diff --git a/lib/jaraco/functools.py b/lib/jaraco/functools.py
index fcdbb4f9..6ae9e31d 100644
--- a/lib/jaraco/functools.py
+++ b/lib/jaraco/functools.py
@@ -4,6 +4,7 @@ import inspect
 import collections
 import types
 import itertools
+import warnings
 
 import more_itertools
 
@@ -266,11 +267,33 @@ def result_invoke(action):
     return wrap
 
 
-def call_aside(f, *args, **kwargs):
+def invoke(f, *args, **kwargs):
     """
     Call a function for its side effect after initialization.
 
-    >>> @call_aside
+    The benefit of using the decorator instead of simply invoking a function
+    after defining it is that it makes explicit the author's intent for the
+    function to be called immediately. Whereas if one simply calls the
+    function immediately, it's less obvious if that was intentional or
+    incidental. It also avoids repeating the name - the two actions, defining
+    the function and calling it immediately are modeled separately, but linked
+    by the decorator construct.
+
+    The benefit of having a function construct (opposed to just invoking some
+    behavior inline) is to serve as a scope in which the behavior occurs. It
+    avoids polluting the global namespace with local variables, provides an
+    anchor on which to attach documentation (docstring), keeps the behavior
+    logically separated (instead of conceptually separated or not separated at
+    all), and provides potential to re-use the behavior for testing or other
+    purposes.
+
+    This function is named as a pithy way to communicate, "call this function
+    primarily for its side effect", or "while defining this function, also
+    take it aside and call it". It exists because there's no Python construct
+    for "define and call" (nor should there be, as decorators serve this need
+    just fine). The behavior happens immediately and synchronously.
+
+    >>> @invoke
     ... def func(): print("called")
     called
     >>> func()
@@ -278,7 +301,7 @@ def call_aside(f, *args, **kwargs):
 
     Use functools.partial to pass parameters to the initial call
 
-    >>> @functools.partial(call_aside, name='bingo')
+    >>> @functools.partial(invoke, name='bingo')
     ... def func(name): print("called with", name)
     called with bingo
     """
@@ -286,6 +309,14 @@ def call_aside(f, *args, **kwargs):
     return f
 
 
+def call_aside(*args, **kwargs):
+    """
+    Deprecated name for invoke.
+    """
+    warnings.warn("call_aside is deprecated, use invoke", DeprecationWarning)
+    return invoke(*args, **kwargs)
+
+
 class Throttler:
     """
     Rate-limit a function (or other callable)
diff --git a/lib/more_itertools/__init__.py b/lib/more_itertools/__init__.py
index 557bfc20..66443971 100644
--- a/lib/more_itertools/__init__.py
+++ b/lib/more_itertools/__init__.py
@@ -3,4 +3,4 @@
 from .more import *  # noqa
 from .recipes import *  # noqa
 
-__version__ = '9.0.0'
+__version__ = '9.1.0'
diff --git a/lib/more_itertools/more.py b/lib/more_itertools/more.py
index 7f73d6ed..cc8b8b48 100755
--- a/lib/more_itertools/more.py
+++ b/lib/more_itertools/more.py
@@ -68,6 +68,7 @@ __all__ = [
     'exactly_n',
     'filter_except',
     'first',
+    'gray_product',
     'groupby_transform',
     'ichunked',
     'iequals',
@@ -658,6 +659,7 @@ def distinct_permutations(iterable, r=None):
         [(0, 1), (0, 2), (1, 0), (1, 2), (2, 0), (2, 1)]
 
     """
+
     # Algorithm: https://w.wiki/Qai
     def _full(A):
         while True:
@@ -1301,7 +1303,7 @@ def split_at(iterable, pred, maxsplit=-1, keep_separator=False):
         [[0], [2], [4, 5, 6, 7, 8, 9]]
 
     By default, the delimiting items are not included in the output.
-    The include them, set *keep_separator* to ``True``.
+    To include them, set *keep_separator* to ``True``.
 
         >>> list(split_at('abcdcba', lambda x: x == 'b', keep_separator=True))
         [['a'], ['b'], ['c', 'd', 'c'], ['b'], ['a']]
@@ -1391,7 +1393,9 @@ def split_after(iterable, pred, maxsplit=-1):
         if pred(item) and buf:
             yield buf
             if maxsplit == 1:
-                yield list(it)
+                buf = list(it)
+                if buf:
+                    yield buf
                 return
             buf = []
             maxsplit -= 1
@@ -2914,6 +2918,7 @@ def make_decorator(wrapping_func, result_index=0):
         '7'
 
     """
+
     # See https://sites.google.com/site/bbayles/index/decorator_factory for
     # notes on how this works.
     def decorator(*wrapping_args, **wrapping_kwargs):
@@ -3464,7 +3469,6 @@ def _sample_unweighted(iterable, k):
     next_index = k + floor(log(random()) / log(1 - W))
 
     for index, element in enumerate(iterable, k):
-
         if index == next_index:
             reservoir[randrange(k)] = element
             # The new W is the largest in a sample of k U(0, `old_W`) numbers
@@ -4284,7 +4288,6 @@ def minmax(iterable_or_value, *others, key=None, default=_marker):
         lo_key = hi_key = key(lo)
 
         for x, y in zip_longest(it, it, fillvalue=lo):
-
             x_key, y_key = key(x), key(y)
 
             if y_key < x_key:
@@ -4345,3 +4348,45 @@ def constrained_batches(
 
     if batch:
         yield tuple(batch)
+
+
+def gray_product(*iterables):
+    """Like :func:`itertools.product`, but return tuples in an order such
+    that only one element in the generated tuple changes from one iteration
+    to the next.
+
+        >>> list(gray_product('AB','CD'))
+        [('A', 'C'), ('B', 'C'), ('B', 'D'), ('A', 'D')]
+
+    This function consumes all of the input iterables before producing output.
+    If any of the input iterables have fewer than two items, ``ValueError``
+    is raised.
+
+    For information on the algorithm, see
+    `this section <https://www-cs-faculty.stanford.edu/~knuth/fasc2a.ps.gz>`__
+    of Donald Knuth's *The Art of Computer Programming*.
+    """
+    all_iterables = tuple(tuple(x) for x in iterables)
+    iterable_count = len(all_iterables)
+    for iterable in all_iterables:
+        if len(iterable) < 2:
+            raise ValueError("each iterable must have two or more items")
+
+    # This is based on "Algorithm H" from section 7.2.1.1, page 20.
+    # a holds the indexes of the source iterables for the n-tuple to be yielded
+    # f is the array of "focus pointers"
+    # o is the array of "directions"
+    a = [0] * iterable_count
+    f = list(range(iterable_count + 1))
+    o = [1] * iterable_count
+    while True:
+        yield tuple(all_iterables[i][a[i]] for i in range(iterable_count))
+        j = f[0]
+        f[0] = 0
+        if j == iterable_count:
+            break
+        a[j] = a[j] + o[j]
+        if a[j] == 0 or a[j] == len(all_iterables[j]) - 1:
+            o[j] = -o[j]
+            f[j] = f[j + 1]
+            f[j + 1] = j + 1
diff --git a/lib/more_itertools/more.pyi b/lib/more_itertools/more.pyi
index 1413fae7..75c5232c 100644
--- a/lib/more_itertools/more.pyi
+++ b/lib/more_itertools/more.pyi
@@ -1,26 +1,25 @@
 """Stubs for more_itertools.more"""
+from __future__ import annotations
 
+from types import TracebackType
 from typing import (
     Any,
     Callable,
     Container,
-    Dict,
+    ContextManager,
     Generic,
     Hashable,
     Iterable,
     Iterator,
-    List,
-    Optional,
+    overload,
     Reversible,
     Sequence,
     Sized,
-    Tuple,
-    Union,
+    Type,
     TypeVar,
     type_check_only,
 )
-from types import TracebackType
-from typing_extensions import ContextManager, Protocol, Type, overload
+from typing_extensions import Protocol
 
 # Type and type variable definitions
 _T = TypeVar('_T')
@@ -31,7 +30,7 @@ _V = TypeVar('_V')
 _W = TypeVar('_W')
 _T_co = TypeVar('_T_co', covariant=True)
 _GenFn = TypeVar('_GenFn', bound=Callable[..., Iterator[object]])
-_Raisable = Union[BaseException, 'Type[BaseException]']
+_Raisable = BaseException | Type[BaseException]
 
 @type_check_only
 class _SizedIterable(Protocol[_T_co], Sized, Iterable[_T_co]): ...
@@ -39,23 +38,25 @@ class _SizedIterable(Protocol[_T_co], Sized, Iterable[_T_co]): ...
 @type_check_only
 class _SizedReversible(Protocol[_T_co], Sized, Reversible[_T_co]): ...
 
+@type_check_only
+class _SupportsSlicing(Protocol[_T_co]):
+    def __getitem__(self, __k: slice) -> _T_co: ...
+
 def chunked(
-    iterable: Iterable[_T], n: Optional[int], strict: bool = ...
-) -> Iterator[List[_T]]: ...
+    iterable: Iterable[_T], n: int | None, strict: bool = ...
+) -> Iterator[list[_T]]: ...
 @overload
 def first(iterable: Iterable[_T]) -> _T: ...
 @overload
-def first(iterable: Iterable[_T], default: _U) -> Union[_T, _U]: ...
+def first(iterable: Iterable[_T], default: _U) -> _T | _U: ...
 @overload
 def last(iterable: Iterable[_T]) -> _T: ...
 @overload
-def last(iterable: Iterable[_T], default: _U) -> Union[_T, _U]: ...
+def last(iterable: Iterable[_T], default: _U) -> _T | _U: ...
 @overload
 def nth_or_last(iterable: Iterable[_T], n: int) -> _T: ...
 @overload
-def nth_or_last(
-    iterable: Iterable[_T], n: int, default: _U
-) -> Union[_T, _U]: ...
+def nth_or_last(iterable: Iterable[_T], n: int, default: _U) -> _T | _U: ...
 
 class peekable(Generic[_T], Iterator[_T]):
     def __init__(self, iterable: Iterable[_T]) -> None: ...
@@ -64,13 +65,13 @@ class peekable(Generic[_T], Iterator[_T]):
     @overload
     def peek(self) -> _T: ...
     @overload
-    def peek(self, default: _U) -> Union[_T, _U]: ...
+    def peek(self, default: _U) -> _T | _U: ...
     def prepend(self, *items: _T) -> None: ...
     def __next__(self) -> _T: ...
     @overload
     def __getitem__(self, index: int) -> _T: ...
     @overload
-    def __getitem__(self, index: slice) -> List[_T]: ...
+    def __getitem__(self, index: slice) -> list[_T]: ...
 
 def consumer(func: _GenFn) -> _GenFn: ...
 def ilen(iterable: Iterable[object]) -> int: ...
@@ -80,42 +81,42 @@ def with_iter(
 ) -> Iterator[_T]: ...
 def one(
     iterable: Iterable[_T],
-    too_short: Optional[_Raisable] = ...,
-    too_long: Optional[_Raisable] = ...,
+    too_short: _Raisable | None = ...,
+    too_long: _Raisable | None = ...,
 ) -> _T: ...
 def raise_(exception: _Raisable, *args: Any) -> None: ...
 def strictly_n(
     iterable: Iterable[_T],
     n: int,
-    too_short: Optional[_GenFn] = ...,
-    too_long: Optional[_GenFn] = ...,
-) -> List[_T]: ...
+    too_short: _GenFn | None = ...,
+    too_long: _GenFn | None = ...,
+) -> list[_T]: ...
 def distinct_permutations(
-    iterable: Iterable[_T], r: Optional[int] = ...
-) -> Iterator[Tuple[_T, ...]]: ...
+    iterable: Iterable[_T], r: int | None = ...
+) -> Iterator[tuple[_T, ...]]: ...
 def intersperse(
     e: _U, iterable: Iterable[_T], n: int = ...
-) -> Iterator[Union[_T, _U]]: ...
-def unique_to_each(*iterables: Iterable[_T]) -> List[List[_T]]: ...
+) -> Iterator[_T | _U]: ...
+def unique_to_each(*iterables: Iterable[_T]) -> list[list[_T]]: ...
 @overload
 def windowed(
     seq: Iterable[_T], n: int, *, step: int = ...
-) -> Iterator[Tuple[Optional[_T], ...]]: ...
+) -> Iterator[tuple[_T | None, ...]]: ...
 @overload
 def windowed(
     seq: Iterable[_T], n: int, fillvalue: _U, step: int = ...
-) -> Iterator[Tuple[Union[_T, _U], ...]]: ...
-def substrings(iterable: Iterable[_T]) -> Iterator[Tuple[_T, ...]]: ...
+) -> Iterator[tuple[_T | _U, ...]]: ...
+def substrings(iterable: Iterable[_T]) -> Iterator[tuple[_T, ...]]: ...
 def substrings_indexes(
     seq: Sequence[_T], reverse: bool = ...
-) -> Iterator[Tuple[Sequence[_T], int, int]]: ...
+) -> Iterator[tuple[Sequence[_T], int, int]]: ...
 
 class bucket(Generic[_T, _U], Container[_U]):
     def __init__(
         self,
         iterable: Iterable[_T],
         key: Callable[[_T], _U],
-        validator: Optional[Callable[[object], object]] = ...,
+        validator: Callable[[object], object] | None = ...,
     ) -> None: ...
     def __contains__(self, value: object) -> bool: ...
     def __iter__(self) -> Iterator[_U]: ...
@@ -123,109 +124,105 @@ class bucket(Generic[_T, _U], Container[_U]):
 
 def spy(
     iterable: Iterable[_T], n: int = ...
-) -> Tuple[List[_T], Iterator[_T]]: ...
+) -> tuple[list[_T], Iterator[_T]]: ...
 def interleave(*iterables: Iterable[_T]) -> Iterator[_T]: ...
 def interleave_longest(*iterables: Iterable[_T]) -> Iterator[_T]: ...
 def interleave_evenly(
-    iterables: List[Iterable[_T]], lengths: Optional[List[int]] = ...
+    iterables: list[Iterable[_T]], lengths: list[int] | None = ...
 ) -> Iterator[_T]: ...
 def collapse(
     iterable: Iterable[Any],
-    base_type: Optional[type] = ...,
-    levels: Optional[int] = ...,
+    base_type: type | None = ...,
+    levels: int | None = ...,
 ) -> Iterator[Any]: ...
 @overload
 def side_effect(
     func: Callable[[_T], object],
     iterable: Iterable[_T],
     chunk_size: None = ...,
-    before: Optional[Callable[[], object]] = ...,
-    after: Optional[Callable[[], object]] = ...,
+    before: Callable[[], object] | None = ...,
+    after: Callable[[], object] | None = ...,
 ) -> Iterator[_T]: ...
 @overload
 def side_effect(
-    func: Callable[[List[_T]], object],
+    func: Callable[[list[_T]], object],
     iterable: Iterable[_T],
     chunk_size: int,
-    before: Optional[Callable[[], object]] = ...,
-    after: Optional[Callable[[], object]] = ...,
+    before: Callable[[], object] | None = ...,
+    after: Callable[[], object] | None = ...,
 ) -> Iterator[_T]: ...
 def sliced(
-    seq: Sequence[_T], n: int, strict: bool = ...
-) -> Iterator[Sequence[_T]]: ...
+    seq: _SupportsSlicing[_T], n: int, strict: bool = ...
+) -> Iterator[_T]: ...
 def split_at(
     iterable: Iterable[_T],
     pred: Callable[[_T], object],
     maxsplit: int = ...,
     keep_separator: bool = ...,
-) -> Iterator[List[_T]]: ...
+) -> Iterator[list[_T]]: ...
 def split_before(
     iterable: Iterable[_T], pred: Callable[[_T], object], maxsplit: int = ...
-) -> Iterator[List[_T]]: ...
+) -> Iterator[list[_T]]: ...
 def split_after(
     iterable: Iterable[_T], pred: Callable[[_T], object], maxsplit: int = ...
-) -> Iterator[List[_T]]: ...
+) -> Iterator[list[_T]]: ...
 def split_when(
     iterable: Iterable[_T],
     pred: Callable[[_T, _T], object],
     maxsplit: int = ...,
-) -> Iterator[List[_T]]: ...
+) -> Iterator[list[_T]]: ...
 def split_into(
-    iterable: Iterable[_T], sizes: Iterable[Optional[int]]
-) -> Iterator[List[_T]]: ...
+    iterable: Iterable[_T], sizes: Iterable[int | None]
+) -> Iterator[list[_T]]: ...
 @overload
 def padded(
     iterable: Iterable[_T],
     *,
-    n: Optional[int] = ...,
+    n: int | None = ...,
     next_multiple: bool = ...,
-) -> Iterator[Optional[_T]]: ...
+) -> Iterator[_T | None]: ...
 @overload
 def padded(
     iterable: Iterable[_T],
     fillvalue: _U,
-    n: Optional[int] = ...,
+    n: int | None = ...,
     next_multiple: bool = ...,
-) -> Iterator[Union[_T, _U]]: ...
+) -> Iterator[_T | _U]: ...
 @overload
 def repeat_last(iterable: Iterable[_T]) -> Iterator[_T]: ...
 @overload
-def repeat_last(
-    iterable: Iterable[_T], default: _U
-) -> Iterator[Union[_T, _U]]: ...
-def distribute(n: int, iterable: Iterable[_T]) -> List[Iterator[_T]]: ...
+def repeat_last(iterable: Iterable[_T], default: _U) -> Iterator[_T | _U]: ...
+def distribute(n: int, iterable: Iterable[_T]) -> list[Iterator[_T]]: ...
 @overload
 def stagger(
     iterable: Iterable[_T],
     offsets: _SizedIterable[int] = ...,
     longest: bool = ...,
-) -> Iterator[Tuple[Optional[_T], ...]]: ...
+) -> Iterator[tuple[_T | None, ...]]: ...
 @overload
 def stagger(
     iterable: Iterable[_T],
     offsets: _SizedIterable[int] = ...,
     longest: bool = ...,
     fillvalue: _U = ...,
-) -> Iterator[Tuple[Union[_T, _U], ...]]: ...
+) -> Iterator[tuple[_T | _U, ...]]: ...
 
 class UnequalIterablesError(ValueError):
-    def __init__(
-        self, details: Optional[Tuple[int, int, int]] = ...
-    ) -> None: ...
+    def __init__(self, details: tuple[int, int, int] | None = ...) -> None: ...
 
 @overload
-def zip_equal(__iter1: Iterable[_T1]) -> Iterator[Tuple[_T1]]: ...
+def zip_equal(__iter1: Iterable[_T1]) -> Iterator[tuple[_T1]]: ...
 @overload
 def zip_equal(
     __iter1: Iterable[_T1], __iter2: Iterable[_T2]
-) -> Iterator[Tuple[_T1, _T2]]: ...
+) -> Iterator[tuple[_T1, _T2]]: ...
 @overload
 def zip_equal(
     __iter1: Iterable[_T],
     __iter2: Iterable[_T],
     __iter3: Iterable[_T],
     *iterables: Iterable[_T],
-) -> Iterator[Tuple[_T, ...]]: ...
+) -> Iterator[tuple[_T, ...]]: ...
 @overload
 def zip_offset(
     __iter1: Iterable[_T1],
@@ -233,7 +230,7 @@ def zip_offset(
     offsets: _SizedIterable[int],
     longest: bool = ...,
     fillvalue: None = None,
-) -> Iterator[Tuple[Optional[_T1]]]: ...
+) -> Iterator[tuple[_T1 | None]]: ...
 @overload
 def zip_offset(
     __iter1: Iterable[_T1],
@@ -242,7 +239,7 @@ def zip_offset(
     offsets: _SizedIterable[int],
     longest: bool = ...,
     fillvalue: None = None,
-) -> Iterator[Tuple[Optional[_T1], Optional[_T2]]]: ...
+) -> Iterator[tuple[_T1 | None, _T2 | None]]: ...
 @overload
 def zip_offset(
     __iter1: Iterable[_T],
@@ -252,7 +249,7 @@ def zip_offset(
     offsets: _SizedIterable[int],
     longest: bool = ...,
     fillvalue: None = None,
-) -> Iterator[Tuple[Optional[_T], ...]]: ...
+) -> Iterator[tuple[_T | None, ...]]: ...
 @overload
 def zip_offset(
     __iter1: Iterable[_T1],
@@ -260,7 +257,7 @@ def zip_offset(
     offsets: _SizedIterable[int],
     longest: bool = ...,
     fillvalue: _U,
-) -> Iterator[Tuple[Union[_T1, _U]]]: ...
+) -> Iterator[tuple[_T1 | _U]]: ...
 @overload
 def zip_offset(
     __iter1: Iterable[_T1],
@@ -269,7 +266,7 @@ def zip_offset(
     offsets: _SizedIterable[int],
     longest: bool = ...,
     fillvalue: _U,
-) -> Iterator[Tuple[Union[_T1, _U], Union[_T2, _U]]]: ...
+) -> Iterator[tuple[_T1 | _U, _T2 | _U]]: ...
 @overload
 def zip_offset(
     __iter1: Iterable[_T],
@@ -279,82 +276,80 @@ def zip_offset(
     offsets: _SizedIterable[int],
     longest: bool = ...,
     fillvalue: _U,
-) -> Iterator[Tuple[Union[_T, _U], ...]]: ...
+) -> Iterator[tuple[_T | _U, ...]]: ...
 def sort_together(
     iterables: Iterable[Iterable[_T]],
     key_list: Iterable[int] = ...,
-    key: Optional[Callable[..., Any]] = ...,
+    key: Callable[..., Any] | None = ...,
     reverse: bool = ...,
-) -> List[Tuple[_T, ...]]: ...
-def unzip(iterable: Iterable[Sequence[_T]]) -> Tuple[Iterator[_T], ...]: ...
-def divide(n: int, iterable: Iterable[_T]) -> List[Iterator[_T]]: ...
+) -> list[tuple[_T, ...]]: ...
+def unzip(iterable: Iterable[Sequence[_T]]) -> tuple[Iterator[_T], ...]: ...
+def divide(n: int, iterable: Iterable[_T]) -> list[Iterator[_T]]: ...
 def always_iterable(
     obj: object,
-    base_type: Union[
-        type, Tuple[Union[type, Tuple[Any, ...]], ...], None
-    ] = ...,
+    base_type: type | tuple[type | tuple[Any, ...], ...] | None = ...,
 ) -> Iterator[Any]: ...
 def adjacent(
     predicate: Callable[[_T], bool],
     iterable: Iterable[_T],
     distance: int = ...,
-) -> Iterator[Tuple[bool, _T]]: ...
+) -> Iterator[tuple[bool, _T]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: None = None,
     valuefunc: None = None,
     reducefunc: None = None,
-) -> Iterator[Tuple[_T, Iterator[_T]]]: ...
+) -> Iterator[tuple[_T, Iterator[_T]]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: Callable[[_T], _U],
     valuefunc: None,
     reducefunc: None,
-) -> Iterator[Tuple[_U, Iterator[_T]]]: ...
+) -> Iterator[tuple[_U, Iterator[_T]]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: None,
     valuefunc: Callable[[_T], _V],
     reducefunc: None,
-) -> Iterable[Tuple[_T, Iterable[_V]]]: ...
+) -> Iterable[tuple[_T, Iterable[_V]]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: Callable[[_T], _U],
     valuefunc: Callable[[_T], _V],
     reducefunc: None,
-) -> Iterable[Tuple[_U, Iterator[_V]]]: ...
+) -> Iterable[tuple[_U, Iterator[_V]]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: None,
     valuefunc: None,
     reducefunc: Callable[[Iterator[_T]], _W],
-) -> Iterable[Tuple[_T, _W]]: ...
+) -> Iterable[tuple[_T, _W]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: Callable[[_T], _U],
     valuefunc: None,
     reducefunc: Callable[[Iterator[_T]], _W],
-) -> Iterable[Tuple[_U, _W]]: ...
+) -> Iterable[tuple[_U, _W]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: None,
     valuefunc: Callable[[_T], _V],
     reducefunc: Callable[[Iterable[_V]], _W],
-) -> Iterable[Tuple[_T, _W]]: ...
+) -> Iterable[tuple[_T, _W]]: ...
 @overload
 def groupby_transform(
     iterable: Iterable[_T],
     keyfunc: Callable[[_T], _U],
     valuefunc: Callable[[_T], _V],
     reducefunc: Callable[[Iterable[_V]], _W],
-) -> Iterable[Tuple[_U, _W]]: ...
+) -> Iterable[tuple[_U, _W]]: ...
 
 class numeric_range(Generic[_T, _U], Sequence[_T], Hashable, Reversible[_T]):
     @overload
@@ -375,22 +370,22 @@ class numeric_range(Generic[_T, _U], Sequence[_T], Hashable, Reversible[_T]):
     def __len__(self) -> int: ...
     def __reduce__(
         self,
-    ) -> Tuple[Type[numeric_range[_T, _U]], Tuple[_T, _T, _U]]: ...
+    ) -> tuple[Type[numeric_range[_T, _U]], tuple[_T, _T, _U]]: ...
     def __repr__(self) -> str: ...
     def __reversed__(self) -> Iterator[_T]: ...
     def count(self, value: _T) -> int: ...
     def index(self, value: _T) -> int: ...  # type: ignore
 
 def count_cycle(
-    iterable: Iterable[_T], n: Optional[int] = ...
-) -> Iterable[Tuple[int, _T]]: ...
+    iterable: Iterable[_T], n: int | None = ...
+) -> Iterable[tuple[int, _T]]: ...
 def mark_ends(
     iterable: Iterable[_T],
-) -> Iterable[Tuple[bool, bool, _T]]: ...
+) -> Iterable[tuple[bool, bool, _T]]: ...
 def locate(
     iterable: Iterable[object],
     pred: Callable[..., Any] = ...,
-    window_size: Optional[int] = ...,
+    window_size: int | None = ...,
 ) -> Iterator[int]: ...
 def lstrip(
     iterable: Iterable[_T], pred: Callable[[_T], object]
@@ -403,9 +398,7 @@ def strip(
 ) -> Iterator[_T]: ...
 
 class islice_extended(Generic[_T], Iterator[_T]):
-    def __init__(
-        self, iterable: Iterable[_T], *args: Optional[int]
-    ) -> None: ...
+    def __init__(self, iterable: Iterable[_T], *args: int | None) -> None: ...
     def __iter__(self) -> islice_extended[_T]: ...
     def __next__(self) -> _T: ...
     def __getitem__(self, index: slice) -> islice_extended[_T]: ...
@@ -420,7 +413,7 @@ def difference(
     func: Callable[[_T, _T], _U] = ...,
     *,
     initial: None = ...,
-) -> Iterator[Union[_T, _U]]: ...
+) -> Iterator[_T | _U]: ...
 @overload
 def difference(
     iterable: Iterable[_T], func: Callable[[_T, _T], _U] = ..., *, initial: _U
@@ -436,7 +429,7 @@ class SequenceView(Generic[_T], Sequence[_T]):
 
 class seekable(Generic[_T], Iterator[_T]):
     def __init__(
-        self, iterable: Iterable[_T], maxlen: Optional[int] = ...
+        self, iterable: Iterable[_T], maxlen: int | None = ...
     ) -> None: ...
     def __iter__(self) -> seekable[_T]: ...
     def __next__(self) -> _T: ...
@@ -444,20 +437,20 @@ class seekable(Generic[_T], Iterator[_T]):
     @overload
     def peek(self) -> _T: ...
     @overload
-    def peek(self, default: _U) -> Union[_T, _U]: ...
+    def peek(self, default: _U) -> _T | _U: ...
     def elements(self) -> SequenceView[_T]: ...
     def seek(self, index: int) -> None: ...
 
 class run_length:
     @staticmethod
-    def encode(iterable: Iterable[_T]) -> Iterator[Tuple[_T, int]]: ...
+    def encode(iterable: Iterable[_T]) -> Iterator[tuple[_T, int]]: ...
     @staticmethod
-    def decode(iterable: Iterable[Tuple[_T, int]]) -> Iterator[_T]: ...
+    def decode(iterable: Iterable[tuple[_T, int]]) -> Iterator[_T]: ...
 
 def exactly_n(
     iterable: Iterable[_T], n: int, predicate: Callable[[_T], object] = ...
 ) -> bool: ...
-def circular_shifts(iterable: Iterable[_T]) -> List[Tuple[_T, ...]]: ...
+def circular_shifts(iterable: Iterable[_T]) -> list[tuple[_T, ...]]: ...
 def make_decorator(
     wrapping_func: Callable[..., _U], result_index: int = ...
 ) -> Callable[..., Callable[[Callable[..., Any]], Callable[..., _U]]]: ...
@@ -467,44 +460,44 @@ def map_reduce(
     keyfunc: Callable[[_T], _U],
     valuefunc: None = ...,
     reducefunc: None = ...,
-) -> Dict[_U, List[_T]]: ...
+) -> dict[_U, list[_T]]: ...
 @overload
 def map_reduce(
     iterable: Iterable[_T],
     keyfunc: Callable[[_T], _U],
     valuefunc: Callable[[_T], _V],
     reducefunc: None = ...,
-) -> Dict[_U, List[_V]]: ...
+) -> dict[_U, list[_V]]: ...
 @overload
 def map_reduce(
     iterable: Iterable[_T],
     keyfunc: Callable[[_T], _U],
     valuefunc: None = ...,
-    reducefunc: Callable[[List[_T]], _W] = ...,
-) -> Dict[_U, _W]: ...
+    reducefunc: Callable[[list[_T]], _W] = ...,
+) -> dict[_U, _W]: ...
 @overload
 def map_reduce(
     iterable: Iterable[_T],
     keyfunc: Callable[[_T], _U],
     valuefunc: Callable[[_T], _V],
-    reducefunc: Callable[[List[_V]], _W],
-) -> Dict[_U, _W]: ...
+    reducefunc: Callable[[list[_V]], _W],
+) -> dict[_U, _W]: ...
 def rlocate(
     iterable: Iterable[_T],
     pred: Callable[..., object] = ...,
-    window_size: Optional[int] = ...,
+    window_size: int | None = ...,
 ) -> Iterator[int]: ...
 def replace(
     iterable: Iterable[_T],
     pred: Callable[..., object],
     substitutes: Iterable[_U],
-    count: Optional[int] = ...,
+    count: int | None = ...,
     window_size: int = ...,
-) -> Iterator[Union[_T, _U]]: ...
-def partitions(iterable: Iterable[_T]) -> Iterator[List[List[_T]]]: ...
+) -> Iterator[_T | _U]: ...
+def partitions(iterable: Iterable[_T]) -> Iterator[list[list[_T]]]: ...
 def set_partitions(
-    iterable: Iterable[_T], k: Optional[int] = ...
-) -> Iterator[List[List[_T]]]: ...
+    iterable: Iterable[_T], k: int | None = ...
+) -> Iterator[list[list[_T]]]: ...
 
 class time_limited(Generic[_T], Iterator[_T]):
     def __init__(
@@ -515,16 +508,16 @@ class time_limited(Generic[_T], Iterator[_T]):
 
 @overload
 def only(
-    iterable: Iterable[_T], *, too_long: Optional[_Raisable] = ...
-) -> Optional[_T]: ...
+    iterable: Iterable[_T], *, too_long: _Raisable | None = ...
+) -> _T | None: ...
 @overload
 def only(
-    iterable: Iterable[_T], default: _U, too_long: Optional[_Raisable] = ...
-) -> Union[_T, _U]: ...
+    iterable: Iterable[_T], default: _U, too_long: _Raisable | None = ...
+) -> _T | _U: ...
 def ichunked(iterable: Iterable[_T], n: int) -> Iterator[Iterator[_T]]: ...
 def distinct_combinations(
     iterable: Iterable[_T], r: int
-) -> Iterator[Tuple[_T, ...]]: ...
+) -> Iterator[tuple[_T, ...]]: ...
 def filter_except(
     validator: Callable[[Any], object],
     iterable: Iterable[_T],
@@ -539,16 +532,16 @@ def map_if(
     iterable: Iterable[Any],
     pred: Callable[[Any], bool],
     func: Callable[[Any], Any],
-    func_else: Optional[Callable[[Any], Any]] = ...,
+    func_else: Callable[[Any], Any] | None = ...,
 ) -> Iterator[Any]: ...
 def sample(
     iterable: Iterable[_T],
     k: int,
-    weights: Optional[Iterable[float]] = ...,
-) -> List[_T]: ...
+    weights: Iterable[float] | None = ...,
+) -> list[_T]: ...
 def is_sorted(
     iterable: Iterable[_T],
-    key: Optional[Callable[[_T], _U]] = ...,
+    key: Callable[[_T], _U] | None = ...,
     reverse: bool = False,
     strict: bool = False,
 ) -> bool: ...
@@ -566,10 +559,10 @@ class callback_iter(Generic[_T], Iterator[_T]):
     def __enter__(self) -> callback_iter[_T]: ...
     def __exit__(
         self,
-        exc_type: Optional[Type[BaseException]],
-        exc_value: Optional[BaseException],
-        traceback: Optional[TracebackType],
-    ) -> Optional[bool]: ...
+        exc_type: Type[BaseException] | None,
+        exc_value: BaseException | None,
+        traceback: TracebackType | None,
+    ) -> bool | None: ...
     def __iter__(self) -> callback_iter[_T]: ...
     def __next__(self) -> _T: ...
     def _reader(self) -> Iterator[_T]: ...
@@ -580,15 +573,15 @@ class callback_iter(Generic[_T], Iterator[_T]):
 
 def windowed_complete(
     iterable: Iterable[_T], n: int
-) -> Iterator[Tuple[_T, ...]]: ...
+) -> Iterator[tuple[_T, ...]]: ...
 def all_unique(
-    iterable: Iterable[_T], key: Optional[Callable[[_T], _U]] = ...
+    iterable: Iterable[_T], key: Callable[[_T], _U] | None = ...
 ) -> bool: ...
-def nth_product(index: int, *args: Iterable[_T]) -> Tuple[_T, ...]: ...
+def nth_product(index: int, *args: Iterable[_T]) -> tuple[_T, ...]: ...
 def nth_permutation(
     iterable: Iterable[_T], r: int, index: int
-) -> Tuple[_T, ...]: ...
-def value_chain(*args: Union[_T, Iterable[_T]]) -> Iterable[_T]: ...
+) -> tuple[_T, ...]: ...
+def value_chain(*args: _T | Iterable[_T]) -> Iterable[_T]: ...
 def product_index(element: Iterable[_T], *args: Iterable[_T]) -> int: ...
 def combination_index(
     element: Iterable[_T], iterable: Iterable[_T]
@@ -603,22 +596,20 @@ class countable(Generic[_T], Iterator[_T]):
     def __iter__(self) -> countable[_T]: ...
     def __next__(self) -> _T: ...
 
-def chunked_even(iterable: Iterable[_T], n: int) -> Iterator[List[_T]]: ...
+def chunked_even(iterable: Iterable[_T], n: int) -> Iterator[list[_T]]: ...
 def zip_broadcast(
-    *objects: Union[_T, Iterable[_T]],
-    scalar_types: Union[
-        type, Tuple[Union[type, Tuple[Any, ...]], ...], None
-    ] = ...,
+    *objects: _T | Iterable[_T],
+    scalar_types: type | tuple[type | tuple[Any, ...], ...] | None = ...,
     strict: bool = ...,
-) -> Iterable[Tuple[_T, ...]]: ...
+) -> Iterable[tuple[_T, ...]]: ...
 def unique_in_window(
-    iterable: Iterable[_T], n: int, key: Optional[Callable[[_T], _U]] = ...
+    iterable: Iterable[_T], n: int, key: Callable[[_T], _U] | None = ...
 ) -> Iterator[_T]: ...
 def duplicates_everseen(
-    iterable: Iterable[_T], key: Optional[Callable[[_T], _U]] = ...
+    iterable: Iterable[_T], key: Callable[[_T], _U] | None = ...
 ) -> Iterator[_T]: ...
 def duplicates_justseen(
-    iterable: Iterable[_T], key: Optional[Callable[[_T], _U]] = ...
+    iterable: Iterable[_T], key: Callable[[_T], _U] | None = ...
 ) -> Iterator[_T]: ...
 
 class _SupportsLessThan(Protocol):
@@ -629,38 +620,38 @@ _SupportsLessThanT = TypeVar("_SupportsLessThanT", bound=_SupportsLessThan)
 @overload
 def minmax(
     iterable_or_value: Iterable[_SupportsLessThanT], *, key: None = None
-) -> Tuple[_SupportsLessThanT, _SupportsLessThanT]: ...
+) -> tuple[_SupportsLessThanT, _SupportsLessThanT]: ...
 @overload
 def minmax(
     iterable_or_value: Iterable[_T], *, key: Callable[[_T], _SupportsLessThan]
-) -> Tuple[_T, _T]: ...
+) -> tuple[_T, _T]: ...
 @overload
 def minmax(
     iterable_or_value: Iterable[_SupportsLessThanT],
     *,
     key: None = None,
     default: _U,
-) -> Union[_U, Tuple[_SupportsLessThanT, _SupportsLessThanT]]: ...
+) -> _U | tuple[_SupportsLessThanT, _SupportsLessThanT]: ...
 @overload
 def minmax(
     iterable_or_value: Iterable[_T],
     *,
     key: Callable[[_T], _SupportsLessThan],
     default: _U,
-) -> Union[_U, Tuple[_T, _T]]: ...
+) -> _U | tuple[_T, _T]: ...
 @overload
 def minmax(
     iterable_or_value: _SupportsLessThanT,
     __other: _SupportsLessThanT,
     *others: _SupportsLessThanT,
-) -> Tuple[_SupportsLessThanT, _SupportsLessThanT]: ...
+) -> tuple[_SupportsLessThanT, _SupportsLessThanT]: ...
 @overload
 def minmax(
     iterable_or_value: _T,
     __other: _T,
     *others: _T,
     key: Callable[[_T], _SupportsLessThan],
-) -> Tuple[_T, _T]: ...
+) -> tuple[_T, _T]: ...
 def longest_common_prefix(
     iterables: Iterable[Iterable[_T]],
 ) -> Iterator[_T]: ...
@@ -668,7 +659,8 @@ def iequals(*iterables: Iterable[object]) -> bool: ...
 def constrained_batches(
     iterable: Iterable[object],
     max_size: int,
-    max_count: Optional[int] = ...,
+    max_count: int | None = ...,
     get_len: Callable[[_T], object] = ...,
     strict: bool = ...,
-) -> Iterator[Tuple[_T]]: ...
+) -> Iterator[tuple[_T]]: ...
+def gray_product(*iterables: Iterable[_T]) -> Iterator[tuple[_T, ...]]: ...
diff --git a/lib/more_itertools/recipes.py b/lib/more_itertools/recipes.py
index 85796207..3facc2e3 100644
--- a/lib/more_itertools/recipes.py
+++ b/lib/more_itertools/recipes.py
@@ -9,6 +9,7 @@ Some backward-compatible usability improvements have been made.
 """
 import math
 import operator
+import warnings
 
 from collections import deque
 from collections.abc import Sized
@@ -21,12 +22,14 @@ from itertools import (
     cycle,
     groupby,
     islice,
+    product,
     repeat,
     starmap,
     tee,
     zip_longest,
 )
 from random import randrange, sample, choice
+from sys import hexversion
 
 __all__ = [
     'all_equal',
@@ -36,9 +39,12 @@ __all__ = [
     'convolve',
     'dotproduct',
     'first_true',
+    'factor',
     'flatten',
     'grouper',
     'iter_except',
+    'iter_index',
+    'matmul',
     'ncycles',
     'nth',
     'nth_combination',
@@ -62,6 +68,7 @@ __all__ = [
     'tabulate',
     'tail',
     'take',
+    'transpose',
     'triplewise',
     'unique_everseen',
     'unique_justseen',
@@ -808,6 +815,35 @@ def polynomial_from_roots(roots):
     ]
 
 
+def iter_index(iterable, value, start=0):
+    """Yield the index of each place in *iterable* that *value* occurs,
+    beginning with index *start*.
+
+    See :func:`locate` for a more general means of finding the indexes
+    associated with particular values.
+
+    >>> list(iter_index('AABCADEAF', 'A'))
+    [0, 1, 4, 7]
+    """
+    try:
+        seq_index = iterable.index
+    except AttributeError:
+        # Slow path for general iterables
+        it = islice(iterable, start, None)
+        for i, element in enumerate(it, start):
+            if element is value or element == value:
+                yield i
+    else:
+        # Fast path for sequences
+        i = start - 1
+        try:
+            while True:
+                i = seq_index(value, i + 1)
+                yield i
+        except ValueError:
+            pass
+
+
 def sieve(n):
     """Yield the primes less than n.
 
@@ -815,13 +851,13 @@ def sieve(n):
     [2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
     """
     isqrt = getattr(math, 'isqrt', lambda x: int(math.sqrt(x)))
+    data = bytearray((0, 1)) * (n // 2)
+    data[:3] = 0, 0, 0
     limit = isqrt(n) + 1
-    data = bytearray([1]) * n
-    data[:2] = 0, 0
     for p in compress(range(limit), data):
-        data[p + p : n : p] = bytearray(len(range(p + p, n, p)))
-
-    return compress(count(), data)
+        data[p * p : n : p + p] = bytes(len(range(p * p, n, p + p)))
+    data[2] = 1
+    return iter_index(data, 1) if n > 2 else iter([])
 
 
 def batched(iterable, n):
@@ -833,9 +869,62 @@ def batched(iterable, n):
     This recipe is from the ``itertools`` docs. This library also provides
     :func:`chunked`, which has a different implementation.
     """
+    if hexversion >= 0x30C00A0:  # Python 3.12.0a0
+        warnings.warn(
+            (
+                'batched will be removed in a future version of '
+                'more-itertools. Use the standard library '
+                'itertools.batched function instead'
+            ),
+            DeprecationWarning,
+        )
+
     it = iter(iterable)
     while True:
         batch = list(islice(it, n))
         if not batch:
             break
         yield batch
+
+
+def transpose(it):
+    """Swap the rows and columns of the input.
+
+    >>> list(transpose([(1, 2, 3), (11, 22, 33)]))
+    [(1, 11), (2, 22), (3, 33)]
+
+    The caller should ensure that the dimensions of the input are compatible.
+    """
+    # TODO: when 3.9 goes end-of-life, add stric=True to this.
+    return zip(*it)
+
+
+def matmul(m1, m2):
+    """Multiply two matrices.
+    >>> list(matmul([(7, 5), (3, 5)], [(2, 5), (7, 9)]))
+    [[49, 80], [41, 60]]
+
+    The caller should ensure that the dimensions of the input matrices are
+    compatible with each other.
+    """
+    n = len(m2[0])
+    return batched(starmap(dotproduct, product(m1, transpose(m2))), n)
+
+
+def factor(n):
+    """Yield the prime factors of n.
+    >>> list(factor(360))
+    [2, 2, 2, 3, 3, 5]
+    """
+    isqrt = getattr(math, 'isqrt', lambda x: int(math.sqrt(x)))
+    for prime in sieve(isqrt(n) + 1):
+        while True:
+            quotient, remainder = divmod(n, prime)
+            if remainder:
+                break
+            yield prime
+            n = quotient
+            if n == 1:
+                return
+    if n >= 2:
+        yield n
diff --git a/lib/more_itertools/recipes.pyi b/lib/more_itertools/recipes.pyi
index 29415c5a..0267ed56 100644
--- a/lib/more_itertools/recipes.pyi
+++ b/lib/more_itertools/recipes.pyi
@@ -1,110 +1,119 @@
 """Stubs for more_itertools.recipes"""
+from __future__ import annotations
+
 from typing import (
     Any,
     Callable,
     Iterable,
     Iterator,
-    List,
-    Optional,
+    overload,
     Sequence,
-    Tuple,
+    Type,
     TypeVar,
-    Union,
 )
-from typing_extensions import overload, Type
 
 # Type and type variable definitions
 _T = TypeVar('_T')
 _U = TypeVar('_U')
 
-def take(n: int, iterable: Iterable[_T]) -> List[_T]: ...
+def take(n: int, iterable: Iterable[_T]) -> list[_T]: ...
 def tabulate(
     function: Callable[[int], _T], start: int = ...
 ) -> Iterator[_T]: ...
 def tail(n: int, iterable: Iterable[_T]) -> Iterator[_T]: ...
-def consume(iterator: Iterable[object], n: Optional[int] = ...) -> None: ...
+def consume(iterator: Iterable[object], n: int | None = ...) -> None: ...
 @overload
-def nth(iterable: Iterable[_T], n: int) -> Optional[_T]: ...
+def nth(iterable: Iterable[_T], n: int) -> _T | None: ...
 @overload
-def nth(iterable: Iterable[_T], n: int, default: _U) -> Union[_T, _U]: ...
+def nth(iterable: Iterable[_T], n: int, default: _U) -> _T | _U: ...
 def all_equal(iterable: Iterable[object]) -> bool: ...
 def quantify(
     iterable: Iterable[_T], pred: Callable[[_T], bool] = ...
 ) -> int: ...
-def pad_none(iterable: Iterable[_T]) -> Iterator[Optional[_T]]: ...
-def padnone(iterable: Iterable[_T]) -> Iterator[Optional[_T]]: ...
+def pad_none(iterable: Iterable[_T]) -> Iterator[_T | None]: ...
+def padnone(iterable: Iterable[_T]) -> Iterator[_T | None]: ...
 def ncycles(iterable: Iterable[_T], n: int) -> Iterator[_T]: ...
 def dotproduct(vec1: Iterable[object], vec2: Iterable[object]) -> object: ...
 def flatten(listOfLists: Iterable[Iterable[_T]]) -> Iterator[_T]: ...
 def repeatfunc(
-    func: Callable[..., _U], times: Optional[int] = ..., *args: Any
+    func: Callable[..., _U], times: int | None = ..., *args: Any
 ) -> Iterator[_U]: ...
-def pairwise(iterable: Iterable[_T]) -> Iterator[Tuple[_T, _T]]: ...
+def pairwise(iterable: Iterable[_T]) -> Iterator[tuple[_T, _T]]: ...
 def grouper(
     iterable: Iterable[_T],
     n: int,
     incomplete: str = ...,
     fillvalue: _U = ...,
-) -> Iterator[Tuple[Union[_T, _U], ...]]: ...
+) -> Iterator[tuple[_T | _U, ...]]: ...
 def roundrobin(*iterables: Iterable[_T]) -> Iterator[_T]: ...
 def partition(
-    pred: Optional[Callable[[_T], object]], iterable: Iterable[_T]
-) -> Tuple[Iterator[_T], Iterator[_T]]: ...
-def powerset(iterable: Iterable[_T]) -> Iterator[Tuple[_T, ...]]: ...
+    pred: Callable[[_T], object] | None, iterable: Iterable[_T]
+) -> tuple[Iterator[_T], Iterator[_T]]: ...
+def powerset(iterable: Iterable[_T]) -> Iterator[tuple[_T, ...]]: ...
 def unique_everseen(
-    iterable: Iterable[_T], key: Optional[Callable[[_T], _U]] = ...
+    iterable: Iterable[_T], key: Callable[[_T], _U] | None = ...
 ) -> Iterator[_T]: ...
 def unique_justseen(
-    iterable: Iterable[_T], key: Optional[Callable[[_T], object]] = ...
+    iterable: Iterable[_T], key: Callable[[_T], object] | None = ...
 ) -> Iterator[_T]: ...
 @overload
 def iter_except(
     func: Callable[[], _T],
-    exception: Union[Type[BaseException], Tuple[Type[BaseException], ...]],
+    exception: Type[BaseException] | tuple[Type[BaseException], ...],
     first: None = ...,
 ) -> Iterator[_T]: ...
 @overload
 def iter_except(
     func: Callable[[], _T],
-    exception: Union[Type[BaseException], Tuple[Type[BaseException], ...]],
+    exception: Type[BaseException] | tuple[Type[BaseException], ...],
     first: Callable[[], _U],
-) -> Iterator[Union[_T, _U]]: ...
+) -> Iterator[_T | _U]: ...
 @overload
 def first_true(
-    iterable: Iterable[_T], *, pred: Optional[Callable[[_T], object]] = ...
-) -> Optional[_T]: ...
+    iterable: Iterable[_T], *, pred: Callable[[_T], object] | None = ...
+) -> _T | None: ...
 @overload
 def first_true(
     iterable: Iterable[_T],
     default: _U,
-    pred: Optional[Callable[[_T], object]] = ...,
-) -> Union[_T, _U]: ...
+    pred: Callable[[_T], object] | None = ...,
+) -> _T | _U: ...
 def random_product(
     *args: Iterable[_T], repeat: int = ...
-) -> Tuple[_T, ...]: ...
+) -> tuple[_T, ...]: ...
 def random_permutation(
-    iterable: Iterable[_T], r: Optional[int] = ...
-) -> Tuple[_T, ...]: ...
-def random_combination(iterable: Iterable[_T], r: int) -> Tuple[_T, ...]: ...
+    iterable: Iterable[_T], r: int | None = ...
+) -> tuple[_T, ...]: ...
+def random_combination(iterable: Iterable[_T], r: int) -> tuple[_T, ...]: ...
 def random_combination_with_replacement(
     iterable: Iterable[_T], r: int
-) -> Tuple[_T, ...]: ...
+) -> tuple[_T, ...]: ...
 def nth_combination(
     iterable: Iterable[_T], r: int, index: int
-) -> Tuple[_T, ...]: ...
-def prepend(value: _T, iterator: Iterable[_U]) -> Iterator[Union[_T, _U]]: ...
+) -> tuple[_T, ...]: ...
+def prepend(value: _T, iterator: Iterable[_U]) -> Iterator[_T | _U]: ...
 def convolve(signal: Iterable[_T], kernel: Iterable[_T]) -> Iterator[_T]: ...
 def before_and_after(
     predicate: Callable[[_T], bool], it: Iterable[_T]
-) -> Tuple[Iterator[_T], Iterator[_T]]: ...
-def triplewise(iterable: Iterable[_T]) -> Iterator[Tuple[_T, _T, _T]]: ...
+) -> tuple[Iterator[_T], Iterator[_T]]: ...
+def triplewise(iterable: Iterable[_T]) -> Iterator[tuple[_T, _T, _T]]: ...
 def sliding_window(
     iterable: Iterable[_T], n: int
-) -> Iterator[Tuple[_T, ...]]: ...
-def subslices(iterable: Iterable[_T]) -> Iterator[List[_T]]: ...
-def polynomial_from_roots(roots: Sequence[int]) -> List[int]: ...
+) -> Iterator[tuple[_T, ...]]: ...
+def subslices(iterable: Iterable[_T]) -> Iterator[list[_T]]: ...
+def polynomial_from_roots(roots: Sequence[int]) -> list[int]: ...
+def iter_index(
+    iterable: Iterable[object],
+    value: Any,
+    start: int | None = ...,
+) -> Iterator[int]: ...
 def sieve(n: int) -> Iterator[int]: ...
 def batched(
     iterable: Iterable[_T],
     n: int,
-) -> Iterator[List[_T]]: ...
+) -> Iterator[list[_T]]: ...
+def transpose(
+    it: Iterable[Iterable[_T]],
+) -> tuple[Iterator[_T], ...]: ...
+def matmul(m1: Sequence[_T], m2: Sequence[_T]) -> Iterator[list[_T]]: ...
+def factor(n: int) -> Iterator[int]: ...
diff --git a/lib/tempora/__init__.py b/lib/tempora/__init__.py
index cece8bb7..27d5e828 100644
--- a/lib/tempora/__init__.py
+++ b/lib/tempora/__init__.py
@@ -11,9 +11,6 @@ from typing import Union, Tuple, Iterable
 from typing import cast
 
 
-from jaraco.functools import once
-
-
 # some useful constants
 osc_per_year = 290_091_329_207_984_000
 """
@@ -36,7 +33,7 @@ seconds_per_month = seconds_per_year / 12
 hours_per_month = hours_per_day * days_per_year / 12
 
 
-@once
+@functools.lru_cache()
 def _needs_year_help() -> bool:
     """
     Some versions of Python render %Y with only three characters :(
diff --git a/lib/tempora/tests/test_schedule.py b/lib/tempora/tests/test_schedule.py
deleted file mode 100644
index 0ce35435..00000000
--- a/lib/tempora/tests/test_schedule.py
+++ /dev/null
@@ -1,149 +0,0 @@
-import time
-import random
-import datetime
-from unittest import mock
-
-import pytest
-import pytz
-import freezegun
-
-from tempora import schedule
-
-
-do_nothing = type(None)
-
-
-def test_delayed_command_order():
-    """
-    delayed commands should be sorted by delay time
-    """
-    delays = [random.randint(0, 99) for x in range(5)]
-    cmds = sorted(
-        [schedule.DelayedCommand.after(delay, do_nothing) for delay in delays]
-    )
-    assert [c.delay.seconds for c in cmds] == sorted(delays)
-
-
-def test_periodic_command_delay():
-    "A PeriodicCommand must have a positive, non-zero delay."
-    with pytest.raises(ValueError) as exc_info:
-        schedule.PeriodicCommand.after(0, None)
-    assert str(exc_info.value) == test_periodic_command_delay.__doc__
-
-
-def test_periodic_command_fixed_delay():
-    """
-    Test that we can construct a periodic command with a fixed initial
-    delay.
-    """
-    fd = schedule.PeriodicCommandFixedDelay.at_time(
-        at=schedule.now(), delay=datetime.timedelta(seconds=2), target=lambda: None
-    )
-    assert fd.due() is True
-    assert fd.next().due() is False
-
-
-class TestCommands:
-    def test_delayed_command_from_timestamp(self):
-        """
-        Ensure a delayed command can be constructed from a timestamp.
-        """
-        t = time.time()
-        schedule.DelayedCommand.at_time(t, do_nothing)
-
-    def test_command_at_noon(self):
-        """
-        Create a periodic command that's run at noon every day.
-        """
-        when = datetime.time(12, 0, tzinfo=pytz.utc)
-        cmd = schedule.PeriodicCommandFixedDelay.daily_at(when, target=None)
-        assert cmd.due() is False
-        next_cmd = cmd.next()
-        daily = datetime.timedelta(days=1)
-        day_from_now = schedule.now() + daily
-        two_days_from_now = day_from_now + daily
-        assert day_from_now < next_cmd < two_days_from_now
-
-    @pytest.mark.parametrize("hour", range(10, 14))
-    @pytest.mark.parametrize("tz_offset", (14, -14))
-    def test_command_at_noon_distant_local(self, hour, tz_offset):
-        """
-        Run test_command_at_noon, but with the local timezone
-        more than 12 hours away from UTC.
-        """
-        with freezegun.freeze_time(f"2020-01-10 {hour:02}:01", tz_offset=tz_offset):
-            self.test_command_at_noon()
-
-
-class TestTimezones:
-    def test_alternate_timezone_west(self):
-        target_tz = pytz.timezone('US/Pacific')
-        target = schedule.now().astimezone(target_tz)
-        cmd = schedule.DelayedCommand.at_time(target, target=None)
-        assert cmd.due()
-
-    def test_alternate_timezone_east(self):
-        target_tz = pytz.timezone('Europe/Amsterdam')
-        target = schedule.now().astimezone(target_tz)
-        cmd = schedule.DelayedCommand.at_time(target, target=None)
-        assert cmd.due()
-
-    def test_daylight_savings(self):
-        """
-        A command at 9am should always be 9am regardless of
-        a DST boundary.
-        """
-        with freezegun.freeze_time('2018-03-10 08:00:00'):
-            target_tz = pytz.timezone('US/Eastern')
-            target_time = datetime.time(9, tzinfo=target_tz)
-            cmd = schedule.PeriodicCommandFixedDelay.daily_at(
-                target_time, target=lambda: None
-            )
-
-        def naive(dt):
-            return dt.replace(tzinfo=None)
-
-        assert naive(cmd) == datetime.datetime(2018, 3, 10, 9, 0, 0)
-        next_ = cmd.next()
-        assert naive(next_) == datetime.datetime(2018, 3, 11, 9, 0, 0)
-        assert next_ - cmd == datetime.timedelta(hours=23)
-
-
-class TestScheduler:
-    def test_invoke_scheduler(self):
-        sched = schedule.InvokeScheduler()
-        target = mock.MagicMock()
-        cmd = schedule.DelayedCommand.after(0, target)
-        sched.add(cmd)
-        sched.run_pending()
-        target.assert_called_once()
-        assert not sched.queue
-
-    def test_callback_scheduler(self):
-        callback = mock.MagicMock()
-        sched = schedule.CallbackScheduler(callback)
-        target = mock.MagicMock()
-        cmd = schedule.DelayedCommand.after(0, target)
-        sched.add(cmd)
-        sched.run_pending()
-        callback.assert_called_once_with(target)
-
-    def test_periodic_command(self):
-        sched = schedule.InvokeScheduler()
-        target = mock.MagicMock()
-
-        before = datetime.datetime.utcnow()
-
-        cmd = schedule.PeriodicCommand.after(10, target)
-        sched.add(cmd)
-        sched.run_pending()
-        target.assert_not_called()
-
-        with freezegun.freeze_time(before + datetime.timedelta(seconds=15)):
-            sched.run_pending()
-        assert sched.queue
-        target.assert_called_once()
-
-        with freezegun.freeze_time(before + datetime.timedelta(seconds=25)):
-            sched.run_pending()
-        assert target.call_count == 2
diff --git a/lib/tempora/tests/test_timing.py b/lib/tempora/tests/test_timing.py
deleted file mode 100644
index 43bf7efc..00000000
--- a/lib/tempora/tests/test_timing.py
+++ /dev/null
@@ -1,50 +0,0 @@
-import datetime
-import time
-import contextlib
-import os
-from unittest import mock
-
-import pytest
-from tempora import timing
-
-
-def test_IntervalGovernor():
-    """
-    IntervalGovernor should prevent a function from being called more than
-    once per interval.
-    """
-    func_under_test = mock.MagicMock()
-    # to look like a function, it needs a __name__ attribute
-    func_under_test.__name__ = 'func_under_test'
-    interval = datetime.timedelta(seconds=1)
-    governed = timing.IntervalGovernor(interval)(func_under_test)
-    governed('a')
-    governed('b')
-    governed(3, 'sir')
-    func_under_test.assert_called_once_with('a')
-
-
-@pytest.fixture
-def alt_tz(monkeypatch):
-    hasattr(time, 'tzset') or pytest.skip("tzset not available")
-
-    @contextlib.contextmanager
-    def change():
-        val = 'AEST-10AEDT-11,M10.5.0,M3.5.0'
-        with monkeypatch.context() as ctx:
-            ctx.setitem(os.environ, 'TZ', val)
-            time.tzset()
-            yield
-        time.tzset()
-
-    return change()
-
-
-def test_Stopwatch_timezone_change(alt_tz):
-    """
-    The stopwatch should provide a consistent duration even
-    if the timezone changes.
-    """
-    watch = timing.Stopwatch()
-    with alt_tz:
-        assert abs(watch.split().total_seconds()) < 0.1
diff --git a/requirements.txt b/requirements.txt
index b88c9efe..73c9308b 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -42,7 +42,7 @@ rumps==0.4.0; platform_system == "Darwin"
 simplejson==3.18.0
 six==1.16.0
 soupsieve==2.3.2.post1
-tempora==5.1.0
+tempora==5.2.1
 tokenize-rt==5.0.0
 tzdata==2022.7
 tzlocal==4.2