%--------------------------------------------------%
% vim: ts=4 sw=4 et ft=mercury
%--------------------------------------------------%
% Copyright (C) 1994-1997, 1999-2012 The University of Melbourne.
% Copyright (C) 2014-2016, 2018-2022 The Mercury team.
% This file is distributed under the terms specified in COPYING.LIB.
%--------------------------------------------------%
%
% File: set.m.
% Main authors: conway, fjh, benyi.
% Stability: high.
%
% This module provides a set ADT.
% The implementation represents sets using ordered lists.
% This file just calls the equivalent predicates in set_ordlist.
%
%--------------------------------------------------%
%--------------------------------------------------%

:- module set.
:- interface.

:- import_module bool.
:- import_module list.

%--------------------------------------------------%

:- type set(T).

%--------------------------------------------------%
%
% Initial creation of sets.
%

    % init(Set) is true iff Set is an empty set.
    %
:- func init = set(T).
:- pred init(set(T)::uo) is det.

    % singleton_set(Elem, Set) is true iff Set is the set
    % containing just the single element Elem.
    %
:- pred singleton_set(T, set(T)).
:- mode singleton_set(in, out) is det.
:- mode singleton_set(out, in) is semidet.

:- func make_singleton_set(T) = set(T).

%--------------------------------------------------%
%
% Emptiness and singleton-ness tests.
%

    % is_empty(Set) is true iff Set is an empty set.
    %
:- pred is_empty(set(T)::in) is semidet.

    % is_non_empty(Set) is true iff Set is not an empty set.
    %
:- pred is_non_empty(set(T)::in) is semidet.

:- pred is_singleton(set(T)::in, T::out) is semidet.

%--------------------------------------------------%
%
% Membership tests.
%

    % member(X, Set) is true iff X is a member of Set.
    %
:- pred member(T, set(T)).
:- mode member(in, in) is semidet.
:- mode member(out, in) is nondet.

    % is_member(X, Set, Result) returns `Result = yes'
    % iff X is a member of Set.
    %
:- pred is_member(T::in, set(T)::in, bool::out) is det.

    % contains(Set, X) is true iff X is a member of Set.
    %
:- pred contains(set(T)::in, T::in) is semidet.

%--------------------------------------------------%
%
% Insertions and deletions.
%

    % insert(X, Set0, Set) is true iff Set is the union of
    % Set0 and the set containing only X.
    %
:- func insert(set(T), T) = set(T).
:- pred insert(T::in, set(T)::in, set(T)::out) is det.

    % insert_new(X, Set0, Set) is true iff Set0 does not contain
    % X, and Set is the union of Set0 and the set containing only X.
    %
:- pred insert_new(T::in, set(T)::in, set(T)::out) is semidet.

    % insert_list(Xs, Set0, Set) is true iff Set is the union of
    % Set0 and the set containing only the members of Xs.
    %
:- func insert_list(set(T), list(T)) = set(T).
:- pred insert_list(list(T)::in, set(T)::in, set(T)::out) is det.

    % delete(X, Set0, Set) is true iff Set is the relative
    % complement of Set0 and the set containing only X, i.e.
    % if Set is the set which contains all the elements of Set0
    % except X.
    %
:- func delete(set(T), T) = set(T).
:- pred delete(T::in, set(T)::in, set(T)::out) is det.

    % delete_list(Set0, Xs, Set) is true iff Set is the relative
    % complement of Set0 and the set containing only the members of Xs.
    %
:- func delete_list(set(T), list(T)) = set(T).
:- pred delete_list(list(T)::in, set(T)::in, set(T)::out) is det.

    % remove(X, Set0, Set) is true iff Set0 contains X,
    % and Set is the relative complement of Set0 and the set
    % containing only X, i.e.  if Set is the set which contains
    % all the elements of Set0 except X.
    %
    % The det_remove version throws an exception instead of failing.
    %
:- pred remove(T::in, set(T)::in, set(T)::out) is semidet.
:- pred det_remove(T::in, set(T)::in, set(T)::out) is det.

    % remove_list(Xs, Set0, Set) is true iff Xs does not
    % contain any duplicates, Set0 contains every member of Xs,
    % and Set is the relative complement of Set0 and the set
    % containing only the members of Xs.
    %
    % The det_remove_list version throws an exception instead of failing.
    %
:- pred remove_list(list(T)::in, set(T)::in, set(T)::out) is semidet.
:- pred det_remove_list(list(T)::in, set(T)::in, set(T)::out) is det.

    % remove_least(Elem, Set0, Set) is true iff
    % Set0 is not empty, Elem is the smallest element in Set0
    % (with elements ordered using the standard ordering given
    % by compare/3), and Set is the set containing all the
    % elements of Set0 except Elem.
    %
:- pred remove_least(T::out, set(T)::in, set(T)::out) is semidet.

%--------------------------------------------------%
%
% Comparisons between sets.
%

    % equal(SetA, SetB) is true iff
    % SetA and SetB contain the same elements.
    %
:- pred equal(set(T)::in, set(T)::in) is semidet.

    % subset(SetA, SetB) is true iff SetA is a subset of SetB.
    %
:- pred subset(set(T)::in, set(T)::in) is semidet.

    % superset(SetA, SetB) is true iff SetA is a
    % superset of SetB.
    %
:- pred superset(set(T)::in, set(T)::in) is semidet.

%--------------------------------------------------%
%
% Operations on two or more sets.
%

    % union(SetA, SetB, Set) is true iff Set is the union of
    % SetA and SetB.  If the sets are known to be of different
    % sizes, then for efficiency make SetA the larger of the two.
    % (The current implementation using sorted lists with duplicates
    % removed is not sensitive to the ordering of the input arguments,
    % but other set implementations may be, so observing this convention
    % will make it less likely that you will encounter problems if
    % the implementation is changed.)
    %
:- func union(set(T), set(T)) = set(T).
:- pred union(set(T)::in, set(T)::in, set(T)::out) is det.

    % union_list(A, B) is true iff B is the union of
    % all the sets in A.
    %
:- func union_list(list(set(T))) = set(T).

    % power_union(A, B) is true iff B is the union of
    % all the sets in A.
    %
:- func power_union(set(set(T))) = set(T).
:- pred power_union(set(set(T))::in, set(T)::out) is det.

    % intersect(SetA, SetB, Set) is true iff Set is the
    % intersection of SetA and SetB. If the two sets are
    % known to be unequal in size, then making SetA be the larger
    % set will usually be more efficient.
    % (The current implementation, using sorted lists with duplicates
    % removed is not sensitive to the ordering of the input arguments
    % but other set implementations may be, so observing this convention
    % will make it less likely that you will encounter problems if
    % the implementation is changed.)
    %
:- func intersect(set(T), set(T)) = set(T).
:- pred intersect(set(T)::in, set(T)::in, set(T)::out) is det.

    % intersect_list(A, B) is true iff B is the intersection of
    % all the sets in A.
    %
:- func intersect_list(list(set(T))) = set(T).

    % power_intersect(A, B) is true iff B is the intersection of
    % all the sets in A.
    %
:- func power_intersect(set(set(T))) = set(T).
:- pred power_intersect(set(set(T))::in, set(T)::out) is det.

    % difference(SetA, SetB, Set) is true iff Set is the
    % set containing all the elements of SetA except those that
    % occur in SetB.
    %
:- func difference(set(T), set(T)) = set(T).
:- pred difference(set(T)::in, set(T)::in, set(T)::out) is det.

    % intersection_and_differences(SetA, SetB, InAandB, OnlyInA, OnlyInB):
    % Given SetA and SetB, return the elements that occur in both sets,
    % and those that occur only in one or the other.
    %
:- pred intersection_and_differences(set(T)::in, set(T)::in,
    set(T)::out, set(T)::out, set(T)::out) is det.

%--------------------------------------------------%
%
% Operations that divide a set into two parts.
%

    % divide(Pred, Set, TruePart, FalsePart):
    % TruePart consists of those elements of Set for which Pred succeeds;
    % FalsePart consists of those elements of Set for which Pred fails.
    %
:- pred divide(pred(T)::in(pred(in) is semidet), set(T)::in,
    set(T)::out, set(T)::out) is det.

    % divide_by_set(DivideBySet, Set, InPart, OutPart):
    % InPart consists of those elements of Set which are also in DivideBySet;
    % OutPart consists of those elements of which are not in DivideBySet.
    %
:- pred divide_by_set(set(T)::in, set(T)::in, set(T)::out, set(T)::out) is det.

%--------------------------------------------------%
%
% Converting lists to sets.
%

    % list_to_set(List, Set) is true iff Set is the set
    % containing only the members of List.
    %
:- func list_to_set(list(T)) = set(T).
:- pred list_to_set(list(T)::in, set(T)::out) is det.

    % Synonyms for list_to_set/1.
    %
:- func from_list(list(T)) = set(T).

    % sorted_list_to_set(List, Set) is true iff Set is the set
    % containing only the members of List. List must be sorted
    % and must not contain any duplicates.
    %
:- func sorted_list_to_set(list(T)) = set(T).
:- pred sorted_list_to_set(list(T)::in, set(T)::out) is det.

    % rev_sorted_list_to_set(List) = Set is true iff Set is the set
    % containing only the members of List. List must be sorted
    % in descending order and must not contain any duplicates.
    %
:- func rev_sorted_list_to_set(list(T)) = set(T).
:- pred rev_sorted_list_to_set(list(T)::in, set(T)::out) is det.

    % A synonym for sorted_list_to_set/1.
    %
:- func from_sorted_list(list(T)) = set(T).

%--------------------------------------------------%
%
% Converting sets to lists.
%

    % to_sorted_list(Set, List) is true iff List is the list
    % of all the members of Set, in sorted order without any
    % duplicates.
    %
:- func to_sorted_list(set(T)) = list(T).
:- pred to_sorted_list(set(T)::in, list(T)::out) is det.

%--------------------------------------------------%
%
% Counting.
%

    % count(Set, Count) is true iff Set has Count elements.
    % i.e. Count is the cardinality (size) of the
    %
:- func count(set(T)) = int.
:- pred count(set(T)::in, int::out) is det.

%--------------------------------------------------%
%
% Standard higher order functions on collections.
%

    % all_true(Pred, Set) succeeds iff Pred(Element) succeeds
    % for all the elements of Set.
    %
:- pred all_true(pred(T)::in(pred(in) is semidet), set(T)::in) is semidet.

    % Return the set of items for which the given predicate succeeds.
    % filter(P, S) =
    %   sorted_list_to_set(list.filter(P, to_sorted_list(S))).
    %
:- func filter(pred(T1), set(T1)) = set(T1).
:- mode filter(in(pred(in) is semidet), in) = out is det.
:- pred filter(pred(T1), set(T1), set(T1)).
:- mode filter(in(pred(in) is semidet), in, out) is det.

    % Return the set of items for which the given predicate succeeds,
    % and the set of items for which it fails.
    %
:- pred filter(pred(T1), set(T1), set(T1), set(T1)).
:- mode filter(in(pred(in) is semidet), in, out, out) is det.

    % filter_map(PF, S) =
    %   list_to_set(list.filter_map(PF, to_sorted_list(S))).
    %
:- func filter_map(func(T1) = T2, set(T1)) = set(T2).
:- mode filter_map(in(func(in) = out is semidet), in) = out is det.
:- pred filter_map(pred(T1, T2), set(T1), set(T2)).
:- mode filter_map(in(pred(in, out) is semidet), in, out) is det.

    % map(F, S) =
    %   list_to_set(list.map(F, to_sorted_list(S))).
    %
:- func map(func(T1) = T2, set(T1)) = set(T2).
:- pred map(pred(T1, T2), set(T1), set(T2)).
:- mode map(in(pred(in, out) is det), in, out) is det.
:- mode map(in(pred(in, out) is cc_multi), in, out) is cc_multi.
:- mode map(in(pred(in, out) is semidet), in, out) is semidet.
:- mode map(in(pred(in, out) is multi), in, out) is multi.
:- mode map(in(pred(in, out) is nondet), in, out) is nondet.

    % map_fold(P, S0, S, A0, A) :-
    %   L0 = to_sorted_list(S0),
    %   list.map_foldl(P, L0, L, A0, A),
    %   S = list_to_set(L).
    %
:- pred map_fold(pred(T1, T2, T3, T3), set(T1), set(T2), T3, T3).
:- mode map_fold(in(pred(in, out, in, out) is det), in, out, in, out) is det.
:- mode map_fold(in(pred(in, out, mdi, muo) is det), in, out, mdi, muo) is det.
:- mode map_fold(in(pred(in, out, di, uo) is det), in, out, di, uo) is det.
:- mode map_fold(in(pred(in, out, in, out) is semidet), in, out,
    in, out) is semidet.
:- mode map_fold(in(pred(in, out, mdi, muo) is semidet), in, out,
    mdi, muo) is semidet.
:- mode map_fold(in(pred(in, out, di, uo) is semidet), in, out,
    di, uo) is semidet.

    % fold(F, S, A) =
    %   list.foldl(F, to_sorted_list(S), A).
    %
:- func fold(func(T, A) = A, set(T), A) = A.
:- func foldl(func(T, A) = A, set(T), A) = A.

:- pred fold(pred(T, A, A), set(T), A, A).
:- mode fold(in(pred(in, in, out) is det), in, in, out) is det.
:- mode fold(in(pred(in, mdi, muo) is det), in, mdi, muo) is det.
:- mode fold(in(pred(in, di, uo) is det), in, di, uo) is det.
:- mode fold(in(pred(in, in, out) is semidet), in, in, out) is semidet.
:- mode fold(in(pred(in, mdi, muo) is semidet), in, mdi, muo) is semidet.
:- mode fold(in(pred(in, di, uo) is semidet), in, di, uo) is semidet.

:- pred foldl(pred(T, A, A), set(T), A, A).
:- mode foldl(in(pred(in, in, out) is det), in, in, out) is det.
:- mode foldl(in(pred(in, mdi, muo) is det), in, mdi, muo) is det.
:- mode foldl(in(pred(in, di, uo) is det), in, di, uo) is det.
:- mode foldl(in(pred(in, in, out) is semidet), in, in, out) is semidet.
:- mode foldl(in(pred(in, mdi, muo) is semidet), in, mdi, muo) is semidet.
:- mode foldl(in(pred(in, di, uo) is semidet), in, di, uo) is semidet.

:- pred fold2(pred(T, A, A, B, B), set(T), A, A, B, B).
:- mode fold2(in(pred(in, in, out, in, out) is det), in,
    in, out, in, out) is det.
:- mode fold2(in(pred(in, in, out, mdi, muo) is det), in,
    in, out, mdi, muo) is det.
:- mode fold2(in(pred(in, in, out, di, uo) is det), in,
    in, out, di, uo) is det.
:- mode fold2(in(pred(in, in, out, in, out) is semidet),
    in, in, out, in, out) is semidet.
:- mode fold2(in(pred(in, in, out, mdi, muo) is semidet),
    in, in, out, mdi, muo) is semidet.
:- mode fold2(in(pred(in, in, out, di, uo) is semidet),
    in, in, out, di, uo) is semidet.

:- pred foldl2(pred(T, A, A, B, B), set(T), A, A, B, B).
:- mode foldl2(in(pred(in, in, out, in, out) is det), in,
    in, out, in, out) is det.
:- mode foldl2(in(pred(in, in, out, mdi, muo) is det), in,
    in, out, mdi, muo) is det.
:- mode foldl2(in(pred(in, in, out, di, uo) is det), in,
    in, out, di, uo) is det.
:- mode foldl2(in(pred(in, in, out, in, out) is semidet),
    in, in, out, in, out) is semidet.
:- mode foldl2(in(pred(in, in, out, mdi, muo) is semidet),
    in, in, out, mdi, muo) is semidet.
:- mode foldl2(in(pred(in, in, out, di, uo) is semidet),
    in, in, out, di, uo) is semidet.

:- pred fold3(pred(T, A, A, B, B, C, C), set(T), A, A, B, B, C, C).
:- mode fold3(in(pred(in, in, out, in, out, in, out) is det), in,
    in, out, in, out, in, out) is det.
:- mode fold3(in(pred(in, in, out, in, out, mdi, muo) is det), in,
    in, out, in, out, mdi, muo) is det.
:- mode fold3(in(pred(in, in, out, in, out, di, uo) is det), in,
    in, out, in, out, di, uo) is det.
:- mode fold3(in(pred(in, in, out, in, out, in, out) is semidet), in,
    in, out, in, out, in, out) is semidet.
:- mode fold3(in(pred(in, in, out, in, out, mdi, muo) is semidet), in,
    in, out, in, out, mdi, muo) is semidet.
:- mode fold3(in(pred(in, in, out, in, out, di, uo) is semidet), in,
    in, out, in, out, di, uo) is semidet.

:- pred foldl3(pred(T, A, A, B, B, C, C), set(T), A, A, B, B, C, C).
:- mode foldl3(in(pred(in, in, out, in, out, in, out) is det), in,
    in, out, in, out, in, out) is det.
:- mode foldl3(in(pred(in, in, out, in, out, mdi, muo) is det), in,
    in, out, in, out, mdi, muo) is det.
:- mode foldl3(in(pred(in, in, out, in, out, di, uo) is det), in,
    in, out, in, out, di, uo) is det.
:- mode foldl3(in(pred(in, in, out, in, out, in, out) is semidet), in,
    in, out, in, out, in, out) is semidet.
:- mode foldl3(in(pred(in, in, out, in, out, mdi, muo) is semidet), in,
    in, out, in, out, mdi, muo) is semidet.
:- mode foldl3(in(pred(in, in, out, in, out, di, uo) is semidet), in,
    in, out, in, out, di, uo) is semidet.

:- pred fold4(pred(T, A, A, B, B, C, C, D, D), set(T), A, A, B, B,
    C, C, D, D).
:- mode fold4(in(pred(in, in, out, in, out, in, out, in, out) is det), in,
    in, out, in, out, in, out, in, out) is det.
:- mode fold4(in(pred(in, in, out, in, out, in, out, mdi, muo) is det), in,
    in, out, in, out, in, out, mdi, muo) is det.
:- mode fold4(in(pred(in, in, out, in, out, in, out, di, uo) is det), in,
    in, out, in, out, in, out, di, uo) is det.
:- mode fold4(in(pred(in, in, out, in, out, in, out, in, out) is semidet), in,
    in, out, in, out, in, out, in, out) is semidet.
:- mode fold4(in(pred(in, in, out, in, out, in, out, mdi, muo) is semidet), in,
    in, out, in, out, in, out, mdi, muo) is semidet.
:- mode fold4(in(pred(in, in, out, in, out, in, out, di, uo) is semidet), in,
    in, out, in, out, in, out, di, uo) is semidet.

:- pred foldl4(pred(T, A, A, B, B, C, C, D, D), set(T), A, A, B, B,
    C, C, D, D).
:- mode foldl4(in(pred(in, in, out, in, out, in, out, in, out) is det),
    in, in, out, in, out, in, out, in, out) is det.
:- mode foldl4(in(pred(in, in, out, in, out, in, out, mdi, muo) is det),
    in, in, out, in, out, in, out, mdi, muo) is det.
:- mode foldl4(in(pred(in, in, out, in, out, in, out, di, uo) is det),
    in, in, out, in, out, in, out, di, uo) is det.
:- mode foldl4(in(pred(in, in, out, in, out, in, out, in, out) is semidet),
    in, in, out, in, out, in, out, in, out) is semidet.
:- mode foldl4(in(pred(in, in, out, in, out, in, out, mdi, muo) is semidet),
    in, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode foldl4(in(pred(in, in, out, in, out, in, out, di, uo) is semidet),
    in, in, out, in, out, in, out, di, uo) is semidet.

:- pred fold5(pred(T, A, A, B, B, C, C, D, D, E, E), set(T), A, A, B, B,
    C, C, D, D, E, E).
:- mode fold5(
    in(pred(in, in, out, in, out, in, out, in, out, in, out) is det),
    in, in, out, in, out, in, out, in, out, in, out) is det.
:- mode fold5(
    in(pred(in, in, out, in, out, in, out, in, out, mdi, muo) is det),
    in, in, out, in, out, in, out, in, out, mdi, muo) is det.
:- mode fold5(
    in(pred(in, in, out, in, out, in, out, in, out, di, uo) is det),
    in, in, out, in, out, in, out, in, out, di, uo) is det.
:- mode fold5(
    in(pred(in, in, out, in, out, in, out, in, out, in, out) is semidet),
    in, in, out, in, out, in, out, in, out, in, out) is semidet.
:- mode fold5(
    in(pred(in, in, out, in, out, in, out, in, out, mdi, muo) is semidet),
    in, in, out, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode fold5(
    in(pred(in, in, out, in, out, in, out, in, out, di, uo) is semidet),
    in, in, out, in, out, in, out, in, out, di, uo) is semidet.

:- pred foldl5(pred(T, A, A, B, B, C, C, D, D, E, E), set(T), A, A, B, B,
    C, C, D, D, E, E).
:- mode foldl5(
    in(pred(in, in, out, in, out, in, out, in, out, in, out) is det),
    in, in, out, in, out, in, out, in, out, in, out) is det.
:- mode foldl5(
    in(pred(in, in, out, in, out, in, out, in, out, mdi, muo) is det),
    in, in, out, in, out, in, out, in, out, mdi, muo) is det.
:- mode foldl5(
    in(pred(in, in, out, in, out, in, out, in, out, di, uo) is det),
    in, in, out, in, out, in, out, in, out, di, uo) is det.
:- mode foldl5(
    in(pred(in, in, out, in, out, in, out, in, out, in, out) is semidet),
    in, in, out, in, out, in, out, in, out, in, out) is semidet.
:- mode foldl5(
    in(pred(in, in, out, in, out, in, out, in, out, mdi, muo) is semidet),
    in, in, out, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode foldl5(
    in(pred(in, in, out, in, out, in, out, in, out, di, uo) is semidet),
    in, in, out, in, out, in, out, in, out, di, uo) is semidet.

:- pred fold6(pred(T, A, A, B, B, C, C, D, D, E, E, F, F), set(T),
    A, A, B, B, C, C, D, D, E, E, F, F).
:- mode fold6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, in, out) is det),
    in, in, out, in, out, in, out, in, out, in, out, in, out) is det.
:- mode fold6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is det),
    in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is det.
:- mode fold6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, di, uo) is det),
    in, in, out, in, out, in, out, in, out, in, out, di, uo) is det.
:- mode fold6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, in, out)
        is semidet),
    in, in, out, in, out, in, out, in, out, in, out, in, out) is semidet.
:- mode fold6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, mdi, muo)
        is semidet),
    in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode fold6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, di, uo)
        is semidet),
    in, in, out, in, out, in, out, in, out, in, out, di, uo) is semidet.

:- pred foldl6(pred(T, A, A, B, B, C, C, D, D, E, E, F, F), set(T),
    A, A, B, B, C, C, D, D, E, E, F, F).
:- mode foldl6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, in, out) is det),
    in, in, out, in, out, in, out, in, out, in, out, in, out) is det.
:- mode foldl6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is det),
    in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is det.
:- mode foldl6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, di, uo) is det),
    in, in, out, in, out, in, out, in, out, in, out, di, uo) is det.
:- mode foldl6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, in, out)
        is semidet),
    in, in, out, in, out, in, out, in, out, in, out, in, out) is semidet.
:- mode foldl6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, mdi, muo)
        is semidet),
    in, in, out, in, out, in, out, in, out, in, out, mdi, muo) is semidet.
:- mode foldl6(
    in(pred(in, in, out, in, out, in, out, in, out, in, out, di, uo)
        is semidet),
    in, in, out, in, out, in, out, in, out, in, out, di, uo) is semidet.

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