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"""
Utility to make a method decorator, with one decorated function per instance.

Applying a regular decorator to a method applies it to the unbound function,
but in many situations what we really would like to do is to decorate each of the
bound instances of the method independently, that is, for each instance of the class.

Consider the method ``MyClass.foo(self, x)``; if we apply the ``functools.lru_cache()``
decorator to it, there will be only one cache for all `MyClass` instances, and it
will be indexed by ``(self, x)`` tuples instead of just ``x``. More probably, what we

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import inspect


class AutoReprEqMixin:
    """
    Adds a generic __repr__ and __eq__ implementation.

    The __repr__ implementation is based on the constructor's signature and relies
    on the existence of attributes with the same name as the parameters they were
    initialised from.

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from typing import Type, Optional


def merge_metaclasses(*bases: Type, metaclass: Optional[Type] = None) -> Type:
    """
    Make an ad-hoc metaclass to resolve conflicts in class declarations.

    Makes a metaclass that inherits from all of the metaclasses involved in a class
    declaration: the metaclasses of the bases and the explicit metaclass. The
    inheritance order is the explicit metaclass first and then the bases'

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extension ListSlice<T> on List<T> {
  List<T> slice([int start = 0, int? end, int step = 1]) {
    end ??= this.length;
    return [for (var i = start; i < end; i += step) this[i]];
  }
}

void main() {
  final list1 = [for (var i = 1; i <= 20; ++i) i];

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extension MoreIterableTools<E> on Iterable<E> {
  /// Group consecutive elements with the same key.
  Iterable<MapEntry<K, Iterator<E>>> groupConsecutiveBy<K>(
    K Function(E) keyOf,
  ) sync* {
    final iterator = this.iterator;

    bool moveNext = iterator.moveNext(), lastGroupConsumed = true;
    while (moveNext) {
      if (!lastGroupConsumed) {

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import itertools
import math
import typing
from collections import Counter

from sympy import factorint


def submultisets(multiset: Counter) -> typing.Iterable[Counter]:
    for counts in itertools.product(*[range(count + 1) for count in multiset.values()]):

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import typing as t
from abc import ABCMeta, abstractmethod
from dataclasses import dataclass, field
from decimal import Decimal
from fractions import Fraction
from functools import cache
from math import lcm

from frozendict import frozendict