/f, y/n, 1/0 (case insensitive)."						)

def     UpperCamelCase_   (   lowerCAmelCase__				:    list						)						->       Callable[[str], Any]:

  """simple docstring"""




  lowerCAmelCase_       :    List[Any]								=			{str(__lowerCamelCase						): choice for choice in choices}
  return lambda lowerCAmelCase__						: str_to_choice.get(__lowerCamelCase   ,       __lowerCamelCase						)

def     UpperCamelCase_   (   *,
    lowerCAmelCase__				:    Union[str, List[str]] = None   ,       lowerCAmelCase__				:    str = None   ,       lowerCAmelCase__				:    Any = dataclasses.MISSING   ,       lowerCAmelCase__				:    Callable[[], Any] = dataclasses.MISSING   ,       lowerCAmelCase__				:    dict = None   ,       **lowerCAmelCase__				:    str   ,       )						->       dataclasses.Field:

  """simple docstring"""




  if metadata is None:
    # Important, don't use as default param in function signature because dict is mutable and shared across function calls
    lowerCAmelCase_       :    List[Any]								=			{}
  if aliases is not None:
    lowerCAmelCase_       :    Union[str, Any]								=			aliases
  if help is not None:
    lowerCAmelCase_       :    Union[str, Any]								=			help

  return dataclasses.field(metadata=__lowerCamelCase   ,       default=__lowerCamelCase   ,       default_factory=__lowerCamelCase   ,       **__lowerCamelCase						)







class 				UpperCamelCase__       (     A_  ):




      """simple docstring"""




      _SCREAMING_SNAKE_CASE      =					42



      def __init__(				self    :				Any   ,      SCREAMING_SNAKE_CASE_    :				Union[DataClassType, Iterable[DataClassType]]   ,      **SCREAMING_SNAKE_CASE_    :				List[Any]	):
        # To make the default appear when using --help
        if "formatter_class" not in kwargs:
          lowerCAmelCase_       :    Union[str, Any]								=			ArgumentDefaultsHelpFormatter
        super().__init__(**_lowerCamelCase	)
        if dataclasses.is_dataclass(_lowerCamelCase	):
          lowerCAmelCase_       :    Tuple								=			[dataclass_types]
        lowerCAmelCase_       :    int								=			list(_lowerCamelCase	)
        for dtype in self.dataclass_types:
          self._add_dataclass_arguments(_lowerCamelCase	)



      @staticmethod
      def 					SCREAMING_SNAKE_CASE__			(				SCREAMING_SNAKE_CASE_    :				ArgumentParser   ,      SCREAMING_SNAKE_CASE_    :				dataclasses.Field	):
        lowerCAmelCase_       :    int								=			F"--{field.name}"
        lowerCAmelCase_       :    Optional[int]								=			field.metadata.copy()
        # field.metadata is not used at all by Data Classes,
        # it is provided as a third-party extension mechanism.
        if isinstance(field.type   ,      _lowerCamelCase	):
          raise RuntimeError(
              'Unresolved type detected, which should have been done with the help of '
              '`typing.get_type_hints` method by default'	)

        lowerCAmelCase_       :    Union[str, Any]								=			kwargs.pop('aliases'   ,      []	)
        if isinstance(_lowerCamelCase   ,      _lowerCamelCase	):
          lowerCAmelCase_       :    Dict								=			[aliases]

        lowerCAmelCase_       :    List[str]								=			getattr(field.type   ,      '__origin__'   ,      field.type	)
        if origin_type is Union or (hasattr(_lowerCamelCase   ,      'UnionType'	) and isinstance(_lowerCamelCase   ,      types.UnionType	)):
          if str not in field.type.__args__ and (
              len(field.type.__args__	) != 2 or type(_lowerCamelCase	) not in field.type.__args__
          ):
            raise ValueError(
                'Only `Union[X, NoneType]` (i.e., `Optional[X]`) is allowed for `Union` because'
                ' the argument parser only supports one type per argument.'
                F" Problem encountered in field \'{field.name}\'."	)
          if type(_lowerCamelCase	) not in field.type.__args__:
            # filter `str` in Union
            lowerCAmelCase_       :    Optional[int]								=			field.type.__args__[0] if field.type.__args__[1] == str else field.type.__args__[1]
            lowerCAmelCase_       :    Dict								=			getattr(field.type   ,      '__origin__'   ,      field.type	)
          elif bool not in field.type.__args__:
            # filter `NoneType` in Union (except for `Union[bool, NoneType]`)
            lowerCAmelCase_       :    Dict								=			(
                field.type.__args__[0] if isinstance(_lowerCamelCase   ,      field.type.__args__[1]	) else field.type.__args__[1]
            )
            lowerCAmelCase_       :    List[Any]								=			getattr(field.type   ,      '__origin__'   ,      field.type	)

        # A variable to store kwargs for a boolean field, if needed
        # so that we can init a `no_*` complement argument (see below)
        lowerCAmelCase_       :    List[Any]								=			{}
        if origin_type is Literal or (isinstance(field.type   ,      _lowerCamelCase	) and issubclass(field.type   ,      _lowerCamelCase	)):
          if origin_type is Literal:
            lowerCAmelCase_       :    Tuple								=			field.type.__args__
          else:
            lowerCAmelCase_       :    Dict								=			[x.value for x in field.type]

          lowerCAmelCase_       :    Any								=			make_choice_type_function(kwargs['choices']	)

          if field.default is not dataclasses.MISSING:
            lowerCAmelCase_       :    Dict								=			field.default
          else:
            lowerCAmelCase_       :    List[Any]								=			True
        elif field.type is bool or field.type == Optional[bool]:
          # Copy the currect kwargs to use to instantiate a `no_*` complement argument below.
          # We do not initialize it here because the `no_*` alternative must be instantiated after the real argument
          lowerCAmelCase_       :    Tuple								=			copy(_lowerCamelCase	)

          # Hack because type=bool in argparse does not behave as we want.
          lowerCAmelCase_       :    Tuple								=			string_to_bool
          if field.type is bool or (field.default is not None and field.default is not dataclasses.MISSING):
            # Default value is False if we have no default when of type bool.
            lowerCAmelCase_       :    Optional[int]								=			False if field.default is dataclasses.MISSING else field.default
            # This is the value that will get picked if we don't include --field_name in any way
            lowerCAmelCase_       :    Optional[int]								=			default
            # This tells argparse we accept 0 or 1 value after --field_name
            lowerCAmelCase_       :    str								=			'?'
            # This is the value that will get picked if we do --field_name (without value)
            lowerCAmelCase_       :    Optional[int]								=			True
        elif isclass(_lowerCamelCase	) and issubclass(_lowerCamelCase   ,      _lowerCamelCase	):
          lowerCAmelCase_       :    List[str]								=			field.type.__args__[0]
          lowerCAmelCase_       :    Any								=			'+'
          if field.default_factory is not dataclasses.MISSING:
            lowerCAmelCase_       :    Any								=			field.default_factory()
          elif field.default is dataclasses.MISSING:
            lowerCAmelCase_       :    Union[str, Any]								=			True
        else:
          lowerCAmelCase_       :    Optional[Any]								=			field.type
          if field.default is not dataclasses.MISSING:
            lowerCAmelCase_       :    Tuple								=			field.default
          elif field.default_factory is not dataclasses.MISSING:
            lowerCAmelCase_       :    List[str]								=			field.default_factory()
          else:
            lowerCAmelCase_       :    List[str]								=			True
        parser.add_argument(_lowerCamelCase   ,      *_lowerCamelCase   ,      **_lowerCamelCase	)

        # Add a complement `no_*` argument for a boolean field AFTER the initial field has already been added.
        # Order is important for arguments with the same destination!
        # We use a copy of earlier kwargs because the original kwargs have changed a lot before reaching down
        # here and we do not need those changes/additional keys.
        if field.default is True and (field.type is bool or field.type == Optional[bool]):
          lowerCAmelCase_       :    Union[str, Any]								=			False
          parser.add_argument(F"--no_{field.name}"   ,      action='store_false'   ,      dest=field.name   ,      **_lowerCamelCase	)



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Any   ,      SCREAMING_SNAKE_CASE_    :				DataClassType	):
        if hasattr(_lowerCamelCase   ,      '_argument_group_name'	):
          lowerCAmelCase_       :    str								=			self.add_argument_group(dtype._argument_group_name	)
        else:
          lowerCAmelCase_       :    Optional[int]								=			self

        try:
          lowerCAmelCase_       :    Dict								=			get_type_hints(_lowerCamelCase	)
        except NameError:
          raise RuntimeError(
              F"Type resolution failed for {dtype}. Try declaring the class in global scope or "
              'removing line of `from __future__ import annotations` which opts in Postponed '
              'Evaluation of Annotations (PEP 563)'	)
        except TypeError as ex:
          # Remove this block when we drop Python 3.9 support
          if sys.version_info[:2] < (3, 1_0) and "unsupported operand type(s) for |" in str(_lowerCamelCase	):
            lowerCAmelCase_       :    Any								=			'.'.join(map(_lowerCamelCase   ,      sys.version_info[:3]	)	)
            raise RuntimeError(
                F"Type resolution failed for {dtype} on Python {python_version}. Try removing "
                'line of `from __future__ import annotations` which opts in union types as '
                '`X | Y` (PEP 604) via Postponed Evaluation of Annotations (PEP 563). To '
                'support Python versions that lower than 3.10, you need to use '
                '`typing.Union[X, Y]` instead of `X | Y` and `typing.Optional[X]` instead of '
                '`X | None`.'	) from ex
          raise

        for field in dataclasses.fields(_lowerCamelCase	):
          if not field.init:
            continue
          lowerCAmelCase_       :    Tuple								=			type_hints[field.name]
          self._parse_dataclass_field(_lowerCamelCase   ,      _lowerCamelCase	)



      def 					SCREAMING_SNAKE_CASE__			(				self    :				List[Any]   ,      SCREAMING_SNAKE_CASE_    :				Optional[int]=None   ,      SCREAMING_SNAKE_CASE_    :				Dict=False   ,      SCREAMING_SNAKE_CASE_    :				Optional[int]=True   ,      SCREAMING_SNAKE_CASE_    :				int=None   ,      SCREAMING_SNAKE_CASE_    :				Tuple=None   ,      ):

        if args_file_flag or args_filename or (look_for_args_file and len(sys.argv	)):
          lowerCAmelCase_       :    Optional[Any]								=			[]

          if args_filename:
            args_files.append(Path(_lowerCamelCase	)	)
          elif look_for_args_file and len(sys.argv	):
            args_files.append(Path(sys.argv[0]	).with_suffix('.args'	)	)

          # args files specified via command line flag should overwrite default args files so we add them last
          if args_file_flag:
            # Create special parser just to extract the args_file_flag values
            lowerCAmelCase_       :    Any								=			ArgumentParser()
            args_file_parser.add_argument(_lowerCamelCase   ,      type=_lowerCamelCase   ,      action='append'	)

            # Use only remaining args for further parsing (remove the args_file_flag)
            lowerCAmelCase_						,lowerCAmelCase_       :    List[str]								=			args_file_parser.parse_known_args(args=_lowerCamelCase	)
            lowerCAmelCase_       :    str								=			vars(_lowerCamelCase	).get(args_file_flag.lstrip('-'	)   ,      _lowerCamelCase	)

            if cmd_args_file_paths:
              args_files.extend([Path(_lowerCamelCase	) for p in cmd_args_file_paths]	)

          lowerCAmelCase_       :    Dict								=			[]
          for args_file in args_files:
            if args_file.exists():
              file_args += args_file.read_text().split()

             # in case of duplicate arguments the last one has precedence
             # args specified via the command line should overwrite args from files, so we add them last
          lowerCAmelCase_       :    Any								=			file_args + args if args is not None else file_args + sys.argv[1:]
        lowerCAmelCase_						,lowerCAmelCase_       :    str								=			self.parse_known_args(args=_lowerCamelCase	)
        lowerCAmelCase_       :    Any								=			[]
        for dtype in self.dataclass_types:
          lowerCAmelCase_       :    Any								=			{f.name for f in dataclasses.fields(_lowerCamelCase	) if f.init}
          lowerCAmelCase_       :    int								=			{k: v for k, v in vars(_lowerCamelCase	).items() if k in keys}
          for k in keys:
            delattr(_lowerCamelCase   ,      _lowerCamelCase	)
          lowerCAmelCase_       :    str								=			dtype(**_lowerCamelCase	)
          outputs.append(_lowerCamelCase	)
        if len(namespace.__dict__	) > 0:
          # additional namespace.
          outputs.append(_lowerCamelCase	)
        if return_remaining_strings:
          return (*outputs, remaining_args)
        else:
          if remaining_args:
            raise ValueError(F"Some specified arguments are not used by the HfArgumentParser: {remaining_args}"	)

          return (*outputs,)



      def 					SCREAMING_SNAKE_CASE__			(				self    :				int   ,      SCREAMING_SNAKE_CASE_    :				Dict[str, Any]   ,      SCREAMING_SNAKE_CASE_    :				bool = False	):
        lowerCAmelCase_       :    Union[str, Any]								=			set(args.keys()	)
        lowerCAmelCase_       :    Optional[int]								=			[]
        for dtype in self.dataclass_types:
          lowerCAmelCase_       :    Optional[Any]								=			{f.name for f in dataclasses.fields(_lowerCamelCase	) if f.init}
          lowerCAmelCase_       :    int								=			{k: v for k, v in args.items() if k in keys}
          unused_keys.difference_update(inputs.keys()	)
          lowerCAmelCase_       :    Optional[Any]								=			dtype(**_lowerCamelCase	)
          outputs.append(_lowerCamelCase	)
        if not allow_extra_keys and unused_keys:
          raise ValueError(F"Some keys are not used by the HfArgumentParser: {sorted(_lowerCamelCase	)}"	)
        return tuple(_lowerCamelCase	)



      def 					SCREAMING_SNAKE_CASE__			(				self    :				Optional[int]   ,      SCREAMING_SNAKE_CASE_    :				str   ,      SCREAMING_SNAKE_CASE_    :				bool = False	):
        with open(Path(_lowerCamelCase	)   ,      encoding='utf-8'	) as open_json_file:
          lowerCAmelCase_       :    Tuple								=			json.loads(open_json_file.read()	)
        lowerCAmelCase_       :    List[Any]								=			self.parse_dict(_lowerCamelCase   ,      allow_extra_keys=_lowerCamelCase	)
        return tuple(_lowerCamelCase	)





      def 					SCREAMING_SNAKE_CASE__			(				self    :				str   ,      SCREAMING_SNAKE_CASE_    :				str   ,      SCREAMING_SNAKE_CASE_    :				bool = False	):
        lowerCAmelCase_       :    Dict								=			self.parse_dict(yaml.safe_load(Path(_lowerCamelCase	).read_text()	)   ,      allow_extra_keys=_lowerCamelCase	)
        return tuple(_lowerCamelCase	)










"""simple docstring"""







from __future__ import annotations

from fractions import Fraction
from math import gcd, sqrt

def     UpperCamelCase_   (   lowerCAmelCase__				:    int						)						->       bool:

  """simple docstring"""




  lowerCAmelCase_       :    int								=			int(number**0.5						)
  return number == sq * sq

def     UpperCamelCase_   (   lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int   ,       lowerCAmelCase__				:    int						)						->       tuple[int, int]:

  """simple docstring"""




  lowerCAmelCase_       :    int								=			x_num * y_den * z_den + y_num * x_den * z_den + z_num * x_den * y_den
  lowerCAmelCase_       :    int								=			x_den * y_den * z_den
  lowerCAmelCase_       :    int								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
  top //= hcf
  bottom //= hcf
  return top, bottom

def     UpperCamelCase_   (   lowerCAmelCase__				:    int = 35						)						->       int:

  """simple docstring"""




  lowerCAmelCase_       :    set								=			set()
  lowerCAmelCase_       :    int
  lowerCAmelCase_       :    Fraction								=			Fraction(0						)
  lowerCAmelCase_       :    tuple[int, int]

  for x_num in range(1   ,       order + 1						):
    for x_den in range(x_num + 1   ,       order + 1						):
      for y_num in range(1   ,       order + 1						):
        for y_den in range(y_num + 1   ,       order + 1						):
          # n=1
          lowerCAmelCase_       :    str								=			x_num * y_den + x_den * y_num
          lowerCAmelCase_       :    int								=			x_den * y_den
          lowerCAmelCase_       :    int								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
          z_num //= hcf
          z_den //= hcf
          if 0 < z_num < z_den <= order:
            lowerCAmelCase_       :    List[str]								=			add_three(
                lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
            unique_s.add(lowerCAmelCase__						)

          # n=2
          lowerCAmelCase_       :    Optional[int]								=			(
              x_num * x_num * y_den * y_den + x_den * x_den * y_num * y_num
          )
          lowerCAmelCase_       :    Dict								=			x_den * x_den * y_den * y_den
          if is_sq(lowerCAmelCase__						) and is_sq(lowerCAmelCase__						):
            lowerCAmelCase_       :    Optional[int]								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    List[str]								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    Union[str, Any]								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
            z_num //= hcf
            z_den //= hcf
            if 0 < z_num < z_den <= order:
              lowerCAmelCase_       :    Union[str, Any]								=			add_three(
                  lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
              unique_s.add(lowerCAmelCase__						)

                    # n=-1
          lowerCAmelCase_       :    Dict								=			x_num * y_num
          lowerCAmelCase_       :    Optional[int]								=			x_den * y_num + x_num * y_den
          lowerCAmelCase_       :    Any								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
          z_num //= hcf
          z_den //= hcf
          if 0 < z_num < z_den <= order:
            lowerCAmelCase_       :    Tuple								=			add_three(
                lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
            unique_s.add(lowerCAmelCase__						)

          # n=2
          lowerCAmelCase_       :    List[str]								=			x_num * x_num * y_num * y_num
          lowerCAmelCase_       :    Optional[Any]								=			(
              x_den * x_den * y_num * y_num + x_num * x_num * y_den * y_den
          )
          if is_sq(lowerCAmelCase__						) and is_sq(lowerCAmelCase__						):
            lowerCAmelCase_       :    Tuple								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    Optional[Any]								=			int(sqrt(lowerCAmelCase__						)						)
            lowerCAmelCase_       :    Optional[int]								=			gcd(lowerCAmelCase__   ,       lowerCAmelCase__						)
            z_num //= hcf
            z_den //= hcf
            if 0 < z_num < z_den <= order:
              lowerCAmelCase_       :    Any								=			add_three(
                  lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__   ,       lowerCAmelCase__						)
              unique_s.add(lowerCAmelCase__						)

  for num, den in unique_s:
    total += Fraction(lowerCAmelCase__   ,       lowerCAmelCase__						)

  return total.denominator + total.numerator


if __name__ == "__main__":
     print(f'{solution() = }')





