// -*- C++ -*-
//===---------------------------- set -------------------------------------===//
//
//                     The LLVM Compiler Infrastructure
//
// This file is dual licensed under the MIT and the University of Illinois Open
// Source Licenses. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP_SET
#define _LIBCPP_SET

/*

    set synopsis

namespace std
{

template <class Key, class Compare = less<Key>,
          class Allocator = allocator<Key>>
class set
{
public:
    // types:
    typedef Key                                      key_type;
    typedef key_type                                 value_type;
    typedef Compare                                  key_compare;
    typedef key_compare                              value_compare;
    typedef Allocator                                allocator_type;
    typedef typename allocator_type::reference       reference;
    typedef typename allocator_type::const_reference const_reference;
    typedef typename allocator_type::size_type       size_type;
    typedef typename allocator_type::difference_type difference_type;
    typedef typename allocator_type::pointer         pointer;
    typedef typename allocator_type::const_pointer   const_pointer;

    typedef implementation-defined                   iterator;
    typedef implementation-defined                   const_iterator;
    typedef std::reverse_iterator<iterator>          reverse_iterator;
    typedef std::reverse_iterator<const_iterator>    const_reverse_iterator;

    // construct/copy/destroy:
    set()
        noexcept(
            is_nothrow_default_constructible<allocator_type>::value &&
            is_nothrow_default_constructible<key_compare>::value &&
            is_nothrow_copy_constructible<key_compare>::value);
    explicit set(const value_compare& comp);
    set(const value_compare& comp, const allocator_type& a);
    template <class InputIterator>
        set(InputIterator first, InputIterator last,
            const value_compare& comp = value_compare());
    template <class InputIterator>
        set(InputIterator first, InputIterator last, const value_compare& comp,
            const allocator_type& a);
    set(const set& s);
    set(set&& s)
        noexcept(
            is_nothrow_move_constructible<allocator_type>::value &&
            is_nothrow_move_constructible<key_compare>::value);
    explicit set(const allocator_type& a);
    set(const set& s, const allocator_type& a);
    set(set&& s, const allocator_type& a);
    set(initializer_list<value_type> il, const value_compare& comp = value_compare());
    set(initializer_list<value_type> il, const value_compare& comp,
        const allocator_type& a);
    ~set();

    set& operator=(const set& s);
    set& operator=(set&& s)
        noexcept(
            allocator_type::propagate_on_container_move_assignment::value &&
            is_nothrow_move_assignable<allocator_type>::value &&
            is_nothrow_move_assignable<key_compare>::value);
    set& operator=(initializer_list<value_type> il);

    // iterators:
          iterator begin() noexcept;
    const_iterator begin() const noexcept;
          iterator end() noexcept;
    const_iterator end()   const noexcept;

          reverse_iterator rbegin() noexcept;
    const_reverse_iterator rbegin() const noexcept;
          reverse_iterator rend() noexcept;
    const_reverse_iterator rend()   const noexcept;

    const_iterator         cbegin()  const noexcept;
    const_iterator         cend()    const noexcept;
    const_reverse_iterator crbegin() const noexcept;
    const_reverse_iterator crend()   const noexcept;

    // capacity:
    bool      empty()    const noexcept;
    size_type size()     const noexcept;
    size_type max_size() const noexcept;

    // modifiers:
    template <class... Args>
        pair<iterator, bool> emplace(Args&&... args);
    template <class... Args>
        iterator emplace_hint(const_iterator position, Args&&... args);
    pair<iterator,bool> insert(const value_type& v);
    pair<iterator,bool> insert(value_type&& v);
    iterator insert(const_iterator position, const value_type& v);
    iterator insert(const_iterator position, value_type&& v);
    template <class InputIterator>
        void insert(InputIterator first, InputIterator last);
    void insert(initializer_list<value_type> il);

    iterator  erase(const_iterator position);
    size_type erase(const key_type& k);
    iterator  erase(const_iterator first, const_iterator last);
    void clear() noexcept;

    void swap(set& s)
        noexcept(
            __is_nothrow_swappable<key_compare>::value &&
            (!allocator_type::propagate_on_container_swap::value ||
             __is_nothrow_swappable<allocator_type>::value));

    // observers:
    allocator_type get_allocator() const noexcept;
    key_compare    key_comp()      const;
    value_compare  value_comp()    const;

    // set operations:
          iterator find(const key_type& k);
    const_iterator find(const key_type& k) const;
    size_type      count(const key_type& k) const;
          iterator lower_bound(const key_type& k);
    const_iterator lower_bound(const key_type& k) const;
          iterator upper_bound(const key_type& k);
    const_iterator upper_bound(const key_type& k) const;
    pair<iterator,iterator>             equal_range(const key_type& k);
    pair<const_iterator,const_iterator> equal_range(const key_type& k) const;
};

template <class Key, class Compare, class Allocator>
bool
operator==(const set<Key, Compare, Allocator>& x,
           const set<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator< (const set<Key, Compare, Allocator>& x,
           const set<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator!=(const set<Key, Compare, Allocator>& x,
           const set<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator> (const set<Key, Compare, Allocator>& x,
           const set<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator>=(const set<Key, Compare, Allocator>& x,
           const set<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator<=(const set<Key, Compare, Allocator>& x,
           const set<Key, Compare, Allocator>& y);

// specialized algorithms:
template <class Key, class Compare, class Allocator>
void
swap(set<Key, Compare, Allocator>& x, set<Key, Compare, Allocator>& y)
    noexcept(noexcept(x.swap(y)));

template <class Key, class Compare = less<Key>,
          class Allocator = allocator<Key>>
class multiset
{
public:
    // types:
    typedef Key                                      key_type;
    typedef key_type                                 value_type;
    typedef Compare                                  key_compare;
    typedef key_compare                              value_compare;
    typedef Allocator                                allocator_type;
    typedef typename allocator_type::reference       reference;
    typedef typename allocator_type::const_reference const_reference;
    typedef typename allocator_type::size_type       size_type;
    typedef typename allocator_type::difference_type difference_type;
    typedef typename allocator_type::pointer         pointer;
    typedef typename allocator_type::const_pointer   const_pointer;

    typedef implementation-defined                   iterator;
    typedef implementation-defined                   const_iterator;
    typedef std::reverse_iterator<iterator>          reverse_iterator;
    typedef std::reverse_iterator<const_iterator>    const_reverse_iterator;

    // construct/copy/destroy:
    multiset()
        noexcept(
            is_nothrow_default_constructible<allocator_type>::value &&
            is_nothrow_default_constructible<key_compare>::value &&
            is_nothrow_copy_constructible<key_compare>::value);
    explicit multiset(const value_compare& comp);
    multiset(const value_compare& comp, const allocator_type& a);
    template <class InputIterator>
        multiset(InputIterator first, InputIterator last,
                 const value_compare& comp = value_compare());
    template <class InputIterator>
        multiset(InputIterator first, InputIterator last,
                 const value_compare& comp, const allocator_type& a);
    multiset(const multiset& s);
    multiset(multiset&& s)
        noexcept(
            is_nothrow_move_constructible<allocator_type>::value &&
            is_nothrow_move_constructible<key_compare>::value);
    explicit multiset(const allocator_type& a);
    multiset(const multiset& s, const allocator_type& a);
    multiset(multiset&& s, const allocator_type& a);
    multiset(initializer_list<value_type> il, const value_compare& comp = value_compare());
    multiset(initializer_list<value_type> il, const value_compare& comp,
             const allocator_type& a);
    ~multiset();

    multiset& operator=(const multiset& s);
    multiset& operator=(multiset&& s)
        noexcept(
            allocator_type::propagate_on_container_move_assignment::value &&
            is_nothrow_move_assignable<allocator_type>::value &&
            is_nothrow_move_assignable<key_compare>::value);
    multiset& operator=(initializer_list<value_type> il);

    // iterators:
          iterator begin() noexcept;
    const_iterator begin() const noexcept;
          iterator end() noexcept;
    const_iterator end()   const noexcept;

          reverse_iterator rbegin() noexcept;
    const_reverse_iterator rbegin() const noexcept;
          reverse_iterator rend() noexcept;
    const_reverse_iterator rend()   const noexcept;

    const_iterator         cbegin()  const noexcept;
    const_iterator         cend()    const noexcept;
    const_reverse_iterator crbegin() const noexcept;
    const_reverse_iterator crend()   const noexcept;

    // capacity:
    bool      empty()    const noexcept;
    size_type size()     const noexcept;
    size_type max_size() const noexcept;

    // modifiers:
    template <class... Args>
        iterator emplace(Args&&... args);
    template <class... Args>
        iterator emplace_hint(const_iterator position, Args&&... args);
    iterator insert(const value_type& v);
    iterator insert(value_type&& v);
    iterator insert(const_iterator position, const value_type& v);
    iterator insert(const_iterator position, value_type&& v);
    template <class InputIterator>
        void insert(InputIterator first, InputIterator last);
    void insert(initializer_list<value_type> il);

    iterator  erase(const_iterator position);
    size_type erase(const key_type& k);
    iterator  erase(const_iterator first, const_iterator last);
    void clear() noexcept;

    void swap(multiset& s)
        noexcept(
            __is_nothrow_swappable<key_compare>::value &&
            (!allocator_type::propagate_on_container_swap::value ||
             __is_nothrow_swappable<allocator_type>::value));

    // observers:
    allocator_type get_allocator() const noexcept;
    key_compare    key_comp()      const;
    value_compare  value_comp()    const;

    // set operations:
          iterator find(const key_type& k);
    const_iterator find(const key_type& k) const;
    size_type      count(const key_type& k) const;
          iterator lower_bound(const key_type& k);
    const_iterator lower_bound(const key_type& k) const;
          iterator upper_bound(const key_type& k);
    const_iterator upper_bound(const key_type& k) const;
    pair<iterator,iterator>             equal_range(const key_type& k);
    pair<const_iterator,const_iterator> equal_range(const key_type& k) const;
};

template <class Key, class Compare, class Allocator>
bool
operator==(const multiset<Key, Compare, Allocator>& x,
           const multiset<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator< (const multiset<Key, Compare, Allocator>& x,
           const multiset<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator!=(const multiset<Key, Compare, Allocator>& x,
           const multiset<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator> (const multiset<Key, Compare, Allocator>& x,
           const multiset<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator>=(const multiset<Key, Compare, Allocator>& x,
           const multiset<Key, Compare, Allocator>& y);

template <class Key, class Compare, class Allocator>
bool
operator<=(const multiset<Key, Compare, Allocator>& x,
           const multiset<Key, Compare, Allocator>& y);

// specialized algorithms:
template <class Key, class Compare, class Allocator>
void
swap(multiset<Key, Compare, Allocator>& x, multiset<Key, Compare, Allocator>& y)
    noexcept(noexcept(x.swap(y)));

}  // std

*/

#include <__config>
#include <__tree>
#include <functional>

#pragma GCC system_header

_LIBCPP_BEGIN_NAMESPACE_STD

template <class _Key, class _Compare = less<_Key>,
          class _Allocator = allocator<_Key> >
class _LIBCPP_VISIBLE set
{
public:
    // types:
    typedef _Key                                     key_type;
    typedef key_type                                 value_type;
    typedef _Compare                                 key_compare;
    typedef key_compare                              value_compare;
    typedef _Allocator                               allocator_type;
    typedef value_type&                              reference;
    typedef const value_type&                        const_reference;

private:
    typedef __tree<value_type, value_compare, allocator_type> __base;
    typedef allocator_traits<allocator_type>                  __alloc_traits;
    typedef typename __base::__node_holder                    __node_holder;

    __base __tree_;

public:
    typedef typename __base::pointer               pointer;
    typedef typename __base::const_pointer         const_pointer;
    typedef typename __base::size_type             size_type;
    typedef typename __base::difference_type       difference_type;
    typedef typename __base::const_iterator        iterator;
    typedef typename __base::const_iterator        const_iterator;
    typedef _STD::reverse_iterator<iterator>       reverse_iterator;
    typedef _STD::reverse_iterator<const_iterator> const_reverse_iterator;

    _LIBCPP_INLINE_VISIBILITY
    explicit set(const value_compare& __comp = value_compare())
        _NOEXCEPT_(
            is_nothrow_default_constructible<allocator_type>::value &&
            is_nothrow_default_constructible<key_compare>::value &&
            is_nothrow_copy_constructible<key_compare>::value)
        : __tree_(__comp) {}
    _LIBCPP_INLINE_VISIBILITY
    set(const value_compare& __comp, const allocator_type& __a)
        : __tree_(__comp, __a) {}
    template <class _InputIterator>
        _LIBCPP_INLINE_VISIBILITY
        set(_InputIterator __f, _InputIterator __l,
            const value_compare& __comp = value_compare())
        : __tree_(__comp)
        {
            insert(__f, __l);
        }

    template <class _InputIterator>
        _LIBCPP_INLINE_VISIBILITY
        set(_InputIterator __f, _InputIterator __l, const value_compare& __comp,
            const allocator_type& __a)
        : __tree_(__comp, __a)
        {
            insert(__f, __l);
        }

    _LIBCPP_INLINE_VISIBILITY
    set(const set& __s)
        : __tree_(__s.__tree_)
        {
            insert(__s.begin(), __s.end());
        }

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    set(set&& __s)
        _NOEXCEPT_(is_nothrow_move_constructible<__base>::value)
        : __tree_(_STD::move(__s.__tree_)) {}
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES

    _LIBCPP_INLINE_VISIBILITY
    explicit set(const allocator_type& __a)
        : __tree_(__a) {}

    _LIBCPP_INLINE_VISIBILITY
    set(const set& __s, const allocator_type& __a)
        : __tree_(__s.__tree_.value_comp(), __a)
        {
            insert(__s.begin(), __s.end());
        }

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    set(set&& __s, const allocator_type& __a);
#endif

    _LIBCPP_INLINE_VISIBILITY
    set(initializer_list<value_type> __il, const value_compare& __comp = value_compare())
        : __tree_(__comp)
        {
            insert(__il.begin(), __il.end());
        }

    _LIBCPP_INLINE_VISIBILITY
    set(initializer_list<value_type> __il, const value_compare& __comp,
        const allocator_type& __a)
        : __tree_(__comp, __a)
        {
            insert(__il.begin(), __il.end());
        }

    _LIBCPP_INLINE_VISIBILITY
    set& operator=(initializer_list<value_type> __il)
        {
            __tree_.__assign_unique(__il.begin(), __il.end());
            return *this;
        }

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    set& operator=(set&& __s)
        _NOEXCEPT_(is_nothrow_move_assignable<__base>::value)
        {
            __tree_ = _STD::move(__s.__tree_);
            return *this;
        }
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES

    _LIBCPP_INLINE_VISIBILITY
          iterator begin() _NOEXCEPT       {return __tree_.begin();}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator begin() const _NOEXCEPT {return __tree_.begin();}
    _LIBCPP_INLINE_VISIBILITY
          iterator end() _NOEXCEPT         {return __tree_.end();}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator end()   const _NOEXCEPT {return __tree_.end();}

    _LIBCPP_INLINE_VISIBILITY
          reverse_iterator rbegin() _NOEXCEPT
            {return reverse_iterator(end());}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator rbegin() const _NOEXCEPT
        {return const_reverse_iterator(end());}
    _LIBCPP_INLINE_VISIBILITY
          reverse_iterator rend() _NOEXCEPT
            {return reverse_iterator(begin());}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator rend() const _NOEXCEPT
        {return const_reverse_iterator(begin());}

    _LIBCPP_INLINE_VISIBILITY
    const_iterator cbegin()  const _NOEXCEPT {return begin();}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator cend() const _NOEXCEPT {return end();}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator crbegin() const _NOEXCEPT {return rbegin();}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator crend() const _NOEXCEPT {return rend();}

    _LIBCPP_INLINE_VISIBILITY
    bool empty() const _NOEXCEPT {return __tree_.size() == 0;}
    _LIBCPP_INLINE_VISIBILITY
    size_type size() const _NOEXCEPT {return __tree_.size();}
    _LIBCPP_INLINE_VISIBILITY
    size_type max_size() const _NOEXCEPT {return __tree_.max_size();}

    // modifiers:
#if !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
    template <class... _Args>
        _LIBCPP_INLINE_VISIBILITY
        pair<iterator, bool> emplace(_Args&&... __args)
            {return __tree_.__emplace_unique(_STD::forward<_Args>(__args)...);}
    template <class... _Args>
        _LIBCPP_INLINE_VISIBILITY
        iterator emplace_hint(const_iterator __p, _Args&&... __args)
            {return __tree_.__emplace_hint_unique(__p, _STD::forward<_Args>(__args)...);}
#endif  // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator,bool> insert(const value_type& __v)
        {return __tree_.__insert_unique(__v);}
#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator,bool> insert(value_type&& __v)
        {return __tree_.__insert_unique(_STD::move(__v));}
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    iterator insert(const_iterator __p, const value_type& __v)
        {return __tree_.__insert_unique(__p, __v);}
#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    iterator insert(const_iterator __p, value_type&& __v)
        {return __tree_.__insert_unique(__p, _STD::move(__v));}
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
    template <class _InputIterator>
        _LIBCPP_INLINE_VISIBILITY
        void insert(_InputIterator __f, _InputIterator __l)
        {
            for (const_iterator __e = cend(); __f != __l; ++__f)
                __tree_.__insert_unique(__e, *__f);
        }

    _LIBCPP_INLINE_VISIBILITY
    void insert(initializer_list<value_type> __il)
        {insert(__il.begin(), __il.end());}

    _LIBCPP_INLINE_VISIBILITY
    iterator  erase(const_iterator __p) {return __tree_.erase(__p);}
    _LIBCPP_INLINE_VISIBILITY
    size_type erase(const key_type& __k)
        {return __tree_.__erase_unique(__k);}
    _LIBCPP_INLINE_VISIBILITY
    iterator  erase(const_iterator __f, const_iterator __l)
        {return __tree_.erase(__f, __l);}
    _LIBCPP_INLINE_VISIBILITY
    void clear() _NOEXCEPT {__tree_.clear();}

    _LIBCPP_INLINE_VISIBILITY
    void swap(set& __s) _NOEXCEPT_(__is_nothrow_swappable<__base>::value)
        {__tree_.swap(__s.__tree_);}

    _LIBCPP_INLINE_VISIBILITY
    allocator_type get_allocator() const _NOEXCEPT {return __tree_.__alloc();}
    _LIBCPP_INLINE_VISIBILITY
    key_compare    key_comp()      const {return __tree_.value_comp();}
    _LIBCPP_INLINE_VISIBILITY
    value_compare  value_comp()    const {return __tree_.value_comp();}

    // set operations:
    _LIBCPP_INLINE_VISIBILITY
    iterator find(const key_type& __k)             {return __tree_.find(__k);}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator find(const key_type& __k) const {return __tree_.find(__k);}
    _LIBCPP_INLINE_VISIBILITY
    size_type      count(const key_type& __k) const
        {return __tree_.__count_unique(__k);}
    _LIBCPP_INLINE_VISIBILITY
    iterator lower_bound(const key_type& __k)
        {return __tree_.lower_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator lower_bound(const key_type& __k) const
        {return __tree_.lower_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    iterator upper_bound(const key_type& __k)
        {return __tree_.upper_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator upper_bound(const key_type& __k) const
        {return __tree_.upper_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator,iterator> equal_range(const key_type& __k)
        {return __tree_.__equal_range_unique(__k);}
    _LIBCPP_INLINE_VISIBILITY
    pair<const_iterator,const_iterator> equal_range(const key_type& __k) const
        {return __tree_.__equal_range_unique(__k);}
};

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES

template <class _Key, class _Compare, class _Allocator>
set<_Key, _Compare, _Allocator>::set(set&& __s, const allocator_type& __a)
    : __tree_(_STD::move(__s.__tree_), __a)
{
    if (__a != __s.get_allocator())
    {
        const_iterator __e = cend();
        while (!__s.empty())
            insert(__e, _STD::move(__s.__tree_.remove(__s.begin())->__value_));
    }
}

#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator==(const set<_Key, _Compare, _Allocator>& __x,
           const set<_Key, _Compare, _Allocator>& __y)
{
    return __x.size() == __y.size() && _STD::equal(__x.begin(), __x.end(), __y.begin());
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator< (const set<_Key, _Compare, _Allocator>& __x,
           const set<_Key, _Compare, _Allocator>& __y)
{
    return _STD::lexicographical_compare(__x.begin(), __x.end(), __y.begin(), __y.end());
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator!=(const set<_Key, _Compare, _Allocator>& __x,
           const set<_Key, _Compare, _Allocator>& __y)
{
    return !(__x == __y);
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator> (const set<_Key, _Compare, _Allocator>& __x,
           const set<_Key, _Compare, _Allocator>& __y)
{
    return __y < __x;
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator>=(const set<_Key, _Compare, _Allocator>& __x,
           const set<_Key, _Compare, _Allocator>& __y)
{
    return !(__x < __y);
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator<=(const set<_Key, _Compare, _Allocator>& __x,
           const set<_Key, _Compare, _Allocator>& __y)
{
    return !(__y < __x);
}

// specialized algorithms:
template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
void
swap(set<_Key, _Compare, _Allocator>& __x,
     set<_Key, _Compare, _Allocator>& __y)
    _NOEXCEPT_(_NOEXCEPT_(__x.swap(__y)))
{
    __x.swap(__y);
}

template <class _Key, class _Compare = less<_Key>,
          class _Allocator = allocator<_Key> >
class _LIBCPP_VISIBLE multiset
{
public:
    // types:
    typedef _Key                                      key_type;
    typedef key_type                                 value_type;
    typedef _Compare                                  key_compare;
    typedef key_compare                              value_compare;
    typedef _Allocator                                allocator_type;
    typedef value_type&                              reference;
    typedef const value_type&                        const_reference;

private:
    typedef __tree<value_type, value_compare, allocator_type> __base;
    typedef allocator_traits<allocator_type>                  __alloc_traits;
    typedef typename __base::__node_holder                    __node_holder;

    __base __tree_;

public:
    typedef typename __base::pointer               pointer;
    typedef typename __base::const_pointer         const_pointer;
    typedef typename __base::size_type             size_type;
    typedef typename __base::difference_type       difference_type;
    typedef typename __base::const_iterator        iterator;
    typedef typename __base::const_iterator        const_iterator;
    typedef _STD::reverse_iterator<iterator>       reverse_iterator;
    typedef _STD::reverse_iterator<const_iterator> const_reverse_iterator;

    // construct/copy/destroy:
    _LIBCPP_INLINE_VISIBILITY
    explicit multiset(const value_compare& __comp = value_compare())
        _NOEXCEPT_(
            is_nothrow_default_constructible<allocator_type>::value &&
            is_nothrow_default_constructible<key_compare>::value &&
            is_nothrow_copy_constructible<key_compare>::value)
        : __tree_(__comp) {}
    _LIBCPP_INLINE_VISIBILITY
    multiset(const value_compare& __comp, const allocator_type& __a)
        : __tree_(__comp, __a) {}
    template <class _InputIterator>
        _LIBCPP_INLINE_VISIBILITY
        multiset(_InputIterator __f, _InputIterator __l,
                 const value_compare& __comp = value_compare())
        : __tree_(__comp)
        {
            insert(__f, __l);
        }

    template <class _InputIterator>
        _LIBCPP_INLINE_VISIBILITY
        multiset(_InputIterator __f, _InputIterator __l,
                 const value_compare& __comp, const allocator_type& __a)
        : __tree_(__comp, __a)
        {
            insert(__f, __l);
        }

    _LIBCPP_INLINE_VISIBILITY
    multiset(const multiset& __s)
        : __tree_(__s.__tree_.value_comp(),
          __alloc_traits::select_on_container_copy_construction(__s.__tree_.__alloc()))
        {
            insert(__s.begin(), __s.end());
        }

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    multiset(multiset&& __s)
        _NOEXCEPT_(is_nothrow_move_constructible<__base>::value)
        : __tree_(_STD::move(__s.__tree_)) {}
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    explicit multiset(const allocator_type& __a)
        : __tree_(__a) {}
    _LIBCPP_INLINE_VISIBILITY
    multiset(const multiset& __s, const allocator_type& __a)
        : __tree_(__s.__tree_.value_comp(), __a)
        {
            insert(__s.begin(), __s.end());
        }
#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    multiset(multiset&& __s, const allocator_type& __a);
#endif

    _LIBCPP_INLINE_VISIBILITY
    multiset(initializer_list<value_type> __il, const value_compare& __comp = value_compare())
        : __tree_(__comp)
        {
            insert(__il.begin(), __il.end());
        }

    _LIBCPP_INLINE_VISIBILITY
    multiset(initializer_list<value_type> __il, const value_compare& __comp,
        const allocator_type& __a)
        : __tree_(__comp, __a)
        {
            insert(__il.begin(), __il.end());
        }

    _LIBCPP_INLINE_VISIBILITY
    multiset& operator=(initializer_list<value_type> __il)
        {
            __tree_.__assign_multi(__il.begin(), __il.end());
            return *this;
        }

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    multiset& operator=(multiset&& __s)
        _NOEXCEPT_(is_nothrow_move_assignable<__base>::value)
        {
            __tree_ = _STD::move(__s.__tree_);
            return *this;
        }
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES

    _LIBCPP_INLINE_VISIBILITY
          iterator begin() _NOEXCEPT       {return __tree_.begin();}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator begin() const _NOEXCEPT {return __tree_.begin();}
    _LIBCPP_INLINE_VISIBILITY
          iterator end() _NOEXCEPT         {return __tree_.end();}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator end()   const _NOEXCEPT {return __tree_.end();}

    _LIBCPP_INLINE_VISIBILITY
          reverse_iterator rbegin() _NOEXCEPT
            {return reverse_iterator(end());}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator rbegin() const _NOEXCEPT
        {return const_reverse_iterator(end());}
    _LIBCPP_INLINE_VISIBILITY
          reverse_iterator rend() _NOEXCEPT
            {return       reverse_iterator(begin());}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator rend() const _NOEXCEPT
        {return const_reverse_iterator(begin());}

    _LIBCPP_INLINE_VISIBILITY
    const_iterator cbegin()  const _NOEXCEPT {return begin();}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator cend() const _NOEXCEPT {return end();}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator crbegin() const _NOEXCEPT {return rbegin();}
    _LIBCPP_INLINE_VISIBILITY
    const_reverse_iterator crend() const _NOEXCEPT {return rend();}

    _LIBCPP_INLINE_VISIBILITY
    bool empty() const _NOEXCEPT {return __tree_.size() == 0;}
    _LIBCPP_INLINE_VISIBILITY
    size_type size() const _NOEXCEPT {return __tree_.size();}
    _LIBCPP_INLINE_VISIBILITY
    size_type max_size() const _NOEXCEPT {return __tree_.max_size();}

    // modifiers:
#if !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
    template <class... _Args>
        _LIBCPP_INLINE_VISIBILITY
        iterator emplace(_Args&&... __args)
            {return __tree_.__emplace_multi(_STD::forward<_Args>(__args)...);}
    template <class... _Args>
        _LIBCPP_INLINE_VISIBILITY
        iterator emplace_hint(const_iterator __p, _Args&&... __args)
            {return __tree_.__emplace_hint_multi(__p, _STD::forward<_Args>(__args)...);}
#endif  // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
    _LIBCPP_INLINE_VISIBILITY
    iterator insert(const value_type& __v)
        {return __tree_.__insert_multi(__v);}
#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    iterator insert(value_type&& __v)
        {return __tree_.__insert_multi(_STD::move(__v));}
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    iterator insert(const_iterator __p, const value_type& __v)
        {return __tree_.__insert_multi(__p, __v);}
#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
    _LIBCPP_INLINE_VISIBILITY
    iterator insert(const_iterator __p, value_type&& __v)
        {return __tree_.__insert_multi(_STD::move(__v));}
#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES
    template <class _InputIterator>
        _LIBCPP_INLINE_VISIBILITY
        void insert(_InputIterator __f, _InputIterator __l)
        {
            for (const_iterator __e = cend(); __f != __l; ++__f)
                __tree_.__insert_multi(__e, *__f);
        }

    _LIBCPP_INLINE_VISIBILITY
    void insert(initializer_list<value_type> __il)
        {insert(__il.begin(), __il.end());}

    _LIBCPP_INLINE_VISIBILITY
    iterator  erase(const_iterator __p) {return __tree_.erase(__p);}
    _LIBCPP_INLINE_VISIBILITY
    size_type erase(const key_type& __k) {return __tree_.__erase_multi(__k);}
    _LIBCPP_INLINE_VISIBILITY
    iterator  erase(const_iterator __f, const_iterator __l)
        {return __tree_.erase(__f, __l);}
    _LIBCPP_INLINE_VISIBILITY
    void clear() _NOEXCEPT {__tree_.clear();}

    _LIBCPP_INLINE_VISIBILITY
    void swap(multiset& __s)
        _NOEXCEPT_(__is_nothrow_swappable<__base>::value)
        {__tree_.swap(__s.__tree_);}

    _LIBCPP_INLINE_VISIBILITY
    allocator_type get_allocator() const _NOEXCEPT {return __tree_.__alloc();}
    _LIBCPP_INLINE_VISIBILITY
    key_compare    key_comp()      const {return __tree_.value_comp();}
    _LIBCPP_INLINE_VISIBILITY
    value_compare  value_comp()    const {return __tree_.value_comp();}

    // set operations:
    _LIBCPP_INLINE_VISIBILITY
    iterator find(const key_type& __k)             {return __tree_.find(__k);}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator find(const key_type& __k) const {return __tree_.find(__k);}
    _LIBCPP_INLINE_VISIBILITY
    size_type      count(const key_type& __k) const
        {return __tree_.__count_multi(__k);}
    _LIBCPP_INLINE_VISIBILITY
    iterator lower_bound(const key_type& __k)
        {return __tree_.lower_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator lower_bound(const key_type& __k) const
            {return __tree_.lower_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    iterator upper_bound(const key_type& __k)
            {return __tree_.upper_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    const_iterator upper_bound(const key_type& __k) const
            {return __tree_.upper_bound(__k);}
    _LIBCPP_INLINE_VISIBILITY
    pair<iterator,iterator>             equal_range(const key_type& __k)
            {return __tree_.__equal_range_multi(__k);}
    _LIBCPP_INLINE_VISIBILITY
    pair<const_iterator,const_iterator> equal_range(const key_type& __k) const
            {return __tree_.__equal_range_multi(__k);}
};

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES

template <class _Key, class _Compare, class _Allocator>
multiset<_Key, _Compare, _Allocator>::multiset(multiset&& __s, const allocator_type& __a)
    : __tree_(_STD::move(__s.__tree_), __a)
{
    if (__a != __s.get_allocator())
    {
        const_iterator __e = cend();
        while (!__s.empty())
            insert(__e, _STD::move(__s.__tree_.remove(__s.begin())->__value_));
    }
}

#endif  // _LIBCPP_HAS_NO_RVALUE_REFERENCES

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator==(const multiset<_Key, _Compare, _Allocator>& __x,
           const multiset<_Key, _Compare, _Allocator>& __y)
{
    return __x.size() == __y.size() && _STD::equal(__x.begin(), __x.end(), __y.begin());
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator< (const multiset<_Key, _Compare, _Allocator>& __x,
           const multiset<_Key, _Compare, _Allocator>& __y)
{
    return _STD::lexicographical_compare(__x.begin(), __x.end(), __y.begin(), __y.end());
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator!=(const multiset<_Key, _Compare, _Allocator>& __x,
           const multiset<_Key, _Compare, _Allocator>& __y)
{
    return !(__x == __y);
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator> (const multiset<_Key, _Compare, _Allocator>& __x,
           const multiset<_Key, _Compare, _Allocator>& __y)
{
    return __y < __x;
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator>=(const multiset<_Key, _Compare, _Allocator>& __x,
           const multiset<_Key, _Compare, _Allocator>& __y)
{
    return !(__x < __y);
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
bool
operator<=(const multiset<_Key, _Compare, _Allocator>& __x,
           const multiset<_Key, _Compare, _Allocator>& __y)
{
    return !(__y < __x);
}

template <class _Key, class _Compare, class _Allocator>
inline _LIBCPP_INLINE_VISIBILITY
void
swap(multiset<_Key, _Compare, _Allocator>& __x,
     multiset<_Key, _Compare, _Allocator>& __y)
    _NOEXCEPT_(_NOEXCEPT_(__x.swap(__y)))
{
    __x.swap(__y);
}

_LIBCPP_END_NAMESPACE_STD

#endif  // _LIBCPP_SET