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"""
formula.py - propositional formulas for Python
by Robin Wellner
Hereby, I waive all rights to this library, as described at <http://creativecommons.org/publicdomain/zero/1.0/>

Examples:

foo = Atom('foo')
bar = Atom('bar')

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from functools import partial

from pint import UnitRegistry, Unit, Quantity

ureg = UnitRegistry()


def rounded_conversion(from_: Quantity, to: Unit) -> Quantity:
    return Quantity(round(from_.to(to).magnitude), to)

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from typing import Optional, Literal, Iterator

Player = Literal['X', 'O']
BoardEntry = Literal['X', 'O', ' ']
Board = tuple[BoardEntry, BoardEntry, BoardEntry, BoardEntry, BoardEntry, BoardEntry, BoardEntry, BoardEntry, BoardEntry] 

def new_board() -> Board:
    return tuple(' ' * 9)

def is_draw(board: Board) -> bool:

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import ast
from pathlib import Path

class Visitor(ast.NodeVisitor):
    def __init__(self):
        self.for_found = 0
        self.for_else_found = 0
        self.while_found = 0
        self.while_else_found = 0
        self.files_tried = 0

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import dis
from typing import Iterable, TypeVar, Any
from collections.abc import Callable
from types import CodeType

F = TypeVar('F', bound=Callable)

def extract_mapping(names: tuple[str, ...], mapping: dict[str, int]) -> dict[int, int]:
    return {names.index(k): v for k, v in mapping.items() if k in names}

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from functools import wraps, partial

def transform_return(transformation, decorated=None):
    if decorated is None:
        return partial(transform_return, transformation)
    @wraps(decorated)
    def wrapper(*args, **kwargs):
        return transformation(decorated(*args, **kwargs))
    return wrapper

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from inspect import signature, Signature, Parameter
from argparse import ArgumentParser

POSITIONAL = (Parameter.POSITIONAL_ONLY, Parameter.POSITIONAL_OR_KEYWORD)

def parse_args(parser, argv=None):
    return parser.parse_args(argv).__dict__

class Command:
    def __init__(self, f, parser):

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# disclaimer: untested code ahead! see https://www.reddit.com/r/Python/comments/fk4wal/i_needed_an_object_that_can_with_one_instance/fkrbodb/

from dataclasses import dataclass
from enum import Enum, auto
from typing import Any, Callable, Tuple

@dataclass
class CacheValue:
    result: Any
    times_changed: int = 1

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from random import choice

with open('/usr/share/dict/nederlands') as f:
    words = f.read().split('\n')

def get_random_pair():
    w1 = choice(words)
    w2 = choice(words)
    return len(w1) + len(w2), w1, w2

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from dataclasses import dataclass, field, fields, MISSING

def immutable_field(*, default=MISSING, default_factory=MISSING):
    return field(default=default, default_factory=default_factory, metadata={'frozen': True})

def mutable_field(*, default=MISSING, default_factory=MISSING):
    return field(default=default, default_factory=default_factory, compare=False)

def halfmutable(_cls=None, *, init=True, repr=True, order=False):
    def wrap(cls):