include/__tree

// -*- C++ -*-
//===----------------------------------------------------------------------===//
//
// The LLVM Compiler Infrastructure
//
// This file is distributed under the University of Illinois Open Source
// License. See LICENSE.TXT for details.
//
//===----------------------------------------------------------------------===//

#ifndef _LIBCPP___TREE
#define _LIBCPP___TREE

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

#pragma GCC system_header

_LIBCPP_BEGIN_NAMESPACE_STD

template <class, class, class> class __tree;
template <class, class, class> class _LIBCPP_VISIBLE __tree_iterator;
template <class, class, class> class _LIBCPP_VISIBLE __tree_const_iterator;
template <class, class, class, class> class _LIBCPP_VISIBLE map;
template <class, class, class, class> class _LIBCPP_VISIBLE multimap;
template <class, class, class> class _LIBCPP_VISIBLE set;
template <class, class, class> class _LIBCPP_VISIBLE multiset;

/*

_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)
{
 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)
{
 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)
{
 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)
{
 if (__x->__right_ != nullptr)
 return __tree_min(__x->__right_);
 while (!__tree_is_left_child(__x))
 __x = __x->__parent_;
 return __x->__parent_;
}

// Returns: pointer to the previous in-order node before __x.
// Precondition: __x != nullptr.
template <class _NodePtr>
_NodePtr
__tree_prev(_NodePtr __x)
{
 if (__x->__left_ != nullptr)
 return __tree_max(__x->__left_);
 while (__tree_is_left_child(__x))
 __x = __x->__parent_;
 return __x->__parent_;
}

// Returns: pointer to a node which has no children
// Precondition: __x != nullptr.
template <class _NodePtr>
_NodePtr
__tree_leaf(_NodePtr __x)
{
 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)
{
 _NodePtr __y = __x->__right_;
 __x->__right_ = __y->__left_;
 if (__x->__right_ != nullptr)
 __x->__right_->__parent_ = __x;
 __y->__parent_ = __x->__parent_;
 if (__tree_is_left_child(__x))
 __x->__parent_->__left_ = __y;
 else
 __x->__parent_->__right_ = __y;
 __y->__left_ = __x;
 __x->__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)
{
 _NodePtr __y = __x->__left_;
 __x->__left_ = __y->__right_;
 if (__x->__left_ != nullptr)
 __x->__left_->__parent_ = __x;
 __y->__parent_ = __x->__parent_;
 if (__tree_is_left_child(__x))
 __x->__parent_->__left_ = __y;
 else
 __x->__parent_->__right_ = __y;
 __y->__right_ = __x;
 __x->__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)
{
 __x->__is_black_ = __x == __root;
 while (__x != __root && !__x->__parent_->__is_black_)
 {
 // __x->__parent_ != __root because __x->__parent_->__is_black == false
 if (__tree_is_left_child(__x->__parent_))
 {
 _NodePtr __y = __x->__parent_->__parent_->__right_;
 if (__y != nullptr && !__y->__is_black_)
 {
 __x = __x->__parent_;
 __x->__is_black_ = true;
 __x = __x->__parent_;
 __x->__is_black_ = __x == __root;
 __y->__is_black_ = true;
 }
 else
 {
 if (!__tree_is_left_child(__x))
 {
 __x = __x->__parent_;
 __tree_left_rotate(__x);
 }
 __x = __x->__parent_;
 __x->__is_black_ = true;
 __x = __x->__parent_;
 __x->__is_black_ = false;
 __tree_right_rotate(__x);
 break;
 }
 }
 else
 {
 _NodePtr __y = __x->__parent_->__parent_->__left_;
 if (__y != nullptr && !__y->__is_black_)
 {
 __x = __x->__parent_;
 __x->__is_black_ = true;
 __x = __x->__parent_;
 __x->__is_black_ = __x == __root;
 __y->__is_black_ = true;
 }
 else
 {
 if (__tree_is_left_child(__x))
 {
 __x = __x->__parent_;
 __tree_right_rotate(__x);
 }
 __x = __x->__parent_;
 __x->__is_black_ = true;
 __x = __x->__parent_;
 __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)
{
 // __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_->__right_;
 else
 __root = __x; // __w == nullptr
 }
 else
 {
 __y->__parent_->__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_->__right_ = __y;
 __y->__left_ = __z->__left_;
 __y->__left_->__parent_ = __y;
 __y->__right_ = __z->__right_;
 if (__y->__right_ != nullptr)
 __y->__right_->__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_->__is_black_ = false;
 __tree_left_rotate(__w->__parent_);
 // __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_;
 // __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_->__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_;
 }
 // __w has a right red child, left child may be null
 __w->__is_black_ = __w->__parent_->__is_black_;
 __w->__parent_->__is_black_ = true;
 __w->__right_->__is_black_ = true;
 __tree_left_rotate(__w->__parent_);
 break;
 }
 }
 else
 {
 if (!__w->__is_black_)
 {
 __w->__is_black_ = true;
 __w->__parent_->__is_black_ = false;
 __tree_right_rotate(__w->__parent_);
 // __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_;
 // __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_->__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_;
 }
 // __w has a left red child, right child may be null
 __w->__is_black_ = __w->__parent_->__is_black_;
 __w->__parent_->__is_black_ = true;
 __w->__left_->__is_black_ = true;
 __tree_right_rotate(__w->__parent_);
 break;
 }
 }
 }
 }
 }
}

template <class> class __map_node_destructor;

template <class _Allocator>
class __tree_node_destructor
{
 typedef _Allocator allocator_type;
 typedef allocator_traits<allocator_type> __alloc_traits;
 typedef typename __alloc_traits::value_type::value_type value_type;
public:
 typedef typename __alloc_traits::pointer pointer;
private:

 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)
 : __na_(__na),
 __value_constructed(false)
 {}

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

 template <class> friend class __map_node_destructor;
};

// node

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

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

template <class _VoidPtr>
class __tree_node_base
 : public __tree_end_node
 <
 typename pointer_traits<_VoidPtr>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<__tree_node_base<_VoidPtr> >
#else
 rebind<__tree_node_base<_VoidPtr> >::other
#endif
 >
{
 __tree_node_base(const __tree_node_base&);
 __tree_node_base& operator=(const __tree_node_base&);
public:
 typedef typename pointer_traits<_VoidPtr>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<__tree_node_base>
#else
 rebind<__tree_node_base>::other
#endif
 pointer;
 typedef typename pointer_traits<_VoidPtr>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<const __tree_node_base>
#else
 rebind<const __tree_node_base>::other
#endif
 const_pointer;
 typedef __tree_end_node<pointer> base;

 pointer __right_;
 pointer __parent_;
 bool __is_black_;

 _LIBCPP_INLINE_VISIBILITY
 __tree_node_base() : __right_(), __parent_(), __is_black_(false) {}
};

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

 value_type __value_;

#if !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
 template <class ..._Args>
 _LIBCPP_INLINE_VISIBILITY
 explicit __tree_node(_Args&& ...__args)
 : __value_(_STD::forward<_Args>(__args)...) {}
#else // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
 _LIBCPP_INLINE_VISIBILITY
 explicit __tree_node(const value_type& __v)
 : __value_(__v) {}
#endif // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
};

template <class> class __map_iterator;
template <class> class __map_const_iterator;

template <class _Tp, class _NodePtr, class _DiffType>
class _LIBCPP_VISIBLE __tree_iterator
{
 typedef _NodePtr __node_pointer;
 typedef typename pointer_traits<__node_pointer>::element_type __node;
 typedef typename __node::base __node_base;
 typedef typename __node_base::pointer __node_base_pointer;

 __node_pointer __ptr_;

 typedef pointer_traits<__node_pointer> __pointer_traits;
public:
 typedef bidirectional_iterator_tag iterator_category;
 typedef _Tp value_type;
 typedef _DiffType difference_type;
 typedef value_type& reference;
 typedef typename pointer_traits<__node_pointer>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<value_type>
#else
 rebind<value_type>::other
#endif
 pointer;

 _LIBCPP_INLINE_VISIBILITY __tree_iterator() {}

 _LIBCPP_INLINE_VISIBILITY reference operator*() const {return __ptr_->__value_;}
 _LIBCPP_INLINE_VISIBILITY pointer operator->() const {return &__ptr_->__value_;}

 _LIBCPP_INLINE_VISIBILITY
 __tree_iterator& operator++()
 {__ptr_ = static_cast<__node_pointer>(__tree_next(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<__node_pointer>(__tree_prev(static_cast<__node_base_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) : __ptr_(__p) {}
 template <class, class, class> friend class __tree;
 template <class, class, class> friend class _LIBCPP_VISIBLE __tree_const_iterator;
 template <class> friend class _LIBCPP_VISIBLE __map_iterator;
 template <class, class, class, class> friend class _LIBCPP_VISIBLE map;
 template <class, class, class, class> friend class _LIBCPP_VISIBLE multimap;
 template <class, class, class> friend class _LIBCPP_VISIBLE set;
 template <class, class, class> friend class _LIBCPP_VISIBLE multiset;
};

template <class _Tp, class _ConstNodePtr, class _DiffType>
class _LIBCPP_VISIBLE __tree_const_iterator
{
 typedef _ConstNodePtr __node_pointer;
 typedef typename pointer_traits<__node_pointer>::element_type __node;
 typedef const typename __node::base __node_base;
 typedef typename pointer_traits<__node_pointer>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<__node_base>
#else
 rebind<__node_base>::other
#endif
 __node_base_pointer;

 __node_pointer __ptr_;

 typedef pointer_traits<__node_pointer> __pointer_traits;
public:
 typedef bidirectional_iterator_tag iterator_category;
 typedef _Tp value_type;
 typedef _DiffType difference_type;
 typedef const value_type& reference;
 typedef typename pointer_traits<__node_pointer>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<const value_type>
#else
 rebind<const value_type>::other
#endif
 pointer;

 _LIBCPP_INLINE_VISIBILITY __tree_const_iterator() {}
private:
 typedef typename remove_const<__node>::type __non_const_node;
 typedef typename pointer_traits<__node_pointer>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<__non_const_node>
#else
 rebind<__non_const_node>::other
#endif
 __non_const_node_pointer;
 typedef __tree_iterator<value_type, __non_const_node_pointer, difference_type>
 __non_const_iterator;
public:
 _LIBCPP_INLINE_VISIBILITY
 __tree_const_iterator(__non_const_iterator __p) : __ptr_(__p.__ptr_) {}

 _LIBCPP_INLINE_VISIBILITY reference operator*() const {return __ptr_->__value_;}
 _LIBCPP_INLINE_VISIBILITY pointer operator->() const {return &__ptr_->__value_;}

 _LIBCPP_INLINE_VISIBILITY
 __tree_const_iterator& operator++()
 {__ptr_ = static_cast<__node_pointer>(__tree_next(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<__node_pointer>(__tree_prev(static_cast<__node_base_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) : __ptr_(__p) {}
 template <class, class, class> friend class __tree;
 template <class, class, class, class> friend class _LIBCPP_VISIBLE map;
 template <class, class, class, class> friend class _LIBCPP_VISIBLE multimap;
 template <class, class, class> friend class _LIBCPP_VISIBLE set;
 template <class, class, class> friend class _LIBCPP_VISIBLE multiset;
 template <class> friend class _LIBCPP_VISIBLE __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;
 typedef allocator_traits<allocator_type> __alloc_traits;
 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;

 typedef __tree_node<value_type, typename __alloc_traits::void_pointer> __node;
 typedef typename __alloc_traits::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind_alloc<__node>
#else
 rebind_alloc<__node>::other
#endif
 __node_allocator;
 typedef allocator_traits<__node_allocator> __node_traits;
 typedef typename __node_traits::pointer __node_pointer;
 typedef typename __node_traits::const_pointer __node_const_pointer;
 typedef typename __node::base::pointer __node_base_pointer;
 typedef typename __node::base::const_pointer __node_base_const_pointer;
private:
 typedef typename __node::base::base __end_node_t;
 typedef typename pointer_traits<__node_pointer>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<__end_node_t>
#else
 rebind<__end_node_t>::other
#endif
 __end_node_ptr;
 typedef typename pointer_traits<__node_pointer>::template
#ifndef _LIBCPP_HAS_NO_TEMPLATE_ALIASES
 rebind<const __end_node_t>
#else
 rebind<const __end_node_t>::other
#endif
 __end_node_const_ptr;

 __node_pointer __begin_node_;
 __compressed_pair<__end_node_t, __node_allocator> __pair1_;
 __compressed_pair<size_type, value_compare> __pair3_;

public:
 _LIBCPP_INLINE_VISIBILITY
 __node_pointer __end_node()
 {
 return static_cast<__node_pointer>
 (
 pointer_traits<__end_node_ptr>::pointer_to(__pair1_.first())
 );
 }
 _LIBCPP_INLINE_VISIBILITY
 __node_const_pointer __end_node() const
 {
 return static_cast<__node_const_pointer>
 (
 pointer_traits<__end_node_const_ptr>::pointer_to(__pair1_.first())
 );
 }
 _LIBCPP_INLINE_VISIBILITY
 __node_allocator& __node_alloc() {return __pair1_.second();}
private:
 _LIBCPP_INLINE_VISIBILITY
 const __node_allocator& __node_alloc() const {return __pair1_.second();}
 _LIBCPP_INLINE_VISIBILITY
 __node_pointer& __begin_node() {return __begin_node_;}
 _LIBCPP_INLINE_VISIBILITY
 const __node_pointer& __begin_node() const {return __begin_node_;}
public:
 _LIBCPP_INLINE_VISIBILITY
 allocator_type __alloc() const {return allocator_type(__node_alloc());}
private:
 _LIBCPP_INLINE_VISIBILITY
 size_type& size() {return __pair3_.first();}
public:
 _LIBCPP_INLINE_VISIBILITY
 const size_type& size() const {return __pair3_.first();}
 _LIBCPP_INLINE_VISIBILITY
 value_compare& value_comp() {return __pair3_.second();}
 _LIBCPP_INLINE_VISIBILITY
 const value_compare& value_comp() const {return __pair3_.second();}
public:
 _LIBCPP_INLINE_VISIBILITY
 __node_pointer __root()
 {return static_cast<__node_pointer> (__end_node()->__left_);}
 _LIBCPP_INLINE_VISIBILITY
 __node_const_pointer __root() const
 {return static_cast<__node_const_pointer>(__end_node()->__left_);}

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

 explicit __tree(const value_compare& __comp);
 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);
 __tree(__tree&& __t, const allocator_type& __a);
 __tree& operator=(__tree&& __t);
#endif // _LIBCPP_HAS_NO_RVALUE_REFERENCES

 ~__tree();

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

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

 void clear();

 void swap(__tree& __t);

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
#ifndef _LIBCPP_HAS_NO_VARIADICS
 template <class... _Args>
 pair<iterator, bool>
 __emplace_unique(_Args&&... __args);
 template <class... _Args>
 iterator
 __emplace_multi(_Args&&... __args);

 template <class... _Args>
 iterator
 __emplace_hint_unique(const_iterator __p, _Args&&... __args);
 template <class... _Args>
 iterator
 __emplace_hint_multi(const_iterator __p, _Args&&... __args);
#endif // _LIBCPP_HAS_NO_VARIADICS

 template <class _V>
 pair<iterator, bool> __insert_unique(_V&& __v);
 template <class _V>
 iterator __insert_unique(const_iterator __p, _V&& __v);
 template <class _V>
 iterator __insert_multi(_V&& __v);
 template <class _V>
 iterator __insert_multi(const_iterator __p, _V&& __v);
#else // _LIBCPP_HAS_NO_RVALUE_REFERENCES

 pair<iterator, bool> __insert_unique(const value_type& __v);
 iterator __insert_unique(const_iterator __p, const value_type& __v);
 iterator __insert_multi(const value_type& __v);
 iterator __insert_multi(const_iterator __p, const value_type& __v);
#endif // _LIBCPP_HAS_NO_RVALUE_REFERENCES

 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(__node_base_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,
 __node_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_const_pointer __root,
 __node_const_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,
 __node_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_const_pointer __root,
 __node_const_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> _D;
 typedef unique_ptr<__node, _D> __node_holder;

 __node_holder remove(const_iterator __p);
private:
 typename __node::base::pointer&
 __find_leaf_low(typename __node::base::pointer& __parent, const value_type& __v);
 typename __node::base::pointer&
 __find_leaf_high(typename __node::base::pointer& __parent, const value_type& __v);
 typename __node::base::pointer&
 __find_leaf(const_iterator __hint,
 typename __node::base::pointer& __parent, const value_type& __v);
 template <class _Key>
 typename __node::base::pointer&
 __find_equal(typename __node::base::pointer& __parent, const _Key& __v);
 template <class _Key>
 typename __node::base::pointer&
 __find_equal(const_iterator __hint, typename __node::base::pointer& __parent,
 const _Key& __v);

#if !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
 template <class ..._Args>
 __node_holder __construct_node(_Args&& ...__args);
#else // !defined(_LIBCPP_HAS_NO_RVALUE_REFERENCES) && !defined(_LIBCPP_HAS_NO_VARIADICS)
 __node_holder __construct_node(const value_type& __v);
#endif

 void destroy(__node_pointer __nd);

 _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)
 {__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);

 _LIBCPP_INLINE_VISIBILITY
 void __move_assign_alloc(__tree& __t)
 {__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)
 {__node_alloc() = _STD::move(__t.__node_alloc());}
 _LIBCPP_INLINE_VISIBILITY
 void __move_assign_alloc(__tree& __t, false_type) {}

 _LIBCPP_INLINE_VISIBILITY
 static void __swap_alloc(__node_allocator& __x, __node_allocator& __y)
 {__swap_alloc(__x, __y, integral_constant<bool,
 __node_traits::propagate_on_container_swap::value>());}
 _LIBCPP_INLINE_VISIBILITY
 static void __swap_alloc(__node_allocator& __x, __node_allocator& __y, true_type)
 {
 using _STD::swap;
 swap(__x, __y);
 }
 _LIBCPP_INLINE_VISIBILITY
 static void __swap_alloc(__node_allocator& __x, __node_allocator& __y, false_type)
 {}

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

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

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const allocator_type& __a)
 : __pair1_(__node_allocator(__a)),
 __begin_node_(__node_pointer()),
 __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)
 : __pair1_(__node_allocator(__a)),
 __begin_node_(__node_pointer()),
 __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 = __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(__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_->__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)
{
 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)
{
 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(*__first);
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>::__tree(const __tree& __t)
 : __begin_node_(__node_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)
 : __begin_node_(_STD::move(__t.__begin_node_)),
 __pair1_(_STD::move(__t.__pair1_)),
 __pair3_(_STD::move(__t.__pair3_))
{
 if (size() == 0)
 __begin_node() = __end_node();
 else
 {
 __end_node()->__left_->__parent_ = __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, _STD::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_ = __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)
{
 destroy(static_cast<__node_pointer>(__end_node()->__left_));
 __begin_node_ = __t.__begin_node_;
 __pair1_.first() = __t.__pair1_.first();
 __move_assign_alloc(__t);
 __pair3_ = _STD::move(__t.__pair3_);
 if (size() == 0)
 __begin_node() = __end_node();
 else
 {
 __end_node()->__left_->__parent_ = __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() = _STD::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_ = _STD::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, _STD::move(__t.remove(__t.begin())->__value_));
 }
}

template <class _Tp, class _Compare, class _Allocator>
__tree<_Tp, _Compare, _Allocator>&
__tree<_Tp, _Compare, _Allocator>::operator=(__tree&& __t)
{
 __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()
{
 destroy(__root());
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::destroy(__node_pointer __nd)
{
 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, addressof(__nd->__value_));
 __node_traits::deallocate(__na, __nd, 1);
 }
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::swap(__tree& __t)
{
 using _STD::swap;
 swap(__begin_node_, __t.__begin_node_);
 swap(__pair1_.first(), __t.__pair1_.first());
 __swap_alloc(__node_alloc(), __t.__node_alloc());
 __pair3_.swap(__t.__pair3_);
 if (size() == 0)
 __begin_node() = __end_node();
 else
 __end_node()->__left_->__parent_ = __end_node();
 if (__t.size() == 0)
 __t.__begin_node() = __t.__end_node();
 else
 __t.__end_node()->__left_->__parent_ = __t.__end_node();
}

template <class _Tp, class _Compare, class _Allocator>
void
__tree<_Tp, _Compare, _Allocator>::clear()
{
 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(typename __node::base::pointer& __parent,
 const value_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 = __nd;
 return __parent->__right_;
 }
 }
 else
 {
 if (__nd->__left_ != nullptr)
 __nd = static_cast<__node_pointer>(__nd->__left_);
 else
 {
 __parent = __nd;
 return __parent->__left_;
 }
 }
 }
 }
 __parent = __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(typename __node::base::pointer& __parent,
 const value_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 = __nd;
 return __parent->__left_;
 }
 }
 else
 {
 if (__nd->__right_ != nullptr)
 __nd = static_cast<__node_pointer>(__nd->__right_);
 else
 {
 __parent = __nd;
 return __parent->__right_;
 }
 }
 }
 }
 __parent = __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,
 typename __node::base::pointer& __parent,
 const value_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 = const_cast<__node_pointer&>(__hint.__ptr_);
 return __parent->__left_;
 }
 else
 {
 __parent = const_cast<__node_pointer&>(__prior.__ptr_);
 return __parent->__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(typename __node::base::pointer& __parent,
 const _Key& __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 = __nd;
 return __parent->__left_;
 }
 }
 else if (value_comp()(__nd->__value_, __v))
 {
 if (__nd->__right_ != nullptr)
 __nd = static_cast<__node_pointer>(__nd->__right_);
 else
 {
 __parent = __nd;
 return __parent->__right_;
 }
 }
 else
 {
 __parent = __nd;
 return __parent;
 }
 }
 }
 __parent = __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,
 typename __node::base::pointer& __parent,
 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 = const_cast<__node_pointer&>(__hint.__ptr_);
 return __parent->__left_;
 }
 else
 {
 __parent = const_cast<__node_pointer&>(__prior.__ptr_);
 return __parent->__right_;
 }
 }
 // __v <= *prev(__hint)
 return __find_equal(__parent, __v);
 }
 else if (value_comp()(*__hint, __v)) // check after
 {
 // *__hint < __v
 const_iterator __next = _STD::next(__hint);
 if (__next == end() || value_comp()(__v, *__next))
 {
 // *__hint < __v < *next(__hint)
 if (__hint.__ptr_->__right_ == nullptr)
 {
 __parent = const_cast<__node_pointer&>(__hint.__ptr_);
 return __parent->__right_;
 }
 else
 {
 __parent = const_cast<__node_pointer&>(__next.__ptr_);
 return __parent->__left_;
 }
 }
 // *next(__hint) <= __v
 return __find_equal(__parent, __v);
 }
 // else __v == *__hint
 __parent = const_cast<__node_pointer&>(__hint.__ptr_);
 return __parent;
}

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

#ifndef _LIBCPP_HAS_NO_RVALUE_REFERENCES
#ifndef _LIBCPP_HAS_NO_VARIADICS

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)
{
 __node_allocator& __na = __node_alloc();
 __node_holder __h(__node_traits::allocate(__na, 1), _D(__na));
 __node_traits::construct(__na, addressof(__h->__value_), _STD::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(_Args&&... __args)
{
 __node_holder __h = __construct_node(_STD::forward<_Args>(__args)...);
 __node_base_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, __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(const_iterator __p, _Args&&... __args)
{
 __node_holder __h = __construct_node(_STD::forward<_Args>(__args)...);
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_equal(__p, __parent, __h->__value_);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 if (__child == nullptr)
 {
 __insert_node_at(__parent, __child, __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(_STD::forward<_Args>(__args)...);
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf_high(__parent, __h->__value_);
 __insert_node_at(__parent, __child, __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(_STD::forward<_Args>(__args)...);
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf(__p, __parent, __h->__value_);
 __insert_node_at(__parent, __child, __h.get());
 return iterator(static_cast<__node_pointer>(__h.release()));
}

#endif // _LIBCPP_HAS_NO_VARIADICS

template <class _Tp, class _Compare, class _Allocator>
template <class _V>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__insert_unique(_V&& __v)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_equal(__parent, __v);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 bool __inserted = false;
 if (__child == nullptr)
 {
 __node_holder __h = __construct_node(_STD::forward<_V>(__v));
 __insert_node_at(__parent, __child, __h.get());
 __r = __h.release();
 __inserted = true;
 }
 return pair<iterator, bool>(iterator(__r), __inserted);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _V>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_unique(const_iterator __p, _V&& __v)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_equal(__p, __parent, __v);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 if (__child == nullptr)
 {
 __node_holder __h = __construct_node(_STD::forward<_V>(__v));
 __insert_node_at(__parent, __child, __h.get());
 __r = __h.release();
 }
 return iterator(__r);
}

template <class _Tp, class _Compare, class _Allocator>
template <class _V>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_multi(_V&& __v)
{
 __node_holder __h = __construct_node(_STD::forward<_V>(__v));
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf_high(__parent, __h->__value_);
 __insert_node_at(__parent, __child, __h.get());
 return iterator(__h.release());
}

template <class _Tp, class _Compare, class _Allocator>
template <class _V>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_multi(const_iterator __p, _V&& __v)
{
 __node_holder __h = __construct_node(_STD::forward<_V>(__v));
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf(__p, __parent, __h->__value_);
 __insert_node_at(__parent, __child, __h.get());
 return iterator(__h.release());
}

#else // _LIBCPP_HAS_NO_RVALUE_REFERENCES

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::__node_holder
__tree<_Tp, _Compare, _Allocator>::__construct_node(const value_type& __v)
{
 __node_allocator& __na = __node_alloc();
 __node_holder __h(__node_traits::allocate(__na, 1), _D(__na));
 __node_traits::construct(__na, addressof(__h->__value_), __v);
 __h.get_deleter().__value_constructed = true;
 return _STD::move(__h);
}

template <class _Tp, class _Compare, class _Allocator>
pair<typename __tree<_Tp, _Compare, _Allocator>::iterator, bool>
__tree<_Tp, _Compare, _Allocator>::__insert_unique(const value_type& __v)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_equal(__parent, __v);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 bool __inserted = false;
 if (__child == nullptr)
 {
 __node_holder __h = __construct_node(__v);
 __insert_node_at(__parent, __child, __h.get());
 __r = __h.release();
 __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>::__insert_unique(const_iterator __p, const value_type& __v)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_equal(__p, __parent, __v);
 __node_pointer __r = static_cast<__node_pointer>(__child);
 if (__child == nullptr)
 {
 __node_holder __h = __construct_node(__v);
 __insert_node_at(__parent, __child, __h.get());
 __r = __h.release();
 }
 return iterator(__r);
}

template <class _Tp, class _Compare, class _Allocator>
typename __tree<_Tp, _Compare, _Allocator>::iterator
__tree<_Tp, _Compare, _Allocator>::__insert_multi(const value_type& __v)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf_high(__parent, __v);
 __node_holder __h = __construct_node(__v);
 __insert_node_at(__parent, __child, __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 value_type& __v)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf(__p, __parent, __v);
 __node_holder __h = __construct_node(__v);
 __insert_node_at(__parent, __child, __h.get());
 return iterator(__h.release());
}

#endif // _LIBCPP_HAS_NO_RVALUE_REFERENCES

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)
{
 __node_base_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, __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)
{
 __node_base_pointer __parent;
 __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, __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)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf_high(__parent, __nd->__value_);
 __insert_node_at(__parent, __child, __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)
{
 __node_base_pointer __parent;
 __node_base_pointer& __child = __find_leaf(__p, __parent, __nd->__value_);
 __insert_node_at(__parent, __child, __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 = const_cast<__node_pointer>(__p.__ptr_);
 iterator __r(__np);
 ++__r;
 if (__begin_node() == __np)
 __begin_node() = __r.__ptr_;
 --size();
 __node_allocator& __na = __node_alloc();
 __node_traits::destroy(__na, const_cast<value_type*>(addressof(*__p)));
 __tree_remove(__end_node()->__left_,
 static_cast<__node_base_pointer>(__np));
 __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(const_cast<__node_pointer>(__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_const_pointer __result = __end_node();
 __node_const_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = __rt;
 __rt = static_cast<__node_const_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_const_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
{
 typedef pair<const_iterator, const_iterator> _P;
 __node_const_pointer __result = __end_node();
 __node_const_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = __rt;
 __rt = static_cast<__node_const_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_const_pointer>(__rt->__right_);
 else
 return _STD::distance(
 __lower_bound(__k, static_cast<__node_const_pointer>(__rt->__left_), __rt),
 __upper_bound(__k, static_cast<__node_const_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,
 __node_pointer __result)
{
 while (__root != nullptr)
 {
 if (!value_comp()(__root->__value_, __v))
 {
 __result = __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_const_pointer __root,
 __node_const_pointer __result) const
{
 while (__root != nullptr)
 {
 if (!value_comp()(__root->__value_, __v))
 {
 __result = __root;
 __root = static_cast<__node_const_pointer>(__root->__left_);
 }
 else
 __root = static_cast<__node_const_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,
 __node_pointer __result)
{
 while (__root != nullptr)
 {
 if (value_comp()(__v, __root->__value_))
 {
 __result = __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_const_pointer __root,
 __node_const_pointer __result) const
{
 while (__root != nullptr)
 {
 if (value_comp()(__v, __root->__value_))
 {
 __result = __root;
 __root = static_cast<__node_const_pointer>(__root->__left_);
 }
 else
 __root = static_cast<__node_const_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> _P;
 __node_pointer __result = __end_node();
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = __rt;
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return _P(iterator(__rt),
 iterator(
 __rt->__right_ != nullptr ?
 static_cast<__node_pointer>(__tree_min(__rt->__right_))
 : __result));
 }
 return _P(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> _P;
 __node_const_pointer __result = __end_node();
 __node_const_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = __rt;
 __rt = static_cast<__node_const_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_const_pointer>(__rt->__right_);
 else
 return _P(const_iterator(__rt),
 const_iterator(
 __rt->__right_ != nullptr ?
 static_cast<__node_const_pointer>(__tree_min(__rt->__right_))
 : __result));
 }
 return _P(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> _P;
 __node_pointer __result = __end_node();
 __node_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = __rt;
 __rt = static_cast<__node_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_pointer>(__rt->__right_);
 else
 return _P(__lower_bound(__k, static_cast<__node_pointer>(__rt->__left_), __rt),
 __upper_bound(__k, static_cast<__node_pointer>(__rt->__right_), __result));
 }
 return _P(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> _P;
 __node_const_pointer __result = __end_node();
 __node_const_pointer __rt = __root();
 while (__rt != nullptr)
 {
 if (value_comp()(__k, __rt->__value_))
 {
 __result = __rt;
 __rt = static_cast<__node_const_pointer>(__rt->__left_);
 }
 else if (value_comp()(__rt->__value_, __k))
 __rt = static_cast<__node_const_pointer>(__rt->__right_);
 else
 return _P(__lower_bound(__k, static_cast<__node_const_pointer>(__rt->__left_), __rt),
 __upper_bound(__k, static_cast<__node_const_pointer>(__rt->__right_), __result));
 }
 return _P(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)
{
 __node_pointer __np = const_cast<__node_pointer>(__p.__ptr_);
 if (__begin_node() == __np)
 {
 if (__np->__right_ != nullptr)
 __begin_node() = static_cast<__node_pointer>(__np->__right_);
 else
 __begin_node() = static_cast<__node_pointer>(__np->__parent_);
 }
 --size();
 __tree_remove(__end_node()->__left_,
 static_cast<__node_base_pointer>(__np));
 return __node_holder(__np, _D(__node_alloc()));
}

_LIBCPP_END_NAMESPACE_STD

#endif // _LIBCPP___TREE