include/__tree

// -*- C++ -*-
//===----------------------------------------------------------------------===//
//
// 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___TREE
#define _LIBCPP___TREE

#include <__config>
#include <iterator>
#include <memory>
#include <stdexcept>
#include <algorithm>

#if !defined(_LIBCPP_HAS_NO_PRAGMA_SYSTEM_HEADER)
#pragma GCC system_header
#endif

_LIBCPP_BEGIN_NAMESPACE_STD

template <class _Tp, class _Compare, class _Allocator> class __tree;
template <class _Tp, class _NodePtr, class _DiffType>
 class _LIBCPP_TYPE_VIS_ONLY __tree_iterator;
template <class _Tp, class _ConstNodePtr, class _DiffType>
 class _LIBCPP_TYPE_VIS_ONLY __tree_const_iterator;

template <class _Pointer> class __tree_end_node;
template <class _VoidPtr> class __tree_node_base;
template <class _Tp, class _VoidPtr> class __tree_node;

#ifndef _LIBCPP_CXX03_LANG
template <class _Key, class _Value>
union __value_type;
#else
template <class _Key, class _Value>
struct __value_type;
#endif

template <class _Allocator> class __map_node_destructor;
template <class _TreeIterator> class _LIBCPP_TYPE_VIS_ONLY __map_iterator;
template <class _TreeIterator> class _LIBCPP_TYPE_VIS_ONLY __map_const_iterator;

/*

_NodePtr algorithms

The algorithms taking _NodePtr are red black tree algorithms. Those
algorithms taking a parameter named __root should assume that __root
points to a proper red black tree (unless otherwise specified).

Each algorithm herein assumes that __root->__parent_ points to a non-null
structure which has a member __left_ which points back to __root. No other
member is read or written to at __root->__parent_.

__root->__parent_ will be referred to below (in comments only) as end_node.
end_node->__left_ is an externably accessible lvalue for __root, and can be
changed by node insertion and removal (without explicit reference to end_node).

All nodes (with the exception of end_node), even the node referred to as
__root, have a non-null __parent_ field.

*/

// Returns: true if __x is a left child of its parent, else false
// Precondition: __x != nullptr.
template <class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
bool
__tree_is_left_child(_NodePtr __x) _NOEXCEPT
{
 return __x == __x->__parent_->__left_;
}

// Determintes if the subtree rooted at __x is a proper red black subtree. If
// __x is a proper subtree, returns the black height (null counts as 1). If
// __x is an improper subtree, returns 0.
template <class _NodePtr>
unsigned
__tree_sub_invariant(_NodePtr __x)
{
 if (__x == nullptr)
 return 1;
 // parent consistency checked by caller
 // check __x->__left_ consistency
 if (__x->__left_ != nullptr && __x->__left_->__parent_ != __x)
 return 0;
 // check __x->__right_ consistency
 if (__x->__right_ != nullptr && __x->__right_->__parent_ != __x)
 return 0;
 // check __x->__left_ != __x->__right_ unless both are nullptr
 if (__x->__left_ == __x->__right_ && __x->__left_ != nullptr)
 return 0;
 // If this is red, neither child can be red
 if (!__x->__is_black_)
 {
 if (__x->__left_ && !__x->__left_->__is_black_)
 return 0;
 if (__x->__right_ && !__x->__right_->__is_black_)
 return 0;
 }
 unsigned __h = __tree_sub_invariant(__x->__left_);
 if (__h == 0)
 return 0; // invalid left subtree
 if (__h != __tree_sub_invariant(__x->__right_))
 return 0; // invalid or different height right subtree
 return __h + __x->__is_black_; // return black height of this node
}

// Determintes if the red black tree rooted at __root is a proper red black tree.
// __root == nullptr is a proper tree. Returns true is __root is a proper
// red black tree, else returns false.
template <class _NodePtr>
bool
__tree_invariant(_NodePtr __root)
{
 if (__root == nullptr)
 return true;
 // check __x->__parent_ consistency
 if (__root->__parent_ == nullptr)
 return false;
 if (!__tree_is_left_child(__root))
 return false;
 // root must be black
 if (!__root->__is_black_)
 return false;
 // do normal node checks
 return __tree_sub_invariant(__root) != 0;
}

// Returns: pointer to the left-most node under __x.
// Precondition: __x != nullptr.
template <class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_NodePtr
__tree_min(_NodePtr __x) _NOEXCEPT
{
 while (__x->__left_ != nullptr)
 __x = __x->__left_;
 return __x;
}

// Returns: pointer to the right-most node under __x.
// Precondition: __x != nullptr.
template <class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_NodePtr
__tree_max(_NodePtr __x) _NOEXCEPT
{
 while (__x->__right_ != nullptr)
 __x = __x->__right_;
 return __x;
}

// Returns: pointer to the next in-order node after __x.
// Precondition: __x != nullptr.
template <class _NodePtr>
_NodePtr
__tree_next(_NodePtr __x) _NOEXCEPT
{
 if (__x->__right_ != nullptr)
 return __tree_min(__x->__right_);
 while (!__tree_is_left_child(__x))
 __x = __x->__parent_unsafe();
 return __x->__parent_unsafe();
}

template <class _EndNodePtr, class _NodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_EndNodePtr
__tree_next_iter(_NodePtr __x) _NOEXCEPT
{
 if (__x->__right_ != nullptr)
 return static_cast<_EndNodePtr>(__tree_min(__x->__right_));
 while (!__tree_is_left_child(__x))
 __x = __x->__parent_unsafe();
 return static_cast<_EndNodePtr>(__x->__parent_);
}

// Returns: pointer to the previous in-order node before __x.
// Precondition: __x != nullptr.
// Note: __x may be the end node.
template <class _NodePtr, class _EndNodePtr>
inline _LIBCPP_INLINE_VISIBILITY
_NodePtr
__tree_prev_iter(_EndNodePtr __x) _NOEXCEPT
{
 if (__x->__left_ != nullptr)
 return __tree_max(__x->__left_);
 _NodePtr __xx = static_cast<_NodePtr>(__x);
 while (__tree_is_left_child(__xx))
 __xx = __xx->__parent_unsafe();
 return __xx->__parent_unsafe();
}

// Returns: pointer to a node which has no children
// Precondition: __x != nullptr.
template <class _NodePtr>
_NodePtr
__tree_leaf(_NodePtr __x) _NOEXCEPT
{
 while (true)
 {
 if (__x->__left_ != nullptr)
 {
 __x = __x->__left_;
 continue;
 }
 if (__x->__right_ != nullptr)
 {
 __x = __x->__right_;
 continue;
 }
 break;
 }
 return __x;
}

// Effects: Makes __x->__right_ the subtree root with __x as its left child
// while preserving in-order order.
// Precondition: __x->__right_ != nullptr
template <class _NodePtr>
void
__tree_left_rotate(_NodePtr __x) _NOEXCEPT
{
 _NodePtr __y = __x->__right_;
 __x->__right_ = __y->__left_;
 if (__x->__right_ != nullptr)
 __x->__right_->__set_parent(__x);
 __y->__parent_ = __x->__parent_;
 if (__tree_is_left_child(__x))
 __x->__parent_->__left_ = __y;
 else
 __x->__parent_unsafe()->__right_ = __y;
 __y->__left_ = __x;
 __x->__set_parent(__y);
}

// Effects: Makes __x->__left_ the subtree root with __x as its right child
// while preserving in-order order.
// Precondition: __x->__left_ != nullptr
template <class _NodePtr>
void
__tree_right_rotate(_NodePtr __x) _NOEXCEPT
{
 _NodePtr __y = __x->__left_;
 __x->__left_ = __y->__right_;
 if (__x->__left_ != nullptr)
 __x->__left_->__set_parent(__x);
 __y->__parent_ = __x->__parent_;
 if (__tree_is_left_child(__x))
 __x->__parent_->__left_ = __y;
 else
 __x->__parent_unsafe()->__right_ = __y;
 __y->__right_ = __x;
 __x->__set_parent(__y);
}

// Effects: Rebalances __root after attaching __x to a leaf.
// Precondition: __root != nulptr && __x != nullptr.
// __x has no children.
// __x == __root or == a direct or indirect child of __root.
// If __x were to be unlinked from __root (setting __root to
// nullptr if __root == __x), __tree_invariant(__root) == true.
// Postcondition: __tree_invariant(end_node->__left_) == true. end_node->__left_
// may be different than the value passed in as __root.
template <class _NodePtr>
void
__tree_balance_after_insert(_NodePtr __root, _NodePtr __x) _NOEXCEPT
{
 __x->__is_black_ = __x == __root;
 while (__x != __root && !__x->__parent_unsafe()->__is_black_)
 {
 // __x->__parent_ != __root because __x->__parent_->__is_black == false
 if (__tree_is_left_child(__x->__parent_unsafe()))
 {
 _NodePtr __y = __x->__parent_unsafe()->__parent_unsafe()->__right_;
 if (__y != nullptr && !__y->__is_black_)
 {
 __x = __x->__parent_unsafe();
 __x->__is_black_ = true;
 __x = __x->__parent_unsafe();
 __x->__is_black_ = __x == __root;
 __y->__is_black_ = true;
 }
 else
 {
 if (!__tree_is_left_child(__x))
 {
 __x = __x->__parent_unsafe();
 __tree_left_rotate(__x);
 }
 __x = __x->__parent_unsafe();
 __x->__is_black_ = true;
 __x = __x->__parent_unsafe();
 __x->__is_black_ = false;
 __tree_right_rotate(__x);
 break;
 }
 }
 else
 {
 _NodePtr __y = __x->__parent_unsafe()->__parent_->__left_;
 if (__y != nullptr && !__y->__is_black_)
 {
 __x = __x->__parent_unsafe();
 __x->__is_black_ = true;
 __x = __x->__parent_unsafe();
 __x->__is_black_ = __x == __root;
 __y->__is_black_ = true;
 }
 else
 {
 if (__tree_is_left_child(__x))
 {
 __x = __x->__parent_unsafe();
 __tree_right_rotate(__x);
 }
 __x = __x->__parent_unsafe();
 __x->__is_black_ = true;
 __x = __x->__parent_unsafe();
 __x->__is_black_ = false;
 __tree_left_rotate(__x);
 break;
 }
 }
 }
}

// Precondition: __root != nullptr && __z != nullptr.
// __tree_invariant(__root) == true.
// __z == __root or == a direct or indirect child of __root.
// Effects: unlinks __z from the tree rooted at __root, rebalancing as needed.
// Postcondition: __tree_invariant(end_node->__left_) == true && end_node->__left_
// nor any of its children refer to __z. end_node->__left_
// may be different than the value passed in as __root.
template <class _NodePtr>
void
__tree_remove(_NodePtr __root, _NodePtr __z) _NOEXCEPT
{
 // __z will be removed from the tree. Client still needs to destruct/deallocate it
 // __y is either __z, or if __z has two children, __tree_next(__z).
 // __y will have at most one child.
 // __y will be the initial hole in the tree (make the hole at a leaf)
 _NodePtr __y = (__z->__left_ == nullptr || __z->__right_ == nullptr) ?
 __z : __tree_next(__z);
 // __x is __y's possibly null single child
 _NodePtr __x = __y->__left_ != nullptr ? __y->__left_ : __y->__right_;
 // __w is __x's possibly null uncle (will become __x's sibling)
 _NodePtr __w = nullptr;
 // link __x to __y's parent, and find __w
 if (__x != nullptr)
 __x->__parent_ = __y->__parent_;
 if (__tree_is_left_child(__y))
 {
 __y->__parent_->__left_ = __x;
 if (__y != __root)
 __w = __y->__parent_unsafe()->__right_;
 else
 __root = __x; // __w == nullptr
 }
 else
 {
 __y->__parent_unsafe()->__right_ = __x;
 // __y can't be root if it is a right child
 __w = __y->__parent_->__left_;
 }
 bool __removed_black = __y->__is_black_;
 // If we didn't remove __z, do so now by splicing in __y for __z,
 // but copy __z's color. This does not impact __x or __w.
 if (__y != __z)
 {
 // __z->__left_ != nulptr but __z->__right_ might == __x == nullptr
 __y->__parent_ = __z->__parent_;
 if (__tree_is_left_child(__z))
 __y->__parent_->__left_ = __y;
 else
 __y->__parent_unsafe()->__right_ = __y;
 __y->__left_ = __z->__left_;
 __y->__left_->__set_parent(__y);
 __y->__right_ = __z->__right_;
 if (__y->__right_ != nullptr)
 __y->__right_->__set_parent(__y);
 __y->__is_black_ = __z->__is_black_;
 if (__root == __z)
 __root = __y;
 }
 // There is no need to rebalance if we removed a red, or if we removed
 // the last node.
 if (__removed_black && __root != nullptr)
 {
 // Rebalance:
 // __x has an implicit black color (transferred from the removed __y)
 // associated with it, no matter what its color is.
 // If __x is __root (in which case it can't be null), it is supposed
 // to be black anyway, and if it is doubly black, then the double
 // can just be ignored.
 // If __x is red (in which case it can't be null), then it can absorb
 // the implicit black just by setting its color to black.
 // Since __y was black and only had one child (which __x points to), __x
 // is either red with no children, else null, otherwise __y would have
 // different black heights under left and right pointers.
 // if (__x == __root || __x != nullptr && !__x->__is_black_)
 if (__x != nullptr)
 __x->__is_black_ = true;
 else
 {
 // Else __x isn't root, and is "doubly black", even though it may
 // be null. __w can not be null here, else the parent would
 // see a black height >= 2 on the __x side and a black height
 // of 1 on the __w side (__w must be a non-null black or a red
 // with a non-null black child).
 while (true)
 {
 if (!__tree_is_left_child(__w)) // if x is left child
 {
 if (!__w->__is_black_)
 {
 __w->__is_black_ = true;
 __w->__parent_unsafe()->__is_black_ = false;
 __tree_left_rotate(__w->__parent_unsafe());
 // __x is still valid
 // reset __root only if necessary
 if (__root == __w->__left_)
 __root = __w;
 // reset sibling, and it still can't be null
 __w = __w->__left_->__right_;
 }
 // __w->__is_black_ is now true, __w may have null children
 if ((__w->__left_ == nullptr || __w->__left_->__is_black_) &&
 (__w->__right_ == nullptr || __w->__right_->__is_black_))
 {
 __w->__is_black_ = false;
 __x = __w->__parent_unsafe();
 // __x can no longer be null
 if (__x == __root || !__x->__is_black_)
 {
 __x->__is_black_ = true;
 break;
 }
 // reset sibling, and it still can't be null
 __w = __tree_is_left_child(__x) ?
 __x->__parent_unsafe()->__right_ :
 __x->__parent_->__left_;
 // continue;
 }
 else // __w has a red child
 {
 if (__w->__right_ == nullptr || __w->__right_->__is_black_)
 {
 // __w left child is non-null and red
 __w->__left_->__is_black_ = true;
 __w->__is_black_ = false;
 __tree_right_rotate(__w);
 // __w is known not to be root, so root hasn't changed
 // reset sibling, and it still can't be null
 __w = __w->__parent_unsafe();
 }
 // __w has a right red child, left child may be null
 __w->__is_black_ = __w->__parent_unsafe()->__is_black_;
 __w->__parent_unsafe()->__is_black_ = true;
 __w->__right_->__is_black_ = true;
 __tree_left_rotate(__w->__parent_unsafe());
 break;
 }
 }
 else
 {
 if (!__w->__is_black_)
 {
 __w->__is_black_ = true;
 __w->__parent_unsafe()->__is_black_ = false;
 __tree_right_rotate(__w->__parent_unsafe());
 // __x is still valid
 // reset __root only if necessary
 if (__root == __w->__right_)
 __root = __w;
 // reset sibling, and it still can't be null
 __w = __w->__right_->__left_;
 }
 // __w->__is_black_ is now true, __w may have null children
 if ((__w->__left_ == nullptr || __w->__left_->__is_black_) &&
 (__w->__right_ == nullptr || __w->__right_->__is_black_))
 {
 __w->__is_black_ = false;
 __x = __w->__parent_unsafe();
 // __x can no longer be null
 if (!__x->__is_black_ || __x == __root)
 {
 __x->__is_black_ = true;
 break;
 }
 // reset sibling, and it still can't be null
 __w = __tree_is_left_child(__x) ?
 __x->__parent_unsafe()->__right_ :
 __x->__parent_->__left_;
 // continue;
 }
 else // __w has a red child
 {
 if (__w->__left_ == nullptr || __w->__left_->__is_black_)
 {
 // __w right child is non-null and red
 __w->__right_->__is_black_ = true;
 __w->__is_black_ = false;
 __tree_left_rotate(__w);
 // __w is known not to be root, so root hasn't changed
 // reset sibling, and it still can't be null
 __w = __w->__parent_unsafe();
 }
 // __w has a left red child, right child may be null
 __w->__is_black_ = __w->__parent_unsafe()->__is_black_;
 __w->__parent_unsafe()->__is_black_ = true;
 __w->__left_->__is_black_ = true;
 __tree_right_rotate(__w->__parent_unsafe());
 break;
 }
 }
 }
 }
 }
}

// node traits


#ifndef _LIBCPP_CXX03_LANG
template <class _Tp>
struct __is_tree_value_type_imp : false_type {};

template <class _Key, class _Value>
struct __is_tree_value_type_imp<__value_type<_Key, _Value>> : true_type {};

template <class ..._Args>
struct __is_tree_value_type : false_type {};

template <class _One>
struct __is_tree_value_type<_One> : __is_tree_value_type_imp<typename __uncvref<_One>::type> {};
#endif

template <class _Tp>
struct __tree_key_value_types {
 typedef _Tp key_type;
 typedef _Tp __node_value_type;
 typedef _Tp __container_value_type;
 static const bool __is_map = false;

 _LIBCPP_INLINE_VISIBILITY
 static key_type const& __get_key(_Tp const& __v) {
 return __v;
 }
 _LIBCPP_INLINE_VISIBILITY
 static __container_value_type const& __get_value(__node_value_type const& __v) {
 return __v;
 }
 _LIBCPP_INLINE_VISIBILITY
 static __container_value_type* __get_ptr(__node_value_type& __n) {
 return _VSTD::addressof(__n);
 }

#ifndef _LIBCPP_CXX03_LANG
 _LIBCPP_INLINE_VISIBILITY
 static __container_value_type&& __move(__node_value_type& __v) {
 return _VSTD::move(__v);
 }
#endif
};

template <class _Key, class _Tp>
struct __tree_key_value_types<__value_type<_Key, _Tp> > {
 typedef _Key key_type;
 typedef _Tp mapped_type;
 typedef __value_type<_Key, _Tp> __node_value_type;
 typedef pair<const _Key, _Tp> __container_value_type;
 typedef pair<_Key, _Tp> __nc_value_type;
 typedef __container_value_type __map_value_type;
 static const bool __is_map = true;

 _LIBCPP_INLINE_VISIBILITY
 static key_type const&
 __get_key(__node_value_type const& __t) {
 return __t.__cc.first;
 }

 template <class _Up>
 _LIBCPP_INLINE_VISIBILITY
 static typename enable_if<__is_same_uncvref<_Up, __container_value_type>::value,
 key_type const&>::type
 __get_key(_Up& __t) {
 return __t.first;
 }

 _LIBCPP_INLINE_VISIBILITY
 static __container_value_type const&
 __get_value(__node_value_type const& __t) {
 return __t.__cc;
 }

 template <class _Up>
 _LIBCPP_INLINE_VISIBILITY
 static typename enable_if<__is_same_uncvref<_Up, __container_value_type>::value,
 __container_value_type const&>::type
 __get_value(_Up& __t) {
 return __t;
 }

 _LIBCPP_INLINE_VISIBILITY
 static __container_value_type* __get_ptr(__node_value_type& __n) {
 return _VSTD::addressof(__n.__cc);
 }

#ifndef _LIBCPP_CXX03_LANG
 _LIBCPP_INLINE_VISIBILITY
 static __nc_value_type&& __move(__node_value_type& __v) {
 return _VSTD::move(__v.__nc);
 }
#endif
};

template <class _VoidPtr>
struct __tree_node_base_types {
 typedef _VoidPtr __void_pointer;

 typedef __tree_node_base<__void_pointer> __node_base_type;
 typedef typename __rebind_pointer<_VoidPtr, __node_base_type>::type
 __node_base_pointer;

 typedef __tree_end_node<__node_base_pointer> __end_node_type;
 typedef typename __rebind_pointer<_VoidPtr, __end_node_type>::type
 __end_node_pointer;
#if defined(_LIBCPP_ABI_TREE_REMOVE_NODE_POINTER_UB)
 typedef __end_node_pointer __parent_pointer;
#else
 typedef typename conditional<
 is_pointer<__end_node_pointer>::value,
 __end_node_pointer,
 __node_base_pointer>::type __parent_pointer;
#endif

private:
 static_assert((is_same<typename pointer_traits<_VoidPtr>::element_type, void>::value),
 "_VoidPtr does not point to unqualified void type");
};

template <class _Tp, class _AllocPtr, class _KVTypes = __tree_key_value_types<_Tp>,
 bool = _KVTypes::__is_map>
struct __tree_map_pointer_types {};

template <class _Tp, class _AllocPtr, class _KVTypes>
struct __tree_map_pointer_types<_Tp, _AllocPtr, _KVTypes, true> {
 typedef typename _KVTypes::__map_value_type _Mv;
 typedef typename __rebind_pointer<_AllocPtr, _Mv>::type
 __map_value_type_pointer;
 typedef typename __rebind_pointer<_AllocPtr, const _Mv>::type
 __const_map_value_type_pointer;
};

template <class _NodePtr, class _NodeT = typename pointer_traits<_NodePtr>::element_type>
struct __tree_node_types;

template <class _NodePtr, class _Tp, class _VoidPtr>
struct __tree_node_types<_NodePtr, __tree_node<_Tp, _VoidPtr> >
 : public __tree_node_base_types<_VoidPtr>,
 __tree_key_value_types<_Tp>,
 __tree_map_pointer_types<_Tp, _VoidPtr>
{
 typedef __tree_node_base_types<_VoidPtr> __base;
 typedef __tree_key_value_types<_Tp> __key_base;
 typedef __tree_map_pointer_types<_Tp, _VoidPtr> __map_pointer_base;
public:

 typedef typename pointer_traits<_NodePtr>::element_type __node_type;
 typedef _NodePtr __node_pointer;

 typedef _Tp __node_value_type;
 typedef typename __rebind_pointer<_VoidPtr, __node_value_type>::type
 __node_value_type_pointer;
 typedef typename __rebind_pointer<_VoidPtr, const __node_value_type>::type
 __const_node_value_type_pointer;
#if defined(_LIBCPP_ABI_TREE_REMOVE_NODE_POINTER_UB)
 typedef typename __base::__end_node_pointer __iter_pointer;
#else
 typedef typename conditional<
 is_pointer<__node_pointer>::value,
 typename __base::__end_node_pointer,
 __node_pointer>::type __iter_pointer;
#endif
private:
 static_assert(!is_const<__node_type>::value,
 "_NodePtr should never be a pointer to const");
 static_assert((is_same<typename __rebind_pointer<_VoidPtr, __node_type>::type,
 _NodePtr>::value), "_VoidPtr does not rebind to _NodePtr.");
};

template <class _ValueTp, class _VoidPtr>
struct __make_tree_node_types {
 typedef typename __rebind_pointer<_VoidPtr, __tree_node<_ValueTp, _VoidPtr> >::type
 _NodePtr;
 typedef __tree_node_types<_NodePtr> type;
};

// node

template <class _Pointer>
class __tree_end_node
{
public:
 typedef _Pointer pointer;
 pointer __left_;

 _LIBCPP_INLINE_VISIBILITY
 __tree_end_node() _NOEXCEPT : __left_() {}
};

template <class _VoidPtr>
class __tree_node_base
 : public __tree_node_base_types<_VoidPtr>::__end_node_type
{
 typedef __tree_node_base_types<_VoidPtr> _NodeBaseTypes;

public:
 typedef typename _NodeBaseTypes::__node_base_pointer pointer;
 typedef typename _NodeBaseTypes::__parent_pointer __parent_pointer;

 pointer __right_;
 __parent_pointer __parent_;
 bool __is_black_;

 _LIBCPP_INLINE_VISIBILITY
 pointer __parent_unsafe() const { return static_cast<pointer>(__parent_);}

 _LIBCPP_INLINE_VISIBILITY
 void __set_parent(pointer __p) {
 __parent_ = static_cast<__parent_pointer>(__p);
 }

private:
 ~__tree_node_base() _LIBCPP_EQUAL_DELETE;
 __tree_node_base(__tree_node_base const&) _LIBCPP_EQUAL_DELETE;
 __tree_node_base& operator=(__tree_node_base const&) _LIBCPP_EQUAL_DELETE;
};

template <class _Tp, class _VoidPtr>
class __tree_node
 : public __tree_node_base<_VoidPtr>
{
public:
 typedef _Tp __node_value_type;

 __node_value_type __value_;

private:
 ~__tree_node() _LIBCPP_EQUAL_DELETE;
 __tree_node(__tree_node const&) _LIBCPP_EQUAL_DELETE;
 __tree_node& operator=(__tree_node const&) _LIBCPP_EQUAL_DELETE;
};


template <class _Allocator>
class __tree_node_destructor
{
 typedef _Allocator allocator_type;
 typedef allocator_traits<allocator_type> __alloc_traits;

public:
 typedef typename __alloc_traits::pointer pointer;
private:
 typedef __tree_node_types<pointer> _NodeTypes;
 allocator_type& __na_;

 __tree_node_destructor& operator=(const __tree_node_destructor&);

public:
 bool __value_constructed;

 _LIBCPP_INLINE_VISIBILITY
 explicit __tree_node_destructor(allocator_type& __na, bool __val = false) _NOEXCEPT
 : __na_(__na),
 __value_constructed(__val)
 {}

 _LIBCPP_INLINE_VISIBILITY
 void operator()(pointer __p) _NOEXCEPT
 {
 if (__value_constructed)
 __alloc_traits::destroy(__na_, _NodeTypes::__get_ptr(__p->__value_));
 if (__p)
 __alloc_traits::deallocate(__na_, __p, 1);
 }

 template <class> friend class __map_node_destructor;
};


template <class _Tp, class _NodePtr, class _DiffType>
class _LIBCPP_TYPE_VIS_ONLY __tree_iterator
{
 typedef __tree_node_types<_NodePtr> _NodeTypes;
 typedef _NodePtr __node_pointer;
 typedef typename _NodeTypes::__node_base_pointer __node_base_pointer;
 typedef typename _NodeTypes::__end_node_pointer __end_node_pointer;
 typedef typename _NodeTypes::__iter_pointer __iter_pointer;
 typedef pointer_traits<__node_pointer> __pointer_traits;

 __iter_pointer __ptr_;

public:
 typedef bidirectional_iterator_tag iterator_category;
 typedef _Tp value_type;
 typedef _DiffType difference_type;
 typedef value_type& reference;
 typedef typename _NodeTypes::__node_value_type_pointer pointer;

 _LIBCPP_INLINE_VISIBILITY __tree_iterator() _NOEXCEPT
#if _LIBCPP_STD_VER > 11
 : __ptr_(nullptr)
#endif
 {}

 _LIBCPP_INLINE_VISIBILITY reference operator*() const
 {return __get_np()->__value_;}
 _LIBCPP_INLINE_VISIBILITY pointer operator->() const
 {return pointer_traits<pointer>::pointer_to(__get_np()->__value_);}

 _LIBCPP_INLINE_VISIBILITY
 __tree_iterator& operator++() {
 __ptr_ = static_cast<__iter_pointer>(
 __tree_next_iter<__end_node_pointer>(static_cast<__node_base_pointer>(__ptr_)));
 return *this;
 }
 _LIBCPP_INLINE_VISIBILITY
 __tree_iterator operator++(int)
 {__tree_iterator __t(*this); ++(*this); return __t;}

 _LIBCPP_INLINE_VISIBILITY
 __tree_iterator& operator--() {
 __ptr_ = static_cast<__iter_pointer>(__tree_prev_iter<__node_base_pointer>(
 static_cast<__end_node_pointer>(__ptr_)));
 return *this;
 }
 _LIBCPP_INLINE_VISIBILITY
 __tree_iterator operator--(int)
 {__tree_iterator __t(*this); --(*this); return __t;}

 friend _LIBCPP_INLINE_VISIBILITY 
 bool operator==(const __tree_iterator& __x, const __tree_iterator& __y)
 {return __x.__ptr_ == __y.__ptr_;}
 friend _LIBCPP_INLINE_VISIBILITY
 bool operator!=(const __tree_iterator& __x, const __tree_iterator& __y)
 {return !(__x == __y);}

private:
 _LIBCPP_INLINE_VISIBILITY
 explicit __tree_iterator(__node_pointer __p) _NOEXCEPT : __ptr_(__p) {}
 _LIBCPP_INLINE_VISIBILITY
 explicit __tree_iterator(__end_node_pointer __p) _NOEXCEPT : __ptr_(__p) {}
 _LIBCPP_INLINE_VISIBILITY
 __node_pointer __get_np() const { return static_cast<__node_pointer>(__ptr_); }
 template <class, class, class> friend class __tree;
 template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY __tree_const_iterator;
 template <class> friend class _LIBCPP_TYPE_VIS_ONLY __map_iterator;
 template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY map;
 template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multimap;
 template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY set;
 template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multiset;
};

template <class _Tp, class _NodePtr, class _DiffType>
class _LIBCPP_TYPE_VIS_ONLY __tree_const_iterator
{
 typedef __tree_node_types<_NodePtr> _NodeTypes;
 typedef typename _NodeTypes::__node_pointer __node_pointer;
 typedef typename _NodeTypes::__node_base_pointer __node_base_pointer;
 typedef typename _NodeTypes::__end_node_pointer __end_node_pointer;
 typedef typename _NodeTypes::__iter_pointer __iter_pointer;
 typedef pointer_traits<__node_pointer> __pointer_traits;

 __iter_pointer __ptr_;

public:
 typedef bidirectional_iterator_tag iterator_category;
 typedef _Tp value_type;
 typedef _DiffType difference_type;
 typedef const value_type& reference;
 typedef typename _NodeTypes::__const_node_value_type_pointer pointer;

 _LIBCPP_INLINE_VISIBILITY __tree_const_iterator() _NOEXCEPT
#if _LIBCPP_STD_VER > 11
 : __ptr_(nullptr)
#endif
 {}

private:
 typedef __tree_iterator<value_type, __node_pointer, difference_type>
 __non_const_iterator;
public:
 _LIBCPP_INLINE_VISIBILITY
 __tree_const_iterator(__non_const_iterator __p) _NOEXCEPT
 : __ptr_(__p.__ptr_) {}

 _LIBCPP_INLINE_VISIBILITY reference operator*() const
 {return __get_np()->__value_;}
 _LIBCPP_INLINE_VISIBILITY pointer operator->() const
 {return pointer_traits<pointer>::pointer_to(__get_np()->__value_);}

 _LIBCPP_INLINE_VISIBILITY
 __tree_const_iterator& operator++() {
 __ptr_ = static_cast<__iter_pointer>(
 __tree_next_iter<__end_node_pointer>(static_cast<__node_base_pointer>(__ptr_)));
 return *this;
 }

 _LIBCPP_INLINE_VISIBILITY
 __tree_const_iterator operator++(int)
 {__tree_const_iterator __t(*this); ++(*this); return __t;}

 _LIBCPP_INLINE_VISIBILITY
 __tree_const_iterator& operator--() {
 __ptr_ = static_cast<__iter_pointer>(__tree_prev_iter<__node_base_pointer>(
 static_cast<__end_node_pointer>(__ptr_)));
 return *this;
 }

 _LIBCPP_INLINE_VISIBILITY
 __tree_const_iterator operator--(int)
 {__tree_const_iterator __t(*this); --(*this); return __t;}

 friend _LIBCPP_INLINE_VISIBILITY
 bool operator==(const __tree_const_iterator& __x, const __tree_const_iterator& __y)
 {return __x.__ptr_ == __y.__ptr_;}
 friend _LIBCPP_INLINE_VISIBILITY
 bool operator!=(const __tree_const_iterator& __x, const __tree_const_iterator& __y)
 {return !(__x == __y);}

private:
 _LIBCPP_INLINE_VISIBILITY
 explicit __tree_const_iterator(__node_pointer __p) _NOEXCEPT
 : __ptr_(__p) {}
 _LIBCPP_INLINE_VISIBILITY
 explicit __tree_const_iterator(__end_node_pointer __p) _NOEXCEPT
 : __ptr_(__p) {}
 _LIBCPP_INLINE_VISIBILITY
 __node_pointer __get_np() const { return static_cast<__node_pointer>(__ptr_); }

 template <class, class, class> friend class __tree;
 template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY map;
 template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multimap;
 template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY set;
 template <class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multiset;
 template <class> friend class _LIBCPP_TYPE_VIS_ONLY __map_const_iterator;

};

template <class _Tp, class _Compare, class _Allocator>
class __tree
{
public:
 typedef _Tp value_type;
 typedef _Compare value_compare;
 typedef _Allocator allocator_type;

private:
 typedef allocator_traits<allocator_type> __alloc_traits;
 typedef typename __make_tree_node_types<value_type,
 typename __alloc_traits::void_pointer>::type
 _NodeTypes;
 typedef typename _NodeTypes::key_type key_type;
public:
 typedef typename _NodeTypes::__node_value_type __node_value_type;
 typedef typename _NodeTypes::__container_value_type __container_value_type;

 typedef typename __alloc_traits::pointer pointer;
 typedef typename __alloc_traits::const_pointer const_pointer;
 typedef typename __alloc_traits::size_type size_type;
 typedef typename __alloc_traits::difference_type difference_type;

public:
 typedef typename _NodeTypes::__void_pointer __void_pointer;

 typedef typename _NodeTypes::__node_type __node;
 typedef typename _NodeTypes::__node_pointer __node_pointer;

 typedef typename _NodeTypes::__node_base_type __node_base;
 typedef typename _NodeTypes::__node_base_pointer __node_base_pointer;

 typedef typename _NodeTypes::__end_node_type __end_node_t;
 typedef typename _NodeTypes::__end_node_pointer __end_node_ptr;

 typedef typename _NodeTypes::__parent_pointer __parent_pointer;
 typedef typename _NodeTypes::__iter_pointer __iter_pointer;

 typedef typename __rebind_alloc_helper<__alloc_traits, __node>::type __node_allocator;
 typedef allocator_traits<__node_allocator> __node_traits;

private:
 // check for sane allocator pointer rebinding semantics. Rebinding the
 // allocator for a new pointer type should be exactly the same as rebinding
 // the pointer using 'pointer_traits'.
 static_assert((is_same<__node_pointer, typename __node_traits::pointer>::value),
 "Allocator does not rebind pointers in a sane manner.");
 typedef typename __rebind_alloc_helper<__node_traits, __node_base>::type
 __node_base_allocator;
 typedef allocator_traits<__node_base_allocator> __node_base_traits;
 static_assert((is_same<__node_base_pointer, typename __node_base_traits::pointer>::value),
 "Allocator does not rebind pointers in a sane manner.");

private:
 __iter_pointer __begin_node_;
 __compressed_pair<__end_node_t, __node_allocator> __pair1_;
 __compressed_pair<size_type, value_compare> __pair3_;

public:
 _LIBCPP_INLINE_VISIBILITY
 __iter_pointer __end_node() _NOEXCEPT
 {
 return static_cast<__iter_pointer>(
 pointer_traits<__end_node_ptr>::pointer_to(__pair1_.first())
 );
 }
 _LIBCPP_INLINE_VISIBILITY
 __iter_pointer __end_node() const _NOEXCEPT
 {
 return static_cast<__iter_pointer>(
 pointer_traits<__end_node_ptr>::pointer_to(
 const_cast<__end_node_t&>(__pair1_.first())
 )
 );
 }
 _LIBCPP_INLINE_VISIBILITY
 __node_allocator& __node_alloc() _NOEXCEPT {return __pair1_.second();}
private:
 _LIBCPP_INLINE_VISIBILITY
 const __node_allocator& __node_alloc() const _NOEXCEPT
 {return __pair1_.second();}
 _LIBCPP_INLINE_VISIBILITY
 __iter_pointer& __begin_node() _NOEXCEPT {return __begin_node_;}
 _LIBCPP_INLINE_VISIBILITY
 const __iter_pointer& __begin_node() const _NOEXCEPT {return __begin_node_;}
public:
 _LIBCPP_INLINE_VISIBILITY
 allocator_type __alloc() const _NOEXCEPT
 {return allocator_type(__node_alloc());}
private:
 _LIBCPP_INLINE_VISIBILITY
 size_type& size() _NOEXCEPT {return __pair3_.first();}
public:
 _LIBCPP_INLINE_VISIBILITY
 const size_type& size() const _NOEXCEPT {return __pair3_.first();}
 _LIBCPP_INLINE_VISIBILITY
 value_compare& value_comp() _NOEXCEPT {return __pair3_.second();}
 _LIBCPP_INLINE_VISIBILITY
 const value_compare& value_comp() const _NOEXCEPT
 {return __pair3_.second();}
public:

 _LIBCPP_INLINE_VISIBILITY
 __node_pointer __root() const _NOEXCEPT
 {return static_cast<__node_pointer>(__end_node()->__left_);}

 __node_base_pointer* __root_ptr() const _NOEXCEPT {
 return _VSTD::addressof(__end_node()->__left_);
 }

 typedef __tree_iterator<value_type, __node_pointer, difference_type> iterator;
 typedef __tree_const_iterator<value_type, __node_pointer, difference_type> const_iterator;

 explicit __tree(const value_compare& __comp)
 _NOEXCEPT_(
 is_nothrow_default_constructible<__node_allocator>::value &&
 is_nothrow_copy_constructible<value_compare>::value);
 explicit __tree(const allocator_type& __a);
 __tree(const value_compare& __comp, const allocator_type& __a);
 __tree(const __tree& __t);
 __tree& operator=(const __tree& __t);
 template <class _InputIterator>
 void __assign_unique(_InputIterator __first, _InputIterator __last);
 template <class _InputIterator>
 void __assign_multi(_InputIterator __first, _InputIterator __last);
#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
 __tree(__tree&& __t)
 _NOEXCEPT_(
 is_nothrow_move_constructible<__node_allocator>::value &&
 is_nothrow_move_constructible<value_compare>::value);
 __tree(__tree&& __t, const allocator_type& __a);
 __tree& operator=(__tree&& __t)
 _NOEXCEPT_(
 __node_traits::propagate_on_container_move_assignment::value &&
 is_nothrow_move_assignable<value_compare>::value &&
 is_nothrow_move_assignable<__node_allocator>::value);
#endif // _LIBCPP_HAS_NO_RVALUE_REFERENCES

 ~__tree();

 _LIBCPP_INLINE_VISIBILITY
 iterator begin() _NOEXCEPT {return iterator(__begin_node());}
 _LIBCPP_INLINE_VISIBILITY
 const_iterator begin() const _NOEXCEPT {return const_iterator(__begin_node());}
 _LIBCPP_INLINE_VISIBILITY
 iterator end() _NOEXCEPT {return iterator(__end_node());}
 _LIBCPP_INLINE_VISIBILITY
 const_iterator end() const _NOEXCEPT {return const_iterator(__end_node());}

 _LIBCPP_INLINE_VISIBILITY
 size_type max_size() const _NOEXCEPT
 {return __node_traits::max_size(__node_alloc());}

 void clear() _NOEXCEPT;

 void swap(__tree& __t)
#if _LIBCPP_STD_VER <= 11
 _NOEXCEPT_(
 __is_nothrow_swappable<value_compare>::value
 && (!__node_traits::propagate_on_container_swap::value ||
 __is_nothrow_swappable<__node_allocator>::value)
 );
#else
 _NOEXCEPT_(__is_nothrow_swappable<value_compare>::value);
#endif

#ifndef _LIBCPP_CXX03_LANG
 template <class _Key, class ..._Args>
 pair<iterator, bool>
 __emplace_unique_key_args(_Key const&, _Args&&... __args);
 template <class _Key, class ..._Args>
 iterator
 __emplace_hint_unique_key_args(const_iterator, _Key const&, _Args&&...);

 template <class... _Args>
 pair<iterator, bool> __emplace_unique_impl(_Args&&... __args);

 template <class... _Args>
 iterator __emplace_hint_unique_impl(const_iterator __p, _Args&&... __args);

 template <class... _Args>
 iterator __emplace_multi(_Args&&... __args);

 template <class... _Args>
 iterator __emplace_hint_multi(const_iterator __p, _Args&&... __args);

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool> __emplace_unique(_Pp&& __x) {
 return __emplace_unique_extract_key(_VSTD::forward<_Pp>(__x),
 __can_extract_key<_Pp, key_type>());
 }

 template <class _First, class _Second>
 _LIBCPP_INLINE_VISIBILITY
 typename enable_if<
 __can_extract_map_key<_First, key_type, __container_value_type>::value,
 pair<iterator, bool>
 >::type __emplace_unique(_First&& __f, _Second&& __s) {
 return __emplace_unique_key_args(__f, _VSTD::forward<_First>(__f),
 _VSTD::forward<_Second>(__s));
 }

 template <class... _Args>
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool> __emplace_unique(_Args&&... __args) {
 return __emplace_unique_impl(_VSTD::forward<_Args>(__args)...);
 }

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool>
 __emplace_unique_extract_key(_Pp&& __x, __extract_key_fail_tag) {
 return __emplace_unique_impl(_VSTD::forward<_Pp>(__x));
 }

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool>
 __emplace_unique_extract_key(_Pp&& __x, __extract_key_self_tag) {
 return __emplace_unique_key_args(__x, _VSTD::forward<_Pp>(__x));
 }

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool>
 __emplace_unique_extract_key(_Pp&& __x, __extract_key_first_tag) {
 return __emplace_unique_key_args(__x.first, _VSTD::forward<_Pp>(__x));
 }

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 iterator __emplace_hint_unique(const_iterator __p, _Pp&& __x) {
 return __emplace_hint_unique_extract_key(__p, _VSTD::forward<_Pp>(__x),
 __can_extract_key<_Pp, key_type>());
 }

 template <class _First, class _Second>
 _LIBCPP_INLINE_VISIBILITY
 typename enable_if<
 __can_extract_map_key<_First, key_type, __container_value_type>::value,
 iterator
 >::type __emplace_hint_unique(const_iterator __p, _First&& __f, _Second&& __s) {
 return __emplace_hint_unique_key_args(__p, __f,
 _VSTD::forward<_First>(__f),
 _VSTD::forward<_Second>(__s));
 }

 template <class... _Args>
 _LIBCPP_INLINE_VISIBILITY
 iterator __emplace_hint_unique(const_iterator __p, _Args&&... __args) {
 return __emplace_hint_unique_impl(__p, _VSTD::forward<_Args>(__args)...);
 }

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 iterator
 __emplace_hint_unique_extract_key(const_iterator __p, _Pp&& __x, __extract_key_fail_tag) {
 return __emplace_hint_unique_impl(__p, _VSTD::forward<_Pp>(__x));
 }

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 iterator
 __emplace_hint_unique_extract_key(const_iterator __p, _Pp&& __x, __extract_key_self_tag) {
 return __emplace_hint_unique_key_args(__p, __x, _VSTD::forward<_Pp>(__x));
 }

 template <class _Pp>
 _LIBCPP_INLINE_VISIBILITY
 iterator
 __emplace_hint_unique_extract_key(const_iterator __p, _Pp&& __x, __extract_key_first_tag) {
 return __emplace_hint_unique_key_args(__p, __x.first, _VSTD::forward<_Pp>(__x));
 }

#else
 template <class _Key, class _Args>
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool> __emplace_unique_key_args(_Key const&, _Args& __args);
 template <class _Key, class _Args>
 _LIBCPP_INLINE_VISIBILITY
 iterator __emplace_hint_unique_key_args(const_iterator, _Key const&, _Args&);
#endif

 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool> __insert_unique(const __container_value_type& __v) {
 return __emplace_unique_key_args(_NodeTypes::__get_key(__v), __v);
 }

 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_unique(const_iterator __p, const __container_value_type& __v) {
 return __emplace_hint_unique_key_args(__p, _NodeTypes::__get_key(__v), __v);
 }

#ifdef _LIBCPP_CXX03_LANG
 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_multi(const __container_value_type& __v);
 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_multi(const_iterator __p, const __container_value_type& __v);
#else
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool> __insert_unique(__container_value_type&& __v) {
 return __emplace_unique_key_args(_NodeTypes::__get_key(__v), _VSTD::move(__v));
 }

 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_unique(const_iterator __p, __container_value_type&& __v) {
 return __emplace_hint_unique_key_args(__p, _NodeTypes::__get_key(__v), _VSTD::move(__v));
 }

 template <class _Vp, class = typename enable_if<
 !is_same<typename __unconstref<_Vp>::type,
 __container_value_type
 >::value
 >::type>
 _LIBCPP_INLINE_VISIBILITY
 pair<iterator, bool> __insert_unique(_Vp&& __v) {
 return __emplace_unique(_VSTD::forward<_Vp>(__v));
 }

 template <class _Vp, class = typename enable_if<
 !is_same<typename __unconstref<_Vp>::type,
 __container_value_type
 >::value
 >::type>
 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_unique(const_iterator __p, _Vp&& __v) {
 return __emplace_hint_unique(__p, _VSTD::forward<_Vp>(__v));
 }

 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_multi(__container_value_type&& __v) {
 return __emplace_multi(_VSTD::move(__v));
 }

 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_multi(const_iterator __p, __container_value_type&& __v) {
 return __emplace_hint_multi(__p, _VSTD::move(__v));
 }

 template <class _Vp>
 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_multi(_Vp&& __v) {
 return __emplace_multi(_VSTD::forward<_Vp>(__v));
 }

 template <class _Vp>
 _LIBCPP_INLINE_VISIBILITY
 iterator __insert_multi(const_iterator __p, _Vp&& __v) {
 return __emplace_hint_multi(__p, _VSTD::forward<_Vp>(__v));
 }

#endif // !_LIBCPP_CXX03_LANG

 pair<iterator, bool> __node_insert_unique(__node_pointer __nd);
 iterator __node_insert_unique(const_iterator __p,
 __node_pointer __nd);

 iterator __node_insert_multi(__node_pointer __nd);
 iterator __node_insert_multi(const_iterator __p, __node_pointer __nd);

 iterator erase(const_iterator __p);
 iterator erase(const_iterator __f, const_iterator __l);
 template <class _Key>
 size_type __erase_unique(const _Key& __k);
 template <class _Key>
 size_type __erase_multi(const _Key& __k);

 void __insert_node_at(__parent_pointer __parent,
 __node_base_pointer& __child,
 __node_base_pointer __new_node);

 template <class _Key>
 iterator find(const _Key& __v);
 template <class _Key>
 const_iterator find(const _Key& __v) const;

 template <class _Key>
 size_type __count_unique(const _Key& __k) const;
 template <class _Key>
 size_type __count_multi(const _Key& __k) const;

 template <class _Key>
 _LIBCPP_INLINE_VISIBILITY
 iterator lower_bound(const _Key& __v)
 {return __lower_bound(__v, __root(), __end_node());}
 template <class _Key>
 iterator __lower_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result);
 template <class _Key>
 _LIBCPP_INLINE_VISIBILITY
 const_iterator lower_bound(const _Key& __v) const
 {return __lower_bound(__v, __root(), __end_node());}
 template <class _Key>
 const_iterator __lower_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result) const;
 template <class _Key>
 _LIBCPP_INLINE_VISIBILITY
 iterator upper_bound(const _Key& __v)
 {return __upper_bound(__v, __root(), __end_node());}
 template <class _Key>
 iterator __upper_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result);
 template <class _Key>
 _LIBCPP_INLINE_VISIBILITY
 const_iterator upper_bound(const _Key& __v) const
 {return __upper_bound(__v, __root(), __end_node());}
 template <class _Key>
 const_iterator __upper_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result) const;
 template <class _Key>
 pair<iterator, iterator>
 __equal_range_unique(const _Key& __k);
 template <class _Key>
 pair<const_iterator, const_iterator>
 __equal_range_unique(const _Key& __k) const;

 template <class _Key>
 pair<iterator, iterator>
 __equal_range_multi(const _Key& __k);
 template <class _Key>
 pair<const_iterator, const_iterator>
 __equal_range_multi(const _Key& __k) const;

 typedef __tree_node_destructor<__node_allocator> _Dp;
 typedef unique_ptr<__node, _Dp> __node_holder;

 __node_holder remove(const_iterator __p) _NOEXCEPT;
private:
 __node_base_pointer&
 __find_leaf_low(__parent_pointer& __parent, const key_type& __v);
 __node_base_pointer&
 __find_leaf_high(__parent_pointer& __parent, const key_type& __v);
 __node_base_pointer&
 __find_leaf(const_iterator __hint,
 __parent_pointer& __parent, const key_type& __v);
 template <class _Key>
 __node_base_pointer&
 __find_equal(__parent_pointer& __parent, const _Key& __v);
 template <class _Key>
 __node_base_pointer&
 __find_equal(const_iterator __hint, __parent_pointer& __parent,
 __node_base_pointer& __dummy,
 const _Key& __v);

#ifndef _LIBCPP_CXX03_LANG
 template <class ..._Args>
 __node_holder __construct_node(_Args&& ...__args);
#else
 __node_holder __construct_node(const __container_value_type& __v);
#endif

 void destroy(__node_pointer __nd) _NOEXCEPT;

 _LIBCPP_INLINE_VISIBILITY
 void __copy_assign_alloc(const __tree& __t)
 {__copy_assign_alloc(__t, integral_constant<bool,
 __node_traits::propagate_on_container_copy_assignment::value>());}

 _LIBCPP_INLINE_VISIBILITY
 void __copy_assign_alloc(const __tree& __t, true_type)
 {
 if (__node_alloc() != __t.__node_alloc())
	clear();
 __node_alloc() = __t.__node_alloc();
 }
 _LIBCPP_INLINE_VISIBILITY
 void __copy_assign_alloc(const __tree& __t, false_type) {}

 void __move_assign(__tree& __t, false_type);
 void __move_assign(__tree& __t, true_type)
 _NOEXCEPT_(is_nothrow_move_assignable<value_compare>::value &&
 is_nothrow_move_assignable<__node_allocator>::value);

 _LIBCPP_INLINE_VISIBILITY
 void __move_assign_alloc(__tree& __t)
 _NOEXCEPT_(
 !__node_traits::propagate_on_container_move_assignment::value ||
 is_nothrow_move_assignable<__node_allocator>::value)
 {__move_assign_alloc(__t, integral_constant<bool,
 __node_traits::propagate_on_container_move_assignment::value>());}

 _LIBCPP_INLINE_VISIBILITY
 void __move_assign_alloc(__tree& __t, true_type)
 _NOEXCEPT_(is_nothrow_move_assignable<__node_allocator>::value)
 {__node_alloc() = _VSTD::move(__t.__node_alloc());}
 _LIBCPP_INLINE_VISIBILITY
 void __move_assign_alloc(__tree& __t, false_type) _NOEXCEPT {}

 __node_pointer __detach();
 static __node_pointer __detach(__node_pointer);

 template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY map;
 template <class, class, class, class> friend class _LIBCPP_TYPE_VIS_ONLY multimap;
};

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const value_compare& __comp)
 _NOEXCEPT_(
 is_nothrow_default_constructible<__node_allocator>::value &&
 is_nothrow_copy_constructible<value_compare>::value)
 : __pair3_(0, __comp)
{
 __begin_node() = __end_node();
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const allocator_type& __a)
 : __begin_node_(__iter_pointer()),
 __pair1_(__node_allocator(__a)),
 __pair3_(0)
{
 __begin_node() = __end_node();
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const value_compare& __comp,
 const allocator_type& __a)
 : __begin_node_(__iter_pointer()),
 __pair1_(__node_allocator(__a)),
 __pair3_(0, __comp)
{
 __begin_node() = __end_node();
}

// Precondition: size() != 0
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_pointer
__tree<_Tp, _Compare, _Allocator>::__detach()
{
 __node_pointer __cache = static_cast<__node_pointer>(__begin_node());
 __begin_node() = __end_node();
 __end_node()->__left_->__parent_ = nullptr;
 __end_node()->__left_ = nullptr;
 size() = 0;
 // __cache->__left_ == nullptr
 if (__cache->__right_ != nullptr)
 __cache = static_cast<__node_pointer>(__cache->__right_);
 // __cache->__left_ == nullptr
 // __cache->__right_ == nullptr
 return __cache;
}

// Precondition: __cache != nullptr
// __cache->left_ == nullptr
// __cache->right_ == nullptr
// This is no longer a red-black tree
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_pointer
__tree<_Tp, _Compare, _Allocator>::__detach(__node_pointer __cache)
{
 if (__cache->__parent_ == nullptr)
 return nullptr;
 if (__tree_is_left_child(static_cast<__node_base_pointer>(__cache)))
 {
 __cache->__parent_->__left_ = nullptr;
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 if (__cache->__right_ == nullptr)
 return __cache;
 return static_cast<__node_pointer>(__tree_leaf(__cache->__right_));
 }
 // __cache is right child
 __cache->__parent_unsafe()->__right_ = nullptr;
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 if (__cache->__left_ == nullptr)
 return __cache;
 return static_cast<__node_pointer>(__tree_leaf(__cache->__left_));
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>&
__tree<_Tp, _Compare, _Allocator>::operator=(const __tree& __t)
{
 if (this != &__t)
 {
 value_comp() = __t.value_comp();
 __copy_assign_alloc(__t);
 __assign_multi(__t.begin(), __t.end());
 }
 return *this;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _InputIterator>
void
__tree<_Tp, _Compare, _Allocator>::__assign_unique(_InputIterator __first, _InputIterator __last)
{
 typedef iterator_traits<_InputIterator> _ITraits;
 typedef typename _ITraits::value_type _ItValueType;
 static_assert((is_same<_ItValueType, __container_value_type>::value),
 "__assign_unique may only be called with the containers value type");

 if (size() != 0)
 {
 __node_pointer __cache = __detach();
#ifndef _LIBCPP_NO_EXCEPTIONS
 try
 {
#endif // _LIBCPP_NO_EXCEPTIONS
 for (; __cache != nullptr && __first != __last; ++__first)
 {
 __cache->__value_ = *__first;
 __node_pointer __next = __detach(__cache);
 __node_insert_unique(__cache);
 __cache = __next;
 }
#ifndef _LIBCPP_NO_EXCEPTIONS
 }
 catch (...)
 {
 while (__cache->__parent_ != nullptr)
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 destroy(__cache);
 throw;
 }
#endif // _LIBCPP_NO_EXCEPTIONS
 if (__cache != nullptr)
 {
 while (__cache->__parent_ != nullptr)
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 destroy(__cache);
 }
 }
 for (; __first != __last; ++__first)
 __insert_unique(*__first);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _InputIterator>
void
__tree<_Tp, _Compare, _Allocator>::__assign_multi(_InputIterator __first, _InputIterator __last)
{
 typedef iterator_traits<_InputIterator> _ITraits;
 typedef typename _ITraits::value_type _ItValueType;
 static_assert((is_same<_ItValueType, __container_value_type>::value ||
 is_same<_ItValueType, __node_value_type>::value),
 "__assign_multi may only be called with the containers value type"
 " or the nodes value type");
 if (size() != 0)
 {
 __node_pointer __cache = __detach();
#ifndef _LIBCPP_NO_EXCEPTIONS
 try
 {
#endif // _LIBCPP_NO_EXCEPTIONS
 for (; __cache != nullptr && __first != __last; ++__first)
 {
 __cache->__value_ = *__first;
 __node_pointer __next = __detach(__cache);
 __node_insert_multi(__cache);
 __cache = __next;
 }
#ifndef _LIBCPP_NO_EXCEPTIONS
 }
 catch (...)
 {
 while (__cache->__parent_ != nullptr)
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 destroy(__cache);
 throw;
 }
#endif // _LIBCPP_NO_EXCEPTIONS
 if (__cache != nullptr)
 {
 while (__cache->__parent_ != nullptr)
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 destroy(__cache);
 }
 }
 for (; __first != __last; ++__first)
 __insert_multi(_NodeTypes::__get_value(*__first));
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const __tree& __t)
 : __begin_node_(__iter_pointer()),
 __pair1_(__node_traits::select_on_container_copy_construction(__t.__node_alloc())),
 __pair3_(0, __t.value_comp())
{
 __begin_node() = __end_node();
}

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(__tree&& __t)
 _NOEXCEPT_(
 is_nothrow_move_constructible<__node_allocator>::value &&
 is_nothrow_move_constructible<value_compare>::value)
 : __begin_node_(_VSTD::move(__t.__begin_node_)),
 __pair1_(_VSTD::move(__t.__pair1_)),
 __pair3_(_VSTD::move(__t.__pair3_))
{
 if (size() == 0)
 __begin_node() = __end_node();
 else
 {
 __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
 __t.__begin_node() = __t.__end_node();
 __t.__end_node()->__left_ = nullptr;
 __t.size() = 0;
 }
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(__tree&& __t, const allocator_type& __a)
 : __pair1_(__node_allocator(__a)),
 __pair3_(0, _VSTD::move(__t.value_comp()))
{
 if (__a == __t.__alloc())
 {
 if (__t.size() == 0)
 __begin_node() = __end_node();
 else
 {
 __begin_node() = __t.__begin_node();
 __end_node()->__left_ = __t.__end_node()->__left_;
 __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
 size() = __t.size();
 __t.__begin_node() = __t.__end_node();
 __t.__end_node()->__left_ = nullptr;
 __t.size() = 0;
 }
 }
 else
 {
 __begin_node() = __end_node();
 }
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::__move_assign(__tree& __t, true_type)
 _NOEXCEPT_(is_nothrow_move_assignable<value_compare>::value &&
 is_nothrow_move_assignable<__node_allocator>::value)
{
 destroy(static_cast<__node_pointer>(__end_node()->__left_));
 __begin_node_ = __t.__begin_node_;
 __pair1_.first() = __t.__pair1_.first();
 __move_assign_alloc(__t);
 __pair3_ = _VSTD::move(__t.__pair3_);
 if (size() == 0)
 __begin_node() = __end_node();
 else
 {
 __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
 __t.__begin_node() = __t.__end_node();
 __t.__end_node()->__left_ = nullptr;
 __t.size() = 0;
 }
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::__move_assign(__tree& __t, false_type)
{
 if (__node_alloc() == __t.__node_alloc())
 __move_assign(__t, true_type());
 else
 {
 value_comp() = _VSTD::move(__t.value_comp());
 const_iterator __e = end();
 if (size() != 0)
 {
 __node_pointer __cache = __detach();
#ifndef _LIBCPP_NO_EXCEPTIONS
 try
 {
#endif // _LIBCPP_NO_EXCEPTIONS
 while (__cache != nullptr && __t.size() != 0)
 {
 __cache->__value_ = _VSTD::move(__t.remove(__t.begin())->__value_);
 __node_pointer __next = __detach(__cache);
 __node_insert_multi(__cache);
 __cache = __next;
 }
#ifndef _LIBCPP_NO_EXCEPTIONS
 }
 catch (...)
 {
 while (__cache->__parent_ != nullptr)
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 destroy(__cache);
 throw;
 }
#endif // _LIBCPP_NO_EXCEPTIONS
 if (__cache != nullptr)
 {
 while (__cache->__parent_ != nullptr)
 __cache = static_cast<__node_pointer>(__cache->__parent_);
 destroy(__cache);
 }
 }
 while (__t.size() != 0)
 __insert_multi(__e, _NodeTypes::__move(__t.remove(__t.begin())->__value_));
 }
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>&
__tree<_Tp, _Compare, _Allocator>::operator=(__tree&& __t)
 _NOEXCEPT_(
 __node_traits::propagate_on_container_move_assignment::value &&
 is_nothrow_move_assignable<value_compare>::value &&
 is_nothrow_move_assignable<__node_allocator>::value)
 
{
 __move_assign(__t, integral_constant<bool,
 __node_traits::propagate_on_container_move_assignment::value>());
 return *this;
}

#endif // _LIBCPP_HAS_NO_RVALUE_REFERENCES

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::~__tree()
{
 static_assert((is_copy_constructible<value_compare>::value),
 "Comparator must be copy-constructible.");
 destroy(__root());
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::destroy(__node_pointer __nd) _NOEXCEPT
{
 if (__nd != nullptr)
 {
 destroy(static_cast<__node_pointer>(__nd->__left_));
 destroy(static_cast<__node_pointer>(__nd->__right_));
 __node_allocator& __na = __node_alloc();
 __node_traits::destroy(__na, _NodeTypes::__get_ptr(__nd->__value_));
 __node_traits::deallocate(__na, __nd, 1);
 }
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::swap(__tree& __t)
#if _LIBCPP_STD_VER <= 11
 _NOEXCEPT_(
 __is_nothrow_swappable<value_compare>::value
 && (!__node_traits::propagate_on_container_swap::value ||
 __is_nothrow_swappable<__node_allocator>::value)
 )
#else
 _NOEXCEPT_(__is_nothrow_swappable<value_compare>::value)
#endif
{
 using _VSTD::swap;
 swap(__begin_node_, __t.__begin_node_);
 swap(__pair1_.first(), __t.__pair1_.first());
 __swap_allocator(__node_alloc(), __t.__node_alloc());
 __pair3_.swap(__t.__pair3_);
 if (size() == 0)
 __begin_node() = __end_node();
 else
 __end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__end_node());
 if (__t.size() == 0)
 __t.__begin_node() = __t.__end_node();
 else
 __t.__end_node()->__left_->__parent_ = static_cast<__parent_pointer>(__t.__end_node());
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::clear() _NOEXCEPT
{
 destroy(__root());
 size() = 0;
 __begin_node() = __end_node();
 __end_node()->__left_ = nullptr;
}

// Find lower_bound place to insert
// Set __parent to parent of null leaf
// Return reference to null leaf
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_leaf_low(__parent_pointer& __parent,
 const key_type& __v)
{
 __node_pointer __nd = __root();
 if (__nd != nullptr)
 {
 while (true)
 {
 if (value_comp()(__nd->__value_, __v))
 {
 if (__nd->__right_ != nullptr)
 __nd = static_cast<__node_pointer>(__nd->__right_);
 else
 {
 __parent = static_cast<__parent_pointer>(__nd);
 return __nd->__right_;
 }
 }
 else
 {
 if (__nd->__left_ != nullptr)
 __nd = static_cast<__node_pointer>(__nd->__left_);
 else
 {
 __parent = static_cast<__parent_pointer>(__nd);
 return __parent->__left_;
 }
 }
 }
 }
 __parent = static_cast<__parent_pointer>(__end_node());
 return __parent->__left_;
}

// Find upper_bound place to insert
// Set __parent to parent of null leaf
// Return reference to null leaf
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_leaf_high(__parent_pointer& __parent,
 const key_type& __v)
{
 __node_pointer __nd = __root();
 if (__nd != nullptr)
 {
 while (true)
 {
 if (value_comp()(__v, __nd->__value_))
 {
 if (__nd->__left_ != nullptr)
 __nd = static_cast<__node_pointer>(__nd->__left_);
 else
 {
 __parent = static_cast<__parent_pointer>(__nd);
 return __parent->__left_;
 }
 }
 else
 {
 if (__nd->__right_ != nullptr)
 __nd = static_cast<__node_pointer>(__nd->__right_);
 else
 {
 __parent = static_cast<__parent_pointer>(__nd);
 return __nd->__right_;
 }
 }
 }
 }
 __parent = static_cast<__parent_pointer>(__end_node());
 return __parent->__left_;
}

// Find leaf place to insert closest to __hint
// First check prior to __hint.
// Next check after __hint.
// Next do O(log N) search.
// Set __parent to parent of null leaf
// Return reference to null leaf
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_leaf(const_iterator __hint,
 __parent_pointer& __parent,
 const key_type& __v)
{
 if (__hint == end() || !value_comp()(*__hint, __v)) // check before
 {
 // __v <= *__hint
 const_iterator __prior = __hint;
 if (__prior == begin() || !value_comp()(__v, *--__prior))
 {
 // *prev(__hint) <= __v <= *__hint
 if (__hint.__ptr_->__left_ == nullptr)
 {
 __parent = static_cast<__parent_pointer>(__hint.__ptr_);
 return __parent->__left_;
 }
 else
 {
 __parent = static_cast<__parent_pointer>(__prior.__ptr_);
 return static_cast<__node_base_pointer>(__prior.__ptr_)->__right_;
 }
 }
 // __v < *prev(__hint)
 return __find_leaf_high(__parent, __v);
 }
 // else __v > *__hint
 return __find_leaf_low(__parent, __v);
}

// Find place to insert if __v doesn't exist
// Set __parent to parent of null leaf
// Return reference to null leaf
// If __v exists, set parent to node of __v and return reference to node of __v
template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_equal(__parent_pointer& __parent,
 const _Key& __v)
{
 __node_pointer __nd = __root();
 __node_base_pointer* __nd_ptr = __root_ptr();
 if (__nd != nullptr)
 {
 while (true)
 {
 if (value_comp()(__v, __nd->__value_))
 {
 if (__nd->__left_ != nullptr) {
 __nd_ptr = _VSTD::addressof(__nd->__left_);
 __nd = static_cast<__node_pointer>(__nd->__left_);
 } else {
 __parent = static_cast<__parent_pointer>(__nd);
 return __parent->__left_;
 }
 }
 else if (value_comp()(__nd->__value_, __v))
 {
 if (__nd->__right_ != nullptr) {
 __nd_ptr = _VSTD::addressof(__nd->__right_);
 __nd = static_cast<__node_pointer>(__nd->__right_);
 } else {
 __parent = static_cast<__parent_pointer>(__nd);
 return __nd->__right_;
 }
 }
 else
 {
 __parent = static_cast<__parent_pointer>(__nd);
 return *__nd_ptr;
 }
 }
 }
 __parent = static_cast<__parent_pointer>(__end_node());
 return __parent->__left_;
}

// Find place to insert if __v doesn't exist
// First check prior to __hint.
// Next check after __hint.
// Next do O(log N) search.
// Set __parent to parent of null leaf
// Return reference to null leaf
// If __v exists, set parent to node of __v and return reference to node of __v
template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::__node_base_pointer&
__tree<_Tp, _Compare, _Allocator>::__find_equal(const_iterator __hint,
 __parent_pointer& __parent,
 __node_base_pointer& __dummy,
 const _Key& __v)
{
 if (__hint == end() || value_comp()(__v, *__hint)) // check before
 {
 // __v < *__hint
 const_iterator __prior = __hint;
 if (__prior == begin() || value_comp()(*--__prior, __v))
 {
 // *prev(__hint) < __v < *__hint
 if (__hint.__ptr_->__left_ == nullptr)
 {
 __parent = static_cast<__parent_pointer>(__hint.__ptr_);
 return __parent->__left_;
 }
 else
 {
 __parent = static_cast<__parent_pointer>(__prior.__ptr_);
 return static_cast<__node_base_pointer>(__prior.__ptr_)->__right_;
 }
 }
 // __v <= *prev(__hint)
 return __find_equal(__parent, __v);
 }
 else if (value_comp()(*__hint, __v)) // check after
 {
 // *__hint < __v
 const_iterator __next = _VSTD::next(__hint);
 if (__next == end() || value_comp()(__v, *__next))
 {
 // *__hint < __v < *_VSTD::next(__hint)
 if (__hint.__get_np()->__right_ == nullptr)
 {
 __parent = static_cast<__parent_pointer>(__hint.__ptr_);
 return static_cast<__node_base_pointer>(__hint.__ptr_)->__right_;
 }
 else
 {
 __parent = static_cast<__parent_pointer>(__next.__ptr_);
 return __parent->__left_;
 }
 }
 // *next(__hint) <= __v
 return __find_equal(__parent, __v);
 }
 // else __v == *__hint
 __parent = static_cast<__parent_pointer>(__hint.__ptr_);
 __dummy = static_cast<__node_base_pointer>(__hint.__ptr_);
 return __dummy;
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::__insert_node_at(__parent_pointer __parent,
 __node_base_pointer& __child,
 __node_base_pointer __new_node)
{
 __new_node->__left_ = nullptr;
 __new_node->__right_ = nullptr;
 __new_node->__parent_ = __parent;
 // __new_node->__is_black_ is initialized in __tree_balance_after_insert
 __child = __new_node;
 if (__begin_node()->__left_ != nullptr)
 __begin_node() = static_cast<__iter_pointer>(__begin_node()->__left_);
 __tree_balance_after_insert(__end_node()->__left_, __child);
 ++size();
}

#ifndef _LIBCPP_CXX03_LANG
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class... _Args>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__emplace_unique_key_args(_Key const& __k, _Args&&... __args)
#else
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class _Args>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__emplace_unique_key_args(_Key const& __k, _Args& __args)
#endif
{
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_equal(__parent, __k);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 bool __inserted = false;
 if (__child == nullptr)
 {
#ifndef _LIBCPP_CXX03_LANG
 __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
#else
 __node_holder __h = __construct_node(__args);
#endif
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 __r = __h.release();
 __inserted = true;
 }
 return pair<iterator, bool>(iterator(__r), __inserted);
}


#ifndef _LIBCPP_CXX03_LANG
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_unique_key_args(
 const_iterator __p, _Key const& __k, _Args&&... __args)
#else
template <class _Tp, class _Compare, class _Allocator>
template <class _Key, class _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_unique_key_args(
 const_iterator __p, _Key const& __k, _Args& __args)
#endif
{
 __parent_pointer __parent;
 __node_base_pointer __dummy;
 __node_base_pointer& __child = __find_equal(__p, __parent, __dummy, __k);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 if (__child == nullptr)
 {
#ifndef _LIBCPP_CXX03_LANG
 __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
#else
 __node_holder __h = __construct_node(__args);
#endif
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 __r = __h.release();
 }
 return iterator(__r);
}


#ifndef _LIBCPP_CXX03_LANG

template <class _Tp, class _Compare, class _Allocator>
template <class ..._Args>
typename __tree<_Tp, _Compare, _Allocator>::__node_holder
__tree<_Tp, _Compare, _Allocator>::__construct_node(_Args&& ...__args)
{
 static_assert(!__is_tree_value_type<_Args...>::value,
 "Cannot construct from __value_type");
 __node_allocator& __na = __node_alloc();
 __node_holder __h(__node_traits::allocate(__na, 1), _Dp(__na));
 __node_traits::construct(__na, _NodeTypes::__get_ptr(__h->__value_), _VSTD::forward<_Args>(__args)...);
 __h.get_deleter().__value_constructed = true;
 return __h;
}


template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__emplace_unique_impl(_Args&&... __args)
{
 __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_equal(__parent, __h->__value_);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 bool __inserted = false;
 if (__child == nullptr)
 {
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 __r = __h.release();
 __inserted = true;
 }
 return pair<iterator, bool>(iterator(__r), __inserted);
}

template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_unique_impl(const_iterator __p, _Args&&... __args)
{
 __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
 __parent_pointer __parent;
 __node_base_pointer __dummy;
 __node_base_pointer& __child = __find_equal(__p, __parent, __dummy, __h->__value_);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 if (__child == nullptr)
 {
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 __r = __h.release();
 }
 return iterator(__r);
}

template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_multi(_Args&&... __args)
{
 __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_leaf_high(__parent, _NodeTypes::__get_key(__h->__value_));
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 return iterator(static_cast<__node_pointer>(__h.release()));
}

template <class _Tp, class _Compare, class _Allocator>
template <class... _Args>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__emplace_hint_multi(const_iterator __p,
 _Args&&... __args)
{
 __node_holder __h = __construct_node(_VSTD::forward<_Args>(__args)...);
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_leaf(__p, __parent, _NodeTypes::__get_key(__h->__value_));
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 return iterator(static_cast<__node_pointer>(__h.release()));
}


#else // _LIBCPP_CXX03_LANG

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_holder
__tree<_Tp, _Compare, _Allocator>::__construct_node(const __container_value_type& __v)
{
 __node_allocator& __na = __node_alloc();
 __node_holder __h(__node_traits::allocate(__na, 1), _Dp(__na));
 __node_traits::construct(__na, _NodeTypes::__get_ptr(__h->__value_), __v);
 __h.get_deleter().__value_constructed = true;
 return _LIBCPP_EXPLICIT_MOVE(__h); // explicitly moved for C++03
}

#endif // _LIBCPP_CXX03_LANG

#ifdef _LIBCPP_CXX03_LANG
template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_multi(const __container_value_type& __v)
{
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_leaf_high(__parent, _NodeTypes::__get_key(__v));
 __node_holder __h = __construct_node(__v);
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 return iterator(__h.release());
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_multi(const_iterator __p, const __container_value_type& __v)
{
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_leaf(__p, __parent, _NodeTypes::__get_key(__v));
 __node_holder __h = __construct_node(__v);
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__h.get()));
 return iterator(__h.release());
}
#endif

template <class _Tp, class _Compare, class _Allocator>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__node_insert_unique(__node_pointer __nd)
{
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_equal(__parent, __nd->__value_);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 bool __inserted = false;
 if (__child == nullptr)
 {
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__nd));
 __r = __nd;
 __inserted = true;
 }
 return pair<iterator, bool>(iterator(__r), __inserted);
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_insert_unique(const_iterator __p,
 __node_pointer __nd)
{
 __parent_pointer __parent;
 __node_base_pointer __dummy;
 __node_base_pointer& __child = __find_equal(__p, __parent, __nd->__value_);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 if (__child == nullptr)
 {
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__nd));
 __r = __nd;
 }
 return iterator(__r);
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_insert_multi(__node_pointer __nd)
{
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_leaf_high(__parent, _NodeTypes::__get_key(__nd->__value_));
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__nd));
 return iterator(__nd);
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__node_insert_multi(const_iterator __p,
 __node_pointer __nd)
{
 __parent_pointer __parent;
 __node_base_pointer& __child = __find_leaf(__p, __parent, _NodeTypes::__get_key(__nd->__value_));
 __insert_node_at(__parent, __child, static_cast<__node_base_pointer>(__nd));
 return iterator(__nd);
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::erase(const_iterator __p)
{
 __node_pointer __np = __p.__get_np();
 iterator __r(__p.__ptr_);
 ++__r;
 if (__begin_node() == __p.__ptr_)
 __begin_node() = __r.__ptr_;
 --size();
 __node_allocator& __na = __node_alloc();
 __tree_remove(__end_node()->__left_,
 static_cast<__node_base_pointer>(__np));
 __node_traits::destroy(__na, _NodeTypes::__get_ptr(
 const_cast<__node_value_type&>(*__p)));
 __node_traits::deallocate(__na, __np, 1);
 return __r;
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::erase(const_iterator __f, const_iterator __l)
{
 while (__f != __l)
 __f = erase(__f);
 return iterator(__l.__ptr_);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__erase_unique(const _Key& __k)
{
 iterator __i = find(__k);
 if (__i == end())
 return 0;
 erase(__i);
 return 1;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__erase_multi(const _Key& __k)
{
 pair<iterator, iterator> __p = __equal_range_multi(__k);
 size_type __r = 0;
 for (; __p.first != __p.second; ++__r)
 __p.first = erase(__p.first);
 return __r;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::find(const _Key& __v)
{
 iterator __p = __lower_bound(__v, __root(), __end_node());
 if (__p != end() && !value_comp()(__v, *__p))
 return __p;
 return end();
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::const_iterator
__tree<_Tp, _Compare, _Allocator>::find(const _Key& __v) const
{
 const_iterator __p = __lower_bound(__v, __root(), __end_node());
 if (__p != end() && !value_comp()(__v, *__p))
 return __p;
 return end();
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__count_unique(const _Key& __k) const
{
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return 1;
 }
 return 0;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::size_type
__tree<_Tp, _Compare, _Allocator>::__count_multi(const _Key& __k) const
{
 __iter_pointer __result = __end_node();
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = static_cast<__iter_pointer>(__rt);
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return _VSTD::distance(
 __lower_bound(__k, static_cast<__node_pointer>(__rt->__left_), static_cast<__iter_pointer>(__rt)),
 __upper_bound(__k, static_cast<__node_pointer>(__rt->__right_), __result)
 );
 }
 return 0;
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__lower_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result)
{
 while (__root != nullptr)
 {
 if (!value_comp()(__root->__value_, __v))
 {
 __result = static_cast<__iter_pointer>(__root);
 __root = static_cast<__node_pointer>(__root->__left_);
 }
 else
 __root = static_cast<__node_pointer>(__root->__right_);
 }
 return iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::const_iterator
__tree<_Tp, _Compare, _Allocator>::__lower_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result) const
{
 while (__root != nullptr)
 {
 if (!value_comp()(__root->__value_, __v))
 {
 __result = static_cast<__iter_pointer>(__root);
 __root = static_cast<__node_pointer>(__root->__left_);
 }
 else
 __root = static_cast<__node_pointer>(__root->__right_);
 }
 return const_iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__upper_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result)
{
 while (__root != nullptr)
 {
 if (value_comp()(__v, __root->__value_))
 {
 __result = static_cast<__iter_pointer>(__root);
 __root = static_cast<__node_pointer>(__root->__left_);
 }
 else
 __root = static_cast<__node_pointer>(__root->__right_);
 }
 return iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
typename __tree<_Tp, _Compare, _Allocator>::const_iterator
__tree<_Tp, _Compare, _Allocator>::__upper_bound(const _Key& __v,
 __node_pointer __root,
 __iter_pointer __result) const
{
 while (__root != nullptr)
 {
 if (value_comp()(__v, __root->__value_))
 {
 __result = static_cast<__iter_pointer>(__root);
 __root = static_cast<__node_pointer>(__root->__left_);
 }
 else
 __root = static_cast<__node_pointer>(__root->__right_);
 }
 return const_iterator(__result);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator,
 typename __tree<_Tp, _Compare, _Allocator>::iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_unique(const _Key& __k)
{
 typedef pair<iterator, iterator> _Pp;
 __iter_pointer __result = __end_node();
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = static_cast<__iter_pointer>(__rt);
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return _Pp(iterator(__rt),
 iterator(
 __rt->__right_ != nullptr ?
 static_cast<__iter_pointer>(__tree_min(__rt->__right_))
 : __result));
 }
 return _Pp(iterator(__result), iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::const_iterator,
 typename __tree<_Tp, _Compare, _Allocator>::const_iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_unique(const _Key& __k) const
{
 typedef pair<const_iterator, const_iterator> _Pp;
 __iter_pointer __result = __end_node();
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = static_cast<__iter_pointer>(__rt);
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return _Pp(const_iterator(__rt),
 const_iterator(
 __rt->__right_ != nullptr ?
 static_cast<__iter_pointer>(__tree_min(__rt->__right_))
 : __result));
 }
 return _Pp(const_iterator(__result), const_iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator,
 typename __tree<_Tp, _Compare, _Allocator>::iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_multi(const _Key& __k)
{
 typedef pair<iterator, iterator> _Pp;
 __iter_pointer __result = __end_node();
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = static_cast<__iter_pointer>(__rt);
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return _Pp(__lower_bound(__k, static_cast<__node_pointer>(__rt->__left_), static_cast<__iter_pointer>(__rt)),
 __upper_bound(__k, static_cast<__node_pointer>(__rt->__right_), __result));
 }
 return _Pp(iterator(__result), iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
template <class _Key>
pair<typename __tree<_Tp, _Compare, _Allocator>::const_iterator,
 typename __tree<_Tp, _Compare, _Allocator>::const_iterator>
__tree<_Tp, _Compare, _Allocator>::__equal_range_multi(const _Key& __k) const
{
 typedef pair<const_iterator, const_iterator> _Pp;
 __iter_pointer __result = __end_node();
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = static_cast<__iter_pointer>(__rt);
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return _Pp(__lower_bound(__k, static_cast<__node_pointer>(__rt->__left_), static_cast<__iter_pointer>(__rt)),
 __upper_bound(__k, static_cast<__node_pointer>(__rt->__right_), __result));
 }
 return _Pp(const_iterator(__result), const_iterator(__result));
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_holder
__tree<_Tp, _Compare, _Allocator>::remove(const_iterator __p) _NOEXCEPT
{
 __node_pointer __np = __p.__get_np();
 if (__begin_node() == __p.__ptr_)
 {
 if (__np->__right_ != nullptr)
 __begin_node() = static_cast<__iter_pointer>(__np->__right_);
 else
 __begin_node() = static_cast<__iter_pointer>(__np->__parent_);
 }
 --size();
 __tree_remove(__end_node()->__left_,
 static_cast<__node_base_pointer>(__np));
 return __node_holder(__np, _Dp(__node_alloc(), true));
}

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

_LIBCPP_END_NAMESPACE_STD

#endif // _LIBCPP___TREE