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diff --git a/.venv/lib/python3.12/site-packages/sqlalchemy/sql/util.py b/.venv/lib/python3.12/site-packages/sqlalchemy/sql/util.py
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+# sql/util.py
+# Copyright (C) 2005-2025 the SQLAlchemy authors and contributors
+# <see AUTHORS file>
+#
+# This module is part of SQLAlchemy and is released under
+# the MIT License: https://www.opensource.org/licenses/mit-license.php
+# mypy: allow-untyped-defs, allow-untyped-calls
+
+"""High level utilities which build upon other modules here.
+
+"""
+from __future__ import annotations
+
+from collections import deque
+import copy
+from itertools import chain
+import typing
+from typing import AbstractSet
+from typing import Any
+from typing import Callable
+from typing import cast
+from typing import Collection
+from typing import Dict
+from typing import Iterable
+from typing import Iterator
+from typing import List
+from typing import Optional
+from typing import overload
+from typing import Sequence
+from typing import Tuple
+from typing import TYPE_CHECKING
+from typing import TypeVar
+from typing import Union
+
+from . import coercions
+from . import operators
+from . import roles
+from . import visitors
+from ._typing import is_text_clause
+from .annotation import _deep_annotate as _deep_annotate  # noqa: F401
+from .annotation import _deep_deannotate as _deep_deannotate  # noqa: F401
+from .annotation import _shallow_annotate as _shallow_annotate  # noqa: F401
+from .base import _expand_cloned
+from .base import _from_objects
+from .cache_key import HasCacheKey as HasCacheKey  # noqa: F401
+from .ddl import sort_tables as sort_tables  # noqa: F401
+from .elements import _find_columns as _find_columns
+from .elements import _label_reference
+from .elements import _textual_label_reference
+from .elements import BindParameter
+from .elements import ClauseElement
+from .elements import ColumnClause
+from .elements import ColumnElement
+from .elements import Grouping
+from .elements import KeyedColumnElement
+from .elements import Label
+from .elements import NamedColumn
+from .elements import Null
+from .elements import UnaryExpression
+from .schema import Column
+from .selectable import Alias
+from .selectable import FromClause
+from .selectable import FromGrouping
+from .selectable import Join
+from .selectable import ScalarSelect
+from .selectable import SelectBase
+from .selectable import TableClause
+from .visitors import _ET
+from .. import exc
+from .. import util
+from ..util.typing import Literal
+from ..util.typing import Protocol
+
+if typing.TYPE_CHECKING:
+    from ._typing import _EquivalentColumnMap
+    from ._typing import _LimitOffsetType
+    from ._typing import _TypeEngineArgument
+    from .elements import BinaryExpression
+    from .elements import TextClause
+    from .selectable import _JoinTargetElement
+    from .selectable import _SelectIterable
+    from .selectable import Selectable
+    from .visitors import _TraverseCallableType
+    from .visitors import ExternallyTraversible
+    from .visitors import ExternalTraversal
+    from ..engine.interfaces import _AnyExecuteParams
+    from ..engine.interfaces import _AnyMultiExecuteParams
+    from ..engine.interfaces import _AnySingleExecuteParams
+    from ..engine.interfaces import _CoreSingleExecuteParams
+    from ..engine.row import Row
+
+_CE = TypeVar("_CE", bound="ColumnElement[Any]")
+
+
+def join_condition(
+    a: FromClause,
+    b: FromClause,
+    a_subset: Optional[FromClause] = None,
+    consider_as_foreign_keys: Optional[AbstractSet[ColumnClause[Any]]] = None,
+) -> ColumnElement[bool]:
+    """Create a join condition between two tables or selectables.
+
+    e.g.::
+
+        join_condition(tablea, tableb)
+
+    would produce an expression along the lines of::
+
+        tablea.c.id == tableb.c.tablea_id
+
+    The join is determined based on the foreign key relationships
+    between the two selectables.   If there are multiple ways
+    to join, or no way to join, an error is raised.
+
+    :param a_subset: An optional expression that is a sub-component
+        of ``a``.  An attempt will be made to join to just this sub-component
+        first before looking at the full ``a`` construct, and if found
+        will be successful even if there are other ways to join to ``a``.
+        This allows the "right side" of a join to be passed thereby
+        providing a "natural join".
+
+    """
+    return Join._join_condition(
+        a,
+        b,
+        a_subset=a_subset,
+        consider_as_foreign_keys=consider_as_foreign_keys,
+    )
+
+
+def find_join_source(
+    clauses: List[FromClause], join_to: FromClause
+) -> List[int]:
+    """Given a list of FROM clauses and a selectable,
+    return the first index and element from the list of
+    clauses which can be joined against the selectable.  returns
+    None, None if no match is found.
+
+    e.g.::
+
+        clause1 = table1.join(table2)
+        clause2 = table4.join(table5)
+
+        join_to = table2.join(table3)
+
+        find_join_source([clause1, clause2], join_to) == clause1
+
+    """
+
+    selectables = list(_from_objects(join_to))
+    idx = []
+    for i, f in enumerate(clauses):
+        for s in selectables:
+            if f.is_derived_from(s):
+                idx.append(i)
+    return idx
+
+
+def find_left_clause_that_matches_given(
+    clauses: Sequence[FromClause], join_from: FromClause
+) -> List[int]:
+    """Given a list of FROM clauses and a selectable,
+    return the indexes from the list of
+    clauses which is derived from the selectable.
+
+    """
+
+    selectables = list(_from_objects(join_from))
+    liberal_idx = []
+    for i, f in enumerate(clauses):
+        for s in selectables:
+            # basic check, if f is derived from s.
+            # this can be joins containing a table, or an aliased table
+            # or select statement matching to a table.  This check
+            # will match a table to a selectable that is adapted from
+            # that table.  With Query, this suits the case where a join
+            # is being made to an adapted entity
+            if f.is_derived_from(s):
+                liberal_idx.append(i)
+                break
+
+    # in an extremely small set of use cases, a join is being made where
+    # there are multiple FROM clauses where our target table is represented
+    # in more than one, such as embedded or similar.   in this case, do
+    # another pass where we try to get a more exact match where we aren't
+    # looking at adaption relationships.
+    if len(liberal_idx) > 1:
+        conservative_idx = []
+        for idx in liberal_idx:
+            f = clauses[idx]
+            for s in selectables:
+                if set(surface_selectables(f)).intersection(
+                    surface_selectables(s)
+                ):
+                    conservative_idx.append(idx)
+                    break
+        if conservative_idx:
+            return conservative_idx
+
+    return liberal_idx
+
+
+def find_left_clause_to_join_from(
+    clauses: Sequence[FromClause],
+    join_to: _JoinTargetElement,
+    onclause: Optional[ColumnElement[Any]],
+) -> List[int]:
+    """Given a list of FROM clauses, a selectable,
+    and optional ON clause, return a list of integer indexes from the
+    clauses list indicating the clauses that can be joined from.
+
+    The presence of an "onclause" indicates that at least one clause can
+    definitely be joined from; if the list of clauses is of length one
+    and the onclause is given, returns that index.   If the list of clauses
+    is more than length one, and the onclause is given, attempts to locate
+    which clauses contain the same columns.
+
+    """
+    idx = []
+    selectables = set(_from_objects(join_to))
+
+    # if we are given more than one target clause to join
+    # from, use the onclause to provide a more specific answer.
+    # otherwise, don't try to limit, after all, "ON TRUE" is a valid
+    # on clause
+    if len(clauses) > 1 and onclause is not None:
+        resolve_ambiguity = True
+        cols_in_onclause = _find_columns(onclause)
+    else:
+        resolve_ambiguity = False
+        cols_in_onclause = None
+
+    for i, f in enumerate(clauses):
+        for s in selectables.difference([f]):
+            if resolve_ambiguity:
+                assert cols_in_onclause is not None
+                if set(f.c).union(s.c).issuperset(cols_in_onclause):
+                    idx.append(i)
+                    break
+            elif onclause is not None or Join._can_join(f, s):
+                idx.append(i)
+                break
+
+    if len(idx) > 1:
+        # this is the same "hide froms" logic from
+        # Selectable._get_display_froms
+        toremove = set(
+            chain(*[_expand_cloned(f._hide_froms) for f in clauses])
+        )
+        idx = [i for i in idx if clauses[i] not in toremove]
+
+    # onclause was given and none of them resolved, so assume
+    # all indexes can match
+    if not idx and onclause is not None:
+        return list(range(len(clauses)))
+    else:
+        return idx
+
+
+def visit_binary_product(
+    fn: Callable[
+        [BinaryExpression[Any], ColumnElement[Any], ColumnElement[Any]], None
+    ],
+    expr: ColumnElement[Any],
+) -> None:
+    """Produce a traversal of the given expression, delivering
+    column comparisons to the given function.
+
+    The function is of the form::
+
+        def my_fn(binary, left, right): ...
+
+    For each binary expression located which has a
+    comparison operator, the product of "left" and
+    "right" will be delivered to that function,
+    in terms of that binary.
+
+    Hence an expression like::
+
+        and_((a + b) == q + func.sum(e + f), j == r)
+
+    would have the traversal:
+
+    .. sourcecode:: text
+
+        a <eq> q
+        a <eq> e
+        a <eq> f
+        b <eq> q
+        b <eq> e
+        b <eq> f
+        j <eq> r
+
+    That is, every combination of "left" and
+    "right" that doesn't further contain
+    a binary comparison is passed as pairs.
+
+    """
+    stack: List[BinaryExpression[Any]] = []
+
+    def visit(element: ClauseElement) -> Iterator[ColumnElement[Any]]:
+        if isinstance(element, ScalarSelect):
+            # we don't want to dig into correlated subqueries,
+            # those are just column elements by themselves
+            yield element
+        elif element.__visit_name__ == "binary" and operators.is_comparison(
+            element.operator  # type: ignore
+        ):
+            stack.insert(0, element)  # type: ignore
+            for l in visit(element.left):  # type: ignore
+                for r in visit(element.right):  # type: ignore
+                    fn(stack[0], l, r)
+            stack.pop(0)
+            for elem in element.get_children():
+                visit(elem)
+        else:
+            if isinstance(element, ColumnClause):
+                yield element
+            for elem in element.get_children():
+                yield from visit(elem)
+
+    list(visit(expr))
+    visit = None  # type: ignore  # remove gc cycles
+
+
+def find_tables(
+    clause: ClauseElement,
+    *,
+    check_columns: bool = False,
+    include_aliases: bool = False,
+    include_joins: bool = False,
+    include_selects: bool = False,
+    include_crud: bool = False,
+) -> List[TableClause]:
+    """locate Table objects within the given expression."""
+
+    tables: List[TableClause] = []
+    _visitors: Dict[str, _TraverseCallableType[Any]] = {}
+
+    if include_selects:
+        _visitors["select"] = _visitors["compound_select"] = tables.append
+
+    if include_joins:
+        _visitors["join"] = tables.append
+
+    if include_aliases:
+        _visitors["alias"] = _visitors["subquery"] = _visitors[
+            "tablesample"
+        ] = _visitors["lateral"] = tables.append
+
+    if include_crud:
+        _visitors["insert"] = _visitors["update"] = _visitors["delete"] = (
+            lambda ent: tables.append(ent.table)
+        )
+
+    if check_columns:
+
+        def visit_column(column):
+            tables.append(column.table)
+
+        _visitors["column"] = visit_column
+
+    _visitors["table"] = tables.append
+
+    visitors.traverse(clause, {}, _visitors)
+    return tables
+
+
+def unwrap_order_by(clause: Any) -> Any:
+    """Break up an 'order by' expression into individual column-expressions,
+    without DESC/ASC/NULLS FIRST/NULLS LAST"""
+
+    cols = util.column_set()
+    result = []
+    stack = deque([clause])
+
+    # examples
+    # column -> ASC/DESC == column
+    # column -> ASC/DESC -> label == column
+    # column -> label -> ASC/DESC -> label == column
+    # scalar_select -> label -> ASC/DESC == scalar_select -> label
+
+    while stack:
+        t = stack.popleft()
+        if isinstance(t, ColumnElement) and (
+            not isinstance(t, UnaryExpression)
+            or not operators.is_ordering_modifier(t.modifier)  # type: ignore
+        ):
+            if isinstance(t, Label) and not isinstance(
+                t.element, ScalarSelect
+            ):
+                t = t.element
+
+                if isinstance(t, Grouping):
+                    t = t.element
+
+                stack.append(t)
+                continue
+            elif isinstance(t, _label_reference):
+                t = t.element
+
+                stack.append(t)
+                continue
+            if isinstance(t, (_textual_label_reference)):
+                continue
+            if t not in cols:
+                cols.add(t)
+                result.append(t)
+
+        else:
+            for c in t.get_children():
+                stack.append(c)
+    return result
+
+
+def unwrap_label_reference(element):
+    def replace(
+        element: ExternallyTraversible, **kw: Any
+    ) -> Optional[ExternallyTraversible]:
+        if isinstance(element, _label_reference):
+            return element.element
+        elif isinstance(element, _textual_label_reference):
+            assert False, "can't unwrap a textual label reference"
+        return None
+
+    return visitors.replacement_traverse(element, {}, replace)
+
+
+def expand_column_list_from_order_by(collist, order_by):
+    """Given the columns clause and ORDER BY of a selectable,
+    return a list of column expressions that can be added to the collist
+    corresponding to the ORDER BY, without repeating those already
+    in the collist.
+
+    """
+    cols_already_present = {
+        col.element if col._order_by_label_element is not None else col
+        for col in collist
+    }
+
+    to_look_for = list(chain(*[unwrap_order_by(o) for o in order_by]))
+
+    return [col for col in to_look_for if col not in cols_already_present]
+
+
+def clause_is_present(clause, search):
+    """Given a target clause and a second to search within, return True
+    if the target is plainly present in the search without any
+    subqueries or aliases involved.
+
+    Basically descends through Joins.
+
+    """
+
+    for elem in surface_selectables(search):
+        if clause == elem:  # use == here so that Annotated's compare
+            return True
+    else:
+        return False
+
+
+def tables_from_leftmost(clause: FromClause) -> Iterator[FromClause]:
+    if isinstance(clause, Join):
+        yield from tables_from_leftmost(clause.left)
+        yield from tables_from_leftmost(clause.right)
+    elif isinstance(clause, FromGrouping):
+        yield from tables_from_leftmost(clause.element)
+    else:
+        yield clause
+
+
+def surface_selectables(clause):
+    stack = [clause]
+    while stack:
+        elem = stack.pop()
+        yield elem
+        if isinstance(elem, Join):
+            stack.extend((elem.left, elem.right))
+        elif isinstance(elem, FromGrouping):
+            stack.append(elem.element)
+
+
+def surface_selectables_only(clause):
+    stack = [clause]
+    while stack:
+        elem = stack.pop()
+        if isinstance(elem, (TableClause, Alias)):
+            yield elem
+        if isinstance(elem, Join):
+            stack.extend((elem.left, elem.right))
+        elif isinstance(elem, FromGrouping):
+            stack.append(elem.element)
+        elif isinstance(elem, ColumnClause):
+            if elem.table is not None:
+                stack.append(elem.table)
+            else:
+                yield elem
+        elif elem is not None:
+            yield elem
+
+
+def extract_first_column_annotation(column, annotation_name):
+    filter_ = (FromGrouping, SelectBase)
+
+    stack = deque([column])
+    while stack:
+        elem = stack.popleft()
+        if annotation_name in elem._annotations:
+            return elem._annotations[annotation_name]
+        for sub in elem.get_children():
+            if isinstance(sub, filter_):
+                continue
+            stack.append(sub)
+    return None
+
+
+def selectables_overlap(left: FromClause, right: FromClause) -> bool:
+    """Return True if left/right have some overlapping selectable"""
+
+    return bool(
+        set(surface_selectables(left)).intersection(surface_selectables(right))
+    )
+
+
+def bind_values(clause):
+    """Return an ordered list of "bound" values in the given clause.
+
+    E.g.::
+
+        >>> expr = and_(table.c.foo == 5, table.c.foo == 7)
+        >>> bind_values(expr)
+        [5, 7]
+    """
+
+    v = []
+
+    def visit_bindparam(bind):
+        v.append(bind.effective_value)
+
+    visitors.traverse(clause, {}, {"bindparam": visit_bindparam})
+    return v
+
+
+def _quote_ddl_expr(element):
+    if isinstance(element, str):
+        element = element.replace("'", "''")
+        return "'%s'" % element
+    else:
+        return repr(element)
+
+
+class _repr_base:
+    _LIST: int = 0
+    _TUPLE: int = 1
+    _DICT: int = 2
+
+    __slots__ = ("max_chars",)
+
+    max_chars: int
+
+    def trunc(self, value: Any) -> str:
+        rep = repr(value)
+        lenrep = len(rep)
+        if lenrep > self.max_chars:
+            segment_length = self.max_chars // 2
+            rep = (
+                rep[0:segment_length]
+                + (
+                    " ... (%d characters truncated) ... "
+                    % (lenrep - self.max_chars)
+                )
+                + rep[-segment_length:]
+            )
+        return rep
+
+
+def _repr_single_value(value):
+    rp = _repr_base()
+    rp.max_chars = 300
+    return rp.trunc(value)
+
+
+class _repr_row(_repr_base):
+    """Provide a string view of a row."""
+
+    __slots__ = ("row",)
+
+    def __init__(self, row: Row[Any], max_chars: int = 300):
+        self.row = row
+        self.max_chars = max_chars
+
+    def __repr__(self) -> str:
+        trunc = self.trunc
+        return "(%s%s)" % (
+            ", ".join(trunc(value) for value in self.row),
+            "," if len(self.row) == 1 else "",
+        )
+
+
+class _long_statement(str):
+    def __str__(self) -> str:
+        lself = len(self)
+        if lself > 500:
+            lleft = 250
+            lright = 100
+            trunc = lself - lleft - lright
+            return (
+                f"{self[0:lleft]} ... {trunc} "
+                f"characters truncated ... {self[-lright:]}"
+            )
+        else:
+            return str.__str__(self)
+
+
+class _repr_params(_repr_base):
+    """Provide a string view of bound parameters.
+
+    Truncates display to a given number of 'multi' parameter sets,
+    as well as long values to a given number of characters.
+
+    """
+
+    __slots__ = "params", "batches", "ismulti", "max_params"
+
+    def __init__(
+        self,
+        params: Optional[_AnyExecuteParams],
+        batches: int,
+        max_params: int = 100,
+        max_chars: int = 300,
+        ismulti: Optional[bool] = None,
+    ):
+        self.params = params
+        self.ismulti = ismulti
+        self.batches = batches
+        self.max_chars = max_chars
+        self.max_params = max_params
+
+    def __repr__(self) -> str:
+        if self.ismulti is None:
+            return self.trunc(self.params)
+
+        if isinstance(self.params, list):
+            typ = self._LIST
+
+        elif isinstance(self.params, tuple):
+            typ = self._TUPLE
+        elif isinstance(self.params, dict):
+            typ = self._DICT
+        else:
+            return self.trunc(self.params)
+
+        if self.ismulti:
+            multi_params = cast(
+                "_AnyMultiExecuteParams",
+                self.params,
+            )
+
+            if len(self.params) > self.batches:
+                msg = (
+                    " ... displaying %i of %i total bound parameter sets ... "
+                )
+                return " ".join(
+                    (
+                        self._repr_multi(
+                            multi_params[: self.batches - 2],
+                            typ,
+                        )[0:-1],
+                        msg % (self.batches, len(self.params)),
+                        self._repr_multi(multi_params[-2:], typ)[1:],
+                    )
+                )
+            else:
+                return self._repr_multi(multi_params, typ)
+        else:
+            return self._repr_params(
+                cast(
+                    "_AnySingleExecuteParams",
+                    self.params,
+                ),
+                typ,
+            )
+
+    def _repr_multi(
+        self,
+        multi_params: _AnyMultiExecuteParams,
+        typ: int,
+    ) -> str:
+        if multi_params:
+            if isinstance(multi_params[0], list):
+                elem_type = self._LIST
+            elif isinstance(multi_params[0], tuple):
+                elem_type = self._TUPLE
+            elif isinstance(multi_params[0], dict):
+                elem_type = self._DICT
+            else:
+                assert False, "Unknown parameter type %s" % (
+                    type(multi_params[0])
+                )
+
+            elements = ", ".join(
+                self._repr_params(params, elem_type) for params in multi_params
+            )
+        else:
+            elements = ""
+
+        if typ == self._LIST:
+            return "[%s]" % elements
+        else:
+            return "(%s)" % elements
+
+    def _get_batches(self, params: Iterable[Any]) -> Any:
+        lparams = list(params)
+        lenparams = len(lparams)
+        if lenparams > self.max_params:
+            lleft = self.max_params // 2
+            return (
+                lparams[0:lleft],
+                lparams[-lleft:],
+                lenparams - self.max_params,
+            )
+        else:
+            return lparams, None, None
+
+    def _repr_params(
+        self,
+        params: _AnySingleExecuteParams,
+        typ: int,
+    ) -> str:
+        if typ is self._DICT:
+            return self._repr_param_dict(
+                cast("_CoreSingleExecuteParams", params)
+            )
+        elif typ is self._TUPLE:
+            return self._repr_param_tuple(cast("Sequence[Any]", params))
+        else:
+            return self._repr_param_list(params)
+
+    def _repr_param_dict(self, params: _CoreSingleExecuteParams) -> str:
+        trunc = self.trunc
+        (
+            items_first_batch,
+            items_second_batch,
+            trunclen,
+        ) = self._get_batches(params.items())
+
+        if items_second_batch:
+            text = "{%s" % (
+                ", ".join(
+                    f"{key!r}: {trunc(value)}"
+                    for key, value in items_first_batch
+                )
+            )
+            text += f" ... {trunclen} parameters truncated ... "
+            text += "%s}" % (
+                ", ".join(
+                    f"{key!r}: {trunc(value)}"
+                    for key, value in items_second_batch
+                )
+            )
+        else:
+            text = "{%s}" % (
+                ", ".join(
+                    f"{key!r}: {trunc(value)}"
+                    for key, value in items_first_batch
+                )
+            )
+        return text
+
+    def _repr_param_tuple(self, params: Sequence[Any]) -> str:
+        trunc = self.trunc
+
+        (
+            items_first_batch,
+            items_second_batch,
+            trunclen,
+        ) = self._get_batches(params)
+
+        if items_second_batch:
+            text = "(%s" % (
+                ", ".join(trunc(value) for value in items_first_batch)
+            )
+            text += f" ... {trunclen} parameters truncated ... "
+            text += "%s)" % (
+                ", ".join(trunc(value) for value in items_second_batch),
+            )
+        else:
+            text = "(%s%s)" % (
+                ", ".join(trunc(value) for value in items_first_batch),
+                "," if len(items_first_batch) == 1 else "",
+            )
+        return text
+
+    def _repr_param_list(self, params: _AnySingleExecuteParams) -> str:
+        trunc = self.trunc
+        (
+            items_first_batch,
+            items_second_batch,
+            trunclen,
+        ) = self._get_batches(params)
+
+        if items_second_batch:
+            text = "[%s" % (
+                ", ".join(trunc(value) for value in items_first_batch)
+            )
+            text += f" ... {trunclen} parameters truncated ... "
+            text += "%s]" % (
+                ", ".join(trunc(value) for value in items_second_batch)
+            )
+        else:
+            text = "[%s]" % (
+                ", ".join(trunc(value) for value in items_first_batch)
+            )
+        return text
+
+
+def adapt_criterion_to_null(crit: _CE, nulls: Collection[Any]) -> _CE:
+    """given criterion containing bind params, convert selected elements
+    to IS NULL.
+
+    """
+
+    def visit_binary(binary):
+        if (
+            isinstance(binary.left, BindParameter)
+            and binary.left._identifying_key in nulls
+        ):
+            # reverse order if the NULL is on the left side
+            binary.left = binary.right
+            binary.right = Null()
+            binary.operator = operators.is_
+            binary.negate = operators.is_not
+        elif (
+            isinstance(binary.right, BindParameter)
+            and binary.right._identifying_key in nulls
+        ):
+            binary.right = Null()
+            binary.operator = operators.is_
+            binary.negate = operators.is_not
+
+    return visitors.cloned_traverse(crit, {}, {"binary": visit_binary})
+
+
+def splice_joins(
+    left: Optional[FromClause],
+    right: Optional[FromClause],
+    stop_on: Optional[FromClause] = None,
+) -> Optional[FromClause]:
+    if left is None:
+        return right
+
+    stack: List[Tuple[Optional[FromClause], Optional[Join]]] = [(right, None)]
+
+    adapter = ClauseAdapter(left)
+    ret = None
+    while stack:
+        (right, prevright) = stack.pop()
+        if isinstance(right, Join) and right is not stop_on:
+            right = right._clone()
+            right.onclause = adapter.traverse(right.onclause)
+            stack.append((right.left, right))
+        else:
+            right = adapter.traverse(right)
+        if prevright is not None:
+            assert right is not None
+            prevright.left = right
+        if ret is None:
+            ret = right
+
+    return ret
+
+
+@overload
+def reduce_columns(
+    columns: Iterable[ColumnElement[Any]],
+    *clauses: Optional[ClauseElement],
+    **kw: bool,
+) -> Sequence[ColumnElement[Any]]: ...
+
+
+@overload
+def reduce_columns(
+    columns: _SelectIterable,
+    *clauses: Optional[ClauseElement],
+    **kw: bool,
+) -> Sequence[Union[ColumnElement[Any], TextClause]]: ...
+
+
+def reduce_columns(
+    columns: _SelectIterable,
+    *clauses: Optional[ClauseElement],
+    **kw: bool,
+) -> Collection[Union[ColumnElement[Any], TextClause]]:
+    r"""given a list of columns, return a 'reduced' set based on natural
+    equivalents.
+
+    the set is reduced to the smallest list of columns which have no natural
+    equivalent present in the list.  A "natural equivalent" means that two
+    columns will ultimately represent the same value because they are related
+    by a foreign key.
+
+    \*clauses is an optional list of join clauses which will be traversed
+    to further identify columns that are "equivalent".
+
+    \**kw may specify 'ignore_nonexistent_tables' to ignore foreign keys
+    whose tables are not yet configured, or columns that aren't yet present.
+
+    This function is primarily used to determine the most minimal "primary
+    key" from a selectable, by reducing the set of primary key columns present
+    in the selectable to just those that are not repeated.
+
+    """
+    ignore_nonexistent_tables = kw.pop("ignore_nonexistent_tables", False)
+    only_synonyms = kw.pop("only_synonyms", False)
+
+    column_set = util.OrderedSet(columns)
+    cset_no_text: util.OrderedSet[ColumnElement[Any]] = column_set.difference(
+        c for c in column_set if is_text_clause(c)  # type: ignore
+    )
+
+    omit = util.column_set()
+    for col in cset_no_text:
+        for fk in chain(*[c.foreign_keys for c in col.proxy_set]):
+            for c in cset_no_text:
+                if c is col:
+                    continue
+                try:
+                    fk_col = fk.column
+                except exc.NoReferencedColumnError:
+                    # TODO: add specific coverage here
+                    # to test/sql/test_selectable ReduceTest
+                    if ignore_nonexistent_tables:
+                        continue
+                    else:
+                        raise
+                except exc.NoReferencedTableError:
+                    # TODO: add specific coverage here
+                    # to test/sql/test_selectable ReduceTest
+                    if ignore_nonexistent_tables:
+                        continue
+                    else:
+                        raise
+                if fk_col.shares_lineage(c) and (
+                    not only_synonyms or c.name == col.name
+                ):
+                    omit.add(col)
+                    break
+
+    if clauses:
+
+        def visit_binary(binary):
+            if binary.operator == operators.eq:
+                cols = util.column_set(
+                    chain(
+                        *[c.proxy_set for c in cset_no_text.difference(omit)]
+                    )
+                )
+                if binary.left in cols and binary.right in cols:
+                    for c in reversed(cset_no_text):
+                        if c.shares_lineage(binary.right) and (
+                            not only_synonyms or c.name == binary.left.name
+                        ):
+                            omit.add(c)
+                            break
+
+        for clause in clauses:
+            if clause is not None:
+                visitors.traverse(clause, {}, {"binary": visit_binary})
+
+    return column_set.difference(omit)
+
+
+def criterion_as_pairs(
+    expression,
+    consider_as_foreign_keys=None,
+    consider_as_referenced_keys=None,
+    any_operator=False,
+):
+    """traverse an expression and locate binary criterion pairs."""
+
+    if consider_as_foreign_keys and consider_as_referenced_keys:
+        raise exc.ArgumentError(
+            "Can only specify one of "
+            "'consider_as_foreign_keys' or "
+            "'consider_as_referenced_keys'"
+        )
+
+    def col_is(a, b):
+        # return a is b
+        return a.compare(b)
+
+    def visit_binary(binary):
+        if not any_operator and binary.operator is not operators.eq:
+            return
+        if not isinstance(binary.left, ColumnElement) or not isinstance(
+            binary.right, ColumnElement
+        ):
+            return
+
+        if consider_as_foreign_keys:
+            if binary.left in consider_as_foreign_keys and (
+                col_is(binary.right, binary.left)
+                or binary.right not in consider_as_foreign_keys
+            ):
+                pairs.append((binary.right, binary.left))
+            elif binary.right in consider_as_foreign_keys and (
+                col_is(binary.left, binary.right)
+                or binary.left not in consider_as_foreign_keys
+            ):
+                pairs.append((binary.left, binary.right))
+        elif consider_as_referenced_keys:
+            if binary.left in consider_as_referenced_keys and (
+                col_is(binary.right, binary.left)
+                or binary.right not in consider_as_referenced_keys
+            ):
+                pairs.append((binary.left, binary.right))
+            elif binary.right in consider_as_referenced_keys and (
+                col_is(binary.left, binary.right)
+                or binary.left not in consider_as_referenced_keys
+            ):
+                pairs.append((binary.right, binary.left))
+        else:
+            if isinstance(binary.left, Column) and isinstance(
+                binary.right, Column
+            ):
+                if binary.left.references(binary.right):
+                    pairs.append((binary.right, binary.left))
+                elif binary.right.references(binary.left):
+                    pairs.append((binary.left, binary.right))
+
+    pairs: List[Tuple[ColumnElement[Any], ColumnElement[Any]]] = []
+    visitors.traverse(expression, {}, {"binary": visit_binary})
+    return pairs
+
+
+class ClauseAdapter(visitors.ReplacingExternalTraversal):
+    """Clones and modifies clauses based on column correspondence.
+
+    E.g.::
+
+      table1 = Table(
+          "sometable",
+          metadata,
+          Column("col1", Integer),
+          Column("col2", Integer),
+      )
+      table2 = Table(
+          "someothertable",
+          metadata,
+          Column("col1", Integer),
+          Column("col2", Integer),
+      )
+
+      condition = table1.c.col1 == table2.c.col1
+
+    make an alias of table1::
+
+      s = table1.alias("foo")
+
+    calling ``ClauseAdapter(s).traverse(condition)`` converts
+    condition to read::
+
+      s.c.col1 == table2.c.col1
+
+    """
+
+    __slots__ = (
+        "__traverse_options__",
+        "selectable",
+        "include_fn",
+        "exclude_fn",
+        "equivalents",
+        "adapt_on_names",
+        "adapt_from_selectables",
+    )
+
+    def __init__(
+        self,
+        selectable: Selectable,
+        equivalents: Optional[_EquivalentColumnMap] = None,
+        include_fn: Optional[Callable[[ClauseElement], bool]] = None,
+        exclude_fn: Optional[Callable[[ClauseElement], bool]] = None,
+        adapt_on_names: bool = False,
+        anonymize_labels: bool = False,
+        adapt_from_selectables: Optional[AbstractSet[FromClause]] = None,
+    ):
+        self.__traverse_options__ = {
+            "stop_on": [selectable],
+            "anonymize_labels": anonymize_labels,
+        }
+        self.selectable = selectable
+        self.include_fn = include_fn
+        self.exclude_fn = exclude_fn
+        self.equivalents = util.column_dict(equivalents or {})
+        self.adapt_on_names = adapt_on_names
+        self.adapt_from_selectables = adapt_from_selectables
+
+    if TYPE_CHECKING:
+
+        @overload
+        def traverse(self, obj: Literal[None]) -> None: ...
+
+        # note this specializes the ReplacingExternalTraversal.traverse()
+        # method to state
+        # that we will return the same kind of ExternalTraversal object as
+        # we were given.  This is probably not 100% true, such as it's
+        # possible for us to swap out Alias for Table at the top level.
+        # Ideally there could be overloads specific to ColumnElement and
+        # FromClause but Mypy is not accepting those as compatible with
+        # the base ReplacingExternalTraversal
+        @overload
+        def traverse(self, obj: _ET) -> _ET: ...
+
+        def traverse(
+            self, obj: Optional[ExternallyTraversible]
+        ) -> Optional[ExternallyTraversible]: ...
+
+    def _corresponding_column(
+        self, col, require_embedded, _seen=util.EMPTY_SET
+    ):
+        newcol = self.selectable.corresponding_column(
+            col, require_embedded=require_embedded
+        )
+        if newcol is None and col in self.equivalents and col not in _seen:
+            for equiv in self.equivalents[col]:
+                newcol = self._corresponding_column(
+                    equiv,
+                    require_embedded=require_embedded,
+                    _seen=_seen.union([col]),
+                )
+                if newcol is not None:
+                    return newcol
+
+        if (
+            self.adapt_on_names
+            and newcol is None
+            and isinstance(col, NamedColumn)
+        ):
+            newcol = self.selectable.exported_columns.get(col.name)
+        return newcol
+
+    @util.preload_module("sqlalchemy.sql.functions")
+    def replace(
+        self, col: _ET, _include_singleton_constants: bool = False
+    ) -> Optional[_ET]:
+        functions = util.preloaded.sql_functions
+
+        # TODO: cython candidate
+
+        if self.include_fn and not self.include_fn(col):  # type: ignore
+            return None
+        elif self.exclude_fn and self.exclude_fn(col):  # type: ignore
+            return None
+
+        if isinstance(col, FromClause) and not isinstance(
+            col, functions.FunctionElement
+        ):
+            if self.selectable.is_derived_from(col):
+                if self.adapt_from_selectables:
+                    for adp in self.adapt_from_selectables:
+                        if adp.is_derived_from(col):
+                            break
+                    else:
+                        return None
+                return self.selectable  # type: ignore
+            elif isinstance(col, Alias) and isinstance(
+                col.element, TableClause
+            ):
+                # we are a SELECT statement and not derived from an alias of a
+                # table (which nonetheless may be a table our SELECT derives
+                # from), so return the alias to prevent further traversal
+                # or
+                # we are an alias of a table and we are not derived from an
+                # alias of a table (which nonetheless may be the same table
+                # as ours) so, same thing
+                return col  # type: ignore
+            else:
+                # other cases where we are a selectable and the element
+                # is another join or selectable that contains a table which our
+                # selectable derives from, that we want to process
+                return None
+
+        elif not isinstance(col, ColumnElement):
+            return None
+        elif not _include_singleton_constants and col._is_singleton_constant:
+            # dont swap out NULL, TRUE, FALSE for a label name
+            # in a SQL statement that's being rewritten,
+            # leave them as the constant.  This is first noted in #6259,
+            # however the logic to check this moved here as of #7154 so that
+            # it is made specific to SQL rewriting and not all column
+            # correspondence
+
+            return None
+
+        if "adapt_column" in col._annotations:
+            col = col._annotations["adapt_column"]
+
+        if TYPE_CHECKING:
+            assert isinstance(col, KeyedColumnElement)
+
+        if self.adapt_from_selectables and col not in self.equivalents:
+            for adp in self.adapt_from_selectables:
+                if adp.c.corresponding_column(col, False) is not None:
+                    break
+            else:
+                return None
+
+        if TYPE_CHECKING:
+            assert isinstance(col, KeyedColumnElement)
+
+        return self._corresponding_column(  # type: ignore
+            col, require_embedded=True
+        )
+
+
+class _ColumnLookup(Protocol):
+    @overload
+    def __getitem__(self, key: None) -> None: ...
+
+    @overload
+    def __getitem__(self, key: ColumnClause[Any]) -> ColumnClause[Any]: ...
+
+    @overload
+    def __getitem__(self, key: ColumnElement[Any]) -> ColumnElement[Any]: ...
+
+    @overload
+    def __getitem__(self, key: _ET) -> _ET: ...
+
+    def __getitem__(self, key: Any) -> Any: ...
+
+
+class ColumnAdapter(ClauseAdapter):
+    """Extends ClauseAdapter with extra utility functions.
+
+    Key aspects of ColumnAdapter include:
+
+    * Expressions that are adapted are stored in a persistent
+      .columns collection; so that an expression E adapted into
+      an expression E1, will return the same object E1 when adapted
+      a second time.   This is important in particular for things like
+      Label objects that are anonymized, so that the ColumnAdapter can
+      be used to present a consistent "adapted" view of things.
+
+    * Exclusion of items from the persistent collection based on
+      include/exclude rules, but also independent of hash identity.
+      This because "annotated" items all have the same hash identity as their
+      parent.
+
+    * "wrapping" capability is added, so that the replacement of an expression
+      E can proceed through a series of adapters.  This differs from the
+      visitor's "chaining" feature in that the resulting object is passed
+      through all replacing functions unconditionally, rather than stopping
+      at the first one that returns non-None.
+
+    * An adapt_required option, used by eager loading to indicate that
+      We don't trust a result row column that is not translated.
+      This is to prevent a column from being interpreted as that
+      of the child row in a self-referential scenario, see
+      inheritance/test_basic.py->EagerTargetingTest.test_adapt_stringency
+
+    """
+
+    __slots__ = (
+        "columns",
+        "adapt_required",
+        "allow_label_resolve",
+        "_wrap",
+        "__weakref__",
+    )
+
+    columns: _ColumnLookup
+
+    def __init__(
+        self,
+        selectable: Selectable,
+        equivalents: Optional[_EquivalentColumnMap] = None,
+        adapt_required: bool = False,
+        include_fn: Optional[Callable[[ClauseElement], bool]] = None,
+        exclude_fn: Optional[Callable[[ClauseElement], bool]] = None,
+        adapt_on_names: bool = False,
+        allow_label_resolve: bool = True,
+        anonymize_labels: bool = False,
+        adapt_from_selectables: Optional[AbstractSet[FromClause]] = None,
+    ):
+        super().__init__(
+            selectable,
+            equivalents,
+            include_fn=include_fn,
+            exclude_fn=exclude_fn,
+            adapt_on_names=adapt_on_names,
+            anonymize_labels=anonymize_labels,
+            adapt_from_selectables=adapt_from_selectables,
+        )
+
+        self.columns = util.WeakPopulateDict(self._locate_col)  # type: ignore
+        if self.include_fn or self.exclude_fn:
+            self.columns = self._IncludeExcludeMapping(self, self.columns)
+        self.adapt_required = adapt_required
+        self.allow_label_resolve = allow_label_resolve
+        self._wrap = None
+
+    class _IncludeExcludeMapping:
+        def __init__(self, parent, columns):
+            self.parent = parent
+            self.columns = columns
+
+        def __getitem__(self, key):
+            if (
+                self.parent.include_fn and not self.parent.include_fn(key)
+            ) or (self.parent.exclude_fn and self.parent.exclude_fn(key)):
+                if self.parent._wrap:
+                    return self.parent._wrap.columns[key]
+                else:
+                    return key
+            return self.columns[key]
+
+    def wrap(self, adapter):
+        ac = copy.copy(self)
+        ac._wrap = adapter
+        ac.columns = util.WeakPopulateDict(ac._locate_col)  # type: ignore
+        if ac.include_fn or ac.exclude_fn:
+            ac.columns = self._IncludeExcludeMapping(ac, ac.columns)
+
+        return ac
+
+    @overload
+    def traverse(self, obj: Literal[None]) -> None: ...
+
+    @overload
+    def traverse(self, obj: _ET) -> _ET: ...
+
+    def traverse(
+        self, obj: Optional[ExternallyTraversible]
+    ) -> Optional[ExternallyTraversible]:
+        return self.columns[obj]
+
+    def chain(self, visitor: ExternalTraversal) -> ColumnAdapter:
+        assert isinstance(visitor, ColumnAdapter)
+
+        return super().chain(visitor)
+
+    if TYPE_CHECKING:
+
+        @property
+        def visitor_iterator(self) -> Iterator[ColumnAdapter]: ...
+
+    adapt_clause = traverse
+    adapt_list = ClauseAdapter.copy_and_process
+
+    def adapt_check_present(
+        self, col: ColumnElement[Any]
+    ) -> Optional[ColumnElement[Any]]:
+        newcol = self.columns[col]
+
+        if newcol is col and self._corresponding_column(col, True) is None:
+            return None
+
+        return newcol
+
+    def _locate_col(
+        self, col: ColumnElement[Any]
+    ) -> Optional[ColumnElement[Any]]:
+        # both replace and traverse() are overly complicated for what
+        # we are doing here and we would do better to have an inlined
+        # version that doesn't build up as much overhead.  the issue is that
+        # sometimes the lookup does in fact have to adapt the insides of
+        # say a labeled scalar subquery.   However, if the object is an
+        # Immutable, i.e. Column objects, we can skip the "clone" /
+        # "copy internals" part since those will be no-ops in any case.
+        # additionally we want to catch singleton objects null/true/false
+        # and make sure they are adapted as well here.
+
+        if col._is_immutable:
+            for vis in self.visitor_iterator:
+                c = vis.replace(col, _include_singleton_constants=True)
+                if c is not None:
+                    break
+            else:
+                c = col
+        else:
+            c = ClauseAdapter.traverse(self, col)
+
+        if self._wrap:
+            c2 = self._wrap._locate_col(c)
+            if c2 is not None:
+                c = c2
+
+        if self.adapt_required and c is col:
+            return None
+
+        # allow_label_resolve is consumed by one case for joined eager loading
+        # as part of its logic to prevent its own columns from being affected
+        # by .order_by().  Before full typing were applied to the ORM, this
+        # logic would set this attribute on the incoming object (which is
+        # typically a column, but we have a test for it being a non-column
+        # object) if no column were found.  While this seemed to
+        # have no negative effects, this adjustment should only occur on the
+        # new column which is assumed to be local to an adapted selectable.
+        if c is not col:
+            c._allow_label_resolve = self.allow_label_resolve
+
+        return c
+
+
+def _offset_or_limit_clause(
+    element: _LimitOffsetType,
+    name: Optional[str] = None,
+    type_: Optional[_TypeEngineArgument[int]] = None,
+) -> ColumnElement[int]:
+    """Convert the given value to an "offset or limit" clause.
+
+    This handles incoming integers and converts to an expression; if
+    an expression is already given, it is passed through.
+
+    """
+    return coercions.expect(
+        roles.LimitOffsetRole, element, name=name, type_=type_
+    )
+
+
+def _offset_or_limit_clause_asint_if_possible(
+    clause: _LimitOffsetType,
+) -> _LimitOffsetType:
+    """Return the offset or limit clause as a simple integer if possible,
+    else return the clause.
+
+    """
+    if clause is None:
+        return None
+    if hasattr(clause, "_limit_offset_value"):
+        value = clause._limit_offset_value
+        return util.asint(value)
+    else:
+        return clause
+
+
+def _make_slice(
+    limit_clause: _LimitOffsetType,
+    offset_clause: _LimitOffsetType,
+    start: int,
+    stop: int,
+) -> Tuple[Optional[ColumnElement[int]], Optional[ColumnElement[int]]]:
+    """Compute LIMIT/OFFSET in terms of slice start/end"""
+
+    # for calculated limit/offset, try to do the addition of
+    # values to offset in Python, however if a SQL clause is present
+    # then the addition has to be on the SQL side.
+
+    # TODO: typing is finding a few gaps in here, see if they can be
+    # closed up
+
+    if start is not None and stop is not None:
+        offset_clause = _offset_or_limit_clause_asint_if_possible(
+            offset_clause
+        )
+        if offset_clause is None:
+            offset_clause = 0
+
+        if start != 0:
+            offset_clause = offset_clause + start  # type: ignore
+
+        if offset_clause == 0:
+            offset_clause = None
+        else:
+            assert offset_clause is not None
+            offset_clause = _offset_or_limit_clause(offset_clause)
+
+        limit_clause = _offset_or_limit_clause(stop - start)
+
+    elif start is None and stop is not None:
+        limit_clause = _offset_or_limit_clause(stop)
+    elif start is not None and stop is None:
+        offset_clause = _offset_or_limit_clause_asint_if_possible(
+            offset_clause
+        )
+        if offset_clause is None:
+            offset_clause = 0
+
+        if start != 0:
+            offset_clause = offset_clause + start
+
+        if offset_clause == 0:
+            offset_clause = None
+        else:
+            offset_clause = _offset_or_limit_clause(offset_clause)
+
+    return limit_clause, offset_clause