/////////////////////////////////////////////////////////////////////////////
	//
	// (C) Copyright Olaf Krzikalla 2004-2006.
	// (C) Copyright Ion Gaztanaga  2006-2014.
	//
	// Distributed under the Boost Software License, Version 1.0.
	//    (See accompanying file LICENSE_1_0.txt or copy at
	//          http://www.boost.org/LICENSE_1_0.txt)
	//
	// See http://www.boost.org/libs/intrusive for documentation.
	//
	/////////////////////////////////////////////////////////////////////////////
	//
	// The tree destruction algorithm is based on Julienne Walker and The EC Team code:
	//
	// This code is in the public domain. Anyone may use it or change it in any way that
	// they see fit. The author assumes no responsibility for damages incurred through
	// use of the original code or any variations thereof.
	//
	// It is requested, but not required, that due credit is given to the original author
	// and anyone who has modified the code through a header comment, such as this one.
	
	#ifndef BOOST_INTRUSIVE_RBTREE_ALGORITHMS_HPP
	#define BOOST_INTRUSIVE_RBTREE_ALGORITHMS_HPP
	
	#include <boost/intrusive/detail/config_begin.hpp>
	#include <boost/intrusive/intrusive_fwd.hpp>
	
	#include <cstddef>
	
	#include <boost/intrusive/detail/assert.hpp>
	#include <boost/intrusive/detail/algo_type.hpp>
	#include <boost/intrusive/bstree_algorithms.hpp>
	#include <boost/intrusive/detail/ebo_functor_holder.hpp>
	
	#if defined(BOOST_HAS_PRAGMA_ONCE)
	#  pragma once
	#endif
	
	namespace boost {
	namespace intrusive {
	
	#ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	
	template<class NodeTraits, class F>
	struct rbtree_node_cloner
	   //Use public inheritance to avoid MSVC bugs with closures
	   :  public detail::ebo_functor_holder<F>
	{
	   typedef typename NodeTraits::node_ptr  node_ptr;
	   typedef detail::ebo_functor_holder<F>  base_t;
	
	   explicit rbtree_node_cloner(F f)
	      :  base_t(f)
	   {}
	
	   node_ptr operator()(const node_ptr & p)
	   {
	      node_ptr n = base_t::get()(p);
	      NodeTraits::set_color(n, NodeTraits::get_color(p));
	      return n;
	   }
	};
	
	namespace detail {
	
	template<class ValueTraits, class NodePtrCompare, class ExtraChecker>
	struct rbtree_node_checker
	   : public bstree_node_checker<ValueTraits, NodePtrCompare, ExtraChecker>
	{
	   typedef bstree_node_checker<ValueTraits, NodePtrCompare, ExtraChecker> base_checker_t;
	   typedef ValueTraits                             value_traits;
	   typedef typename value_traits::node_traits      node_traits;
	   typedef typename node_traits::const_node_ptr    const_node_ptr;
	   typedef typename node_traits::node_ptr          node_ptr;
	
	   struct return_type
	         : public base_checker_t::return_type
	   {
	      return_type() : black_count_(0) {}
	      std::size_t black_count_;
	   };
	
	   rbtree_node_checker(const NodePtrCompare& comp, ExtraChecker extra_checker)
	      : base_checker_t(comp, extra_checker)
	   {}
	
	   void operator () (const const_node_ptr& p,
	                     const return_type& check_return_left, const return_type& check_return_right,
	                     return_type& check_return)
	   {
	
	      if (node_traits::get_color(p) == node_traits::red()){
	         //Red nodes have black children
	         const node_ptr p_left(node_traits::get_left(p));   (void)p_left;
	         const node_ptr p_right(node_traits::get_right(p)); (void)p_right;
	         BOOST_INTRUSIVE_INVARIANT_ASSERT(!p_left  || node_traits::get_color(p_left)  == node_traits::black());
	         BOOST_INTRUSIVE_INVARIANT_ASSERT(!p_right || node_traits::get_color(p_right) == node_traits::black());
	         //Red node can't be root
	         BOOST_INTRUSIVE_INVARIANT_ASSERT(node_traits::get_parent(node_traits::get_parent(p)) != p);
	      }
	      //Every path to p contains the same number of black nodes
	      const std::size_t l_black_count = check_return_left.black_count_;
	      BOOST_INTRUSIVE_INVARIANT_ASSERT(l_black_count == check_return_right.black_count_);
	      check_return.black_count_ = l_black_count +
	         static_cast<std::size_t>(node_traits::get_color(p) == node_traits::black());
	      base_checker_t::operator()(p, check_return_left, check_return_right, check_return);
	   }
	};
	
	} // namespace detail
	
	#endif   //#ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	
	//! rbtree_algorithms provides basic algorithms to manipulate
	//! nodes forming a red-black tree. The insertion and deletion algorithms are
	//! based on those in Cormen, Leiserson, and Rivest, Introduction to Algorithms
	//! (MIT Press, 1990), except that
	//!
	//! (1) the header node is maintained with links not only to the root
	//! but also to the leftmost node of the tree, to enable constant time
	//! begin(), and to the rightmost node of the tree, to enable linear time
	//! performance when used with the generic set algorithms (set_union,
	//! etc.);
	//!
	//! (2) when a node being deleted has two children its successor node is
	//! relinked into its place, rather than copied, so that the only
	//! pointers invalidated are those referring to the deleted node.
	//!
	//! rbtree_algorithms is configured with a NodeTraits class, which encapsulates the
	//! information about the node to be manipulated. NodeTraits must support the
	//! following interface:
	//!
	//! <b>Typedefs</b>:
	//!
	//! <tt>node</tt>: The type of the node that forms the binary search tree
	//!
	//! <tt>node_ptr</tt>: A pointer to a node
	//!
	//! <tt>const_node_ptr</tt>: A pointer to a const node
	//!
	//! <tt>color</tt>: The type that can store the color of a node
	//!
	//! <b>Static functions</b>:
	//!
	//! <tt>static node_ptr get_parent(const_node_ptr n);</tt>
	//!
	//! <tt>static void set_parent(node_ptr n, node_ptr parent);</tt>
	//!
	//! <tt>static node_ptr get_left(const_node_ptr n);</tt>
	//!
	//! <tt>static void set_left(node_ptr n, node_ptr left);</tt>
	//!
	//! <tt>static node_ptr get_right(const_node_ptr n);</tt>
	//!
	//! <tt>static void set_right(node_ptr n, node_ptr right);</tt>
	//!
	//! <tt>static color get_color(const_node_ptr n);</tt>
	//!
	//! <tt>static void set_color(node_ptr n, color c);</tt>
	//!
	//! <tt>static color black();</tt>
	//!
	//! <tt>static color red();</tt>
	template<class NodeTraits>
	class rbtree_algorithms
	   #ifndef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	   : public bstree_algorithms<NodeTraits>
	   #endif
	{
	   public:
	   typedef NodeTraits                           node_traits;
	   typedef typename NodeTraits::node            node;
	   typedef typename NodeTraits::node_ptr        node_ptr;
	   typedef typename NodeTraits::const_node_ptr  const_node_ptr;
	   typedef typename NodeTraits::color           color;
	
	   /// @cond
	   private:
	
	   typedef bstree_algorithms<NodeTraits>  bstree_algo;
	
	   /// @endcond
	
	   public:
	
	   //! This type is the information that will be
	   //! filled by insert_unique_check
	   typedef typename bstree_algo::insert_commit_data insert_commit_data;
	
	   #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::get_header(const const_node_ptr&)
	   static node_ptr get_header(const const_node_ptr & n);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::begin_node
	   static node_ptr begin_node(const const_node_ptr & header);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::end_node
	   static node_ptr end_node(const const_node_ptr & header);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::swap_tree
	   static void swap_tree(const node_ptr & header1, const node_ptr & header2);
	
	   #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::swap_nodes(const node_ptr&,const node_ptr&)
	   static void swap_nodes(const node_ptr & node1, const node_ptr & node2)
	   {
	      if(node1 == node2)
	         return;
	
	      node_ptr header1(bstree_algo::get_header(node1)), header2(bstree_algo::get_header(node2));
	      swap_nodes(node1, header1, node2, header2);
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::swap_nodes(const node_ptr&,const node_ptr&,const node_ptr&,const node_ptr&)
	   static void swap_nodes(const node_ptr & node1, const node_ptr & header1, const node_ptr & node2, const node_ptr & header2)
	   {
	      if(node1 == node2)   return;
	
	      bstree_algo::swap_nodes(node1, header1, node2, header2);
	      //Swap color
	      color c = NodeTraits::get_color(node1);
	      NodeTraits::set_color(node1, NodeTraits::get_color(node2));
	      NodeTraits::set_color(node2, c);
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::replace_node(const node_ptr&,const node_ptr&)
	   static void replace_node(const node_ptr & node_to_be_replaced, const node_ptr & new_node)
	   {
	      if(node_to_be_replaced == new_node)
	         return;
	      replace_node(node_to_be_replaced, bstree_algo::get_header(node_to_be_replaced), new_node);
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::replace_node(const node_ptr&,const node_ptr&,const node_ptr&)
	   static void replace_node(const node_ptr & node_to_be_replaced, const node_ptr & header, const node_ptr & new_node)
	   {
	      bstree_algo::replace_node(node_to_be_replaced, header, new_node);
	      NodeTraits::set_color(new_node, NodeTraits::get_color(node_to_be_replaced));
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::unlink(const node_ptr&)
	   static void unlink(const node_ptr& node)
	   {
	      node_ptr x = NodeTraits::get_parent(node);
	      if(x){
	         while(!is_header(x))
	            x = NodeTraits::get_parent(x);
	         erase(x, node);
	      }
	   }
	
	   #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	   //! @copydoc ::boost::intrusive::bstree_algorithms::unlink_leftmost_without_rebalance
	   static node_ptr unlink_leftmost_without_rebalance(const node_ptr & header);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::unique(const const_node_ptr&)
	   static bool unique(const const_node_ptr & node);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::size(const const_node_ptr&)
	   static std::size_t size(const const_node_ptr & header);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::next_node(const node_ptr&)
	   static node_ptr next_node(const node_ptr & node);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::prev_node(const node_ptr&)
	   static node_ptr prev_node(const node_ptr & node);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::init(const node_ptr&)
	   static void init(const node_ptr & node);
	   #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::init_header(const node_ptr&)
	   static void init_header(const node_ptr & header)
	   {
	      bstree_algo::init_header(header);
	      NodeTraits::set_color(header, NodeTraits::red());
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::erase(const node_ptr&,const node_ptr&)
	   static node_ptr erase(const node_ptr & header, const node_ptr & z)
	   {
	      typename bstree_algo::data_for_rebalance info;
	      bstree_algo::erase(header, z, info);
	      rebalance_after_erasure(header, z, info);
	      return z;
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::transfer_unique
	   template<class NodePtrCompare>
	   static bool transfer_unique
	      (const node_ptr & header1, NodePtrCompare comp, const node_ptr &header2, const node_ptr & z)
	   {
	      typename bstree_algo::data_for_rebalance info;
	      bool const transferred = bstree_algo::transfer_unique(header1, comp, header2, z, info);
	      if(transferred){
	         rebalance_after_erasure(header2, z, info);
	         rebalance_after_insertion(header1, z);
	      }
	      return transferred;
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::transfer_equal
	   template<class NodePtrCompare>
	   static void transfer_equal
	      (const node_ptr & header1, NodePtrCompare comp, const node_ptr &header2, const node_ptr & z)
	   {
	      typename bstree_algo::data_for_rebalance info;
	      bstree_algo::transfer_equal(header1, comp, header2, z, info);
	      rebalance_after_erasure(header2, z, info);
	      rebalance_after_insertion(header1, z);
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::clone(const const_node_ptr&,const node_ptr&,Cloner,Disposer)
	   template <class Cloner, class Disposer>
	   static void clone
	      (const const_node_ptr & source_header, const node_ptr & target_header, Cloner cloner, Disposer disposer)
	   {
	      rbtree_node_cloner<NodeTraits, Cloner> new_cloner(cloner);
	      bstree_algo::clone(source_header, target_header, new_cloner, disposer);
	   }
	
	   #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	   //! @copydoc ::boost::intrusive::bstree_algorithms::clear_and_dispose(const node_ptr&,Disposer)
	   template<class Disposer>
	   static void clear_and_dispose(const node_ptr & header, Disposer disposer);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::lower_bound(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
	   template<class KeyType, class KeyNodePtrCompare>
	   static node_ptr lower_bound
	      (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::upper_bound(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
	   template<class KeyType, class KeyNodePtrCompare>
	   static node_ptr upper_bound
	      (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::find(const const_node_ptr&, const KeyType&,KeyNodePtrCompare)
	   template<class KeyType, class KeyNodePtrCompare>
	   static node_ptr find
	      (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::equal_range(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
	   template<class KeyType, class KeyNodePtrCompare>
	   static std::pair<node_ptr, node_ptr> equal_range
	      (const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::bounded_range(const const_node_ptr&,const KeyType&,const KeyType&,KeyNodePtrCompare,bool,bool)
	   template<class KeyType, class KeyNodePtrCompare>
	   static std::pair<node_ptr, node_ptr> bounded_range
	      (const const_node_ptr & header, const KeyType &lower_key, const KeyType &upper_key, KeyNodePtrCompare comp
	      , bool left_closed, bool right_closed);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::count(const const_node_ptr&,const KeyType&,KeyNodePtrCompare)
	   template<class KeyType, class KeyNodePtrCompare>
	   static std::size_t count(const const_node_ptr & header, const KeyType &key, KeyNodePtrCompare comp);
	
	   #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal_upper_bound(const node_ptr&,const node_ptr&,NodePtrCompare)
	   template<class NodePtrCompare>
	   static node_ptr insert_equal_upper_bound
	      (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp)
	   {
	      bstree_algo::insert_equal_upper_bound(h, new_node, comp);
	      rebalance_after_insertion(h, new_node);
	      return new_node;
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal_lower_bound(const node_ptr&,const node_ptr&,NodePtrCompare)
	   template<class NodePtrCompare>
	   static node_ptr insert_equal_lower_bound
	      (const node_ptr & h, const node_ptr & new_node, NodePtrCompare comp)
	   {
	      bstree_algo::insert_equal_lower_bound(h, new_node, comp);
	      rebalance_after_insertion(h, new_node);
	      return new_node;
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::insert_equal(const node_ptr&,const node_ptr&,const node_ptr&,NodePtrCompare)
	   template<class NodePtrCompare>
	   static node_ptr insert_equal
	      (const node_ptr & header, const node_ptr & hint, const node_ptr & new_node, NodePtrCompare comp)
	   {
	      bstree_algo::insert_equal(header, hint, new_node, comp);
	      rebalance_after_insertion(header, new_node);
	      return new_node;
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::insert_before(const node_ptr&,const node_ptr&,const node_ptr&)
	   static node_ptr insert_before
	      (const node_ptr & header, const node_ptr & pos, const node_ptr & new_node)
	   {
	      bstree_algo::insert_before(header, pos, new_node);
	      rebalance_after_insertion(header, new_node);
	      return new_node;
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::push_back(const node_ptr&,const node_ptr&)
	   static void push_back(const node_ptr & header, const node_ptr & new_node)
	   {
	      bstree_algo::push_back(header, new_node);
	      rebalance_after_insertion(header, new_node);
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::push_front(const node_ptr&,const node_ptr&)
	   static void push_front(const node_ptr & header, const node_ptr & new_node)
	   {
	      bstree_algo::push_front(header, new_node);
	      rebalance_after_insertion(header, new_node);
	   }
	
	   #ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	   //! @copydoc ::boost::intrusive::bstree_algorithms::insert_unique_check(const const_node_ptr&,const KeyType&,KeyNodePtrCompare,insert_commit_data&)
	   template<class KeyType, class KeyNodePtrCompare>
	   static std::pair<node_ptr, bool> insert_unique_check
	      (const const_node_ptr & header,  const KeyType &key
	      ,KeyNodePtrCompare comp, insert_commit_data &commit_data);
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::insert_unique_check(const const_node_ptr&,const node_ptr&,const KeyType&,KeyNodePtrCompare,insert_commit_data&)
	   template<class KeyType, class KeyNodePtrCompare>
	   static std::pair<node_ptr, bool> insert_unique_check
	      (const const_node_ptr & header, const node_ptr &hint, const KeyType &key
	      ,KeyNodePtrCompare comp, insert_commit_data &commit_data);
	   #endif   //#ifdef BOOST_INTRUSIVE_DOXYGEN_INVOKED
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::insert_unique_commit(const node_ptr&,const node_ptr&,const insert_commit_data&)
	   static void insert_unique_commit
	      (const node_ptr & header, const node_ptr & new_value, const insert_commit_data &commit_data)
	   {
	      bstree_algo::insert_unique_commit(header, new_value, commit_data);
	      rebalance_after_insertion(header, new_value);
	   }
	
	   //! @copydoc ::boost::intrusive::bstree_algorithms::is_header
	   static bool is_header(const const_node_ptr & p)
	   {
	      return NodeTraits::get_color(p) == NodeTraits::red() &&
	            bstree_algo::is_header(p);
	   }
	
	   /// @cond
	   private:
	
	   static void rebalance_after_erasure
	      ( const node_ptr & header, const node_ptr &z, const typename bstree_algo::data_for_rebalance &info)
	   {
	      color new_z_color;
	      if(info.y != z){
	         new_z_color = NodeTraits::get_color(info.y);
	         NodeTraits::set_color(info.y, NodeTraits::get_color(z));
	      }
	      else{
	         new_z_color = NodeTraits::get_color(z);
	      }
	      //Rebalance rbtree if needed
	      if(new_z_color != NodeTraits::red()){
	         rebalance_after_erasure_restore_invariants(header, info.x, info.x_parent);
	      }
	   }
	
	   static void rebalance_after_erasure_restore_invariants(const node_ptr & header, node_ptr x, node_ptr x_parent)
	   {

	      while(1){

	         if(x_parent == header || (x && NodeTraits::get_color(x) != NodeTraits::black())){
	            break;

	         }
	         //Don't cache x_is_leftchild or similar because x can be null and
	         //equal to both x_parent_left and x_parent_right
	         const node_ptr x_parent_left(NodeTraits::get_left(x_parent));

	         if(x == x_parent_left){ //x is left child
	            node_ptr w = NodeTraits::get_right(x_parent);

	            BOOST_INTRUSIVE_INVARIANT_ASSERT(w);

	            if(NodeTraits::get_color(w) == NodeTraits::red()){
	               NodeTraits::set_color(w, NodeTraits::black());
	               NodeTraits::set_color(x_parent, NodeTraits::red());
	               bstree_algo::rotate_left(x_parent, w, NodeTraits::get_parent(x_parent), header);
	               w = NodeTraits::get_right(x_parent);

	               BOOST_INTRUSIVE_INVARIANT_ASSERT(w);
	            }
	            node_ptr const w_left (NodeTraits::get_left(w));
	            node_ptr const w_right(NodeTraits::get_right(w));

	            if((!w_left  || NodeTraits::get_color(w_left)  == NodeTraits::black()) &&
	               (!w_right || NodeTraits::get_color(w_right) == NodeTraits::black())){
	               NodeTraits::set_color(w, NodeTraits::red());
	               x = x_parent;
	               x_parent = NodeTraits::get_parent(x_parent);

	            }
	            else {
	               if(!w_right || NodeTraits::get_color(w_right) == NodeTraits::black()){
	                  NodeTraits::set_color(w_left, NodeTraits::black());
	                  NodeTraits::set_color(w, NodeTraits::red());
	                  bstree_algo::rotate_right(w, w_left, NodeTraits::get_parent(w), header);
	                  w = NodeTraits::get_right(x_parent);
	                  BOOST_INTRUSIVE_INVARIANT_ASSERT(w);
	               }
	               NodeTraits::set_color(w, NodeTraits::get_color(x_parent));
	               NodeTraits::set_color(x_parent, NodeTraits::black());
	               const node_ptr new_wright(NodeTraits::get_right(w));
	               if(new_wright)
	                  NodeTraits::set_color(new_wright, NodeTraits::black());
	               bstree_algo::rotate_left(x_parent, NodeTraits::get_right(x_parent), NodeTraits::get_parent(x_parent), header);
	               break;

	            }

	         }

	         else {
	            // same as above, with right_ <-> left_.
	            node_ptr w = x_parent_left;

	            if(NodeTraits::get_color(w) == NodeTraits::red()){
	               NodeTraits::set_color(w, NodeTraits::black());
	               NodeTraits::set_color(x_parent, NodeTraits::red());
	               bstree_algo::rotate_right(x_parent, w, NodeTraits::get_parent(x_parent), header);
	               w = NodeTraits::get_left(x_parent);

	               BOOST_INTRUSIVE_INVARIANT_ASSERT(w);

	            }
	            node_ptr const w_left (NodeTraits::get_left(w));
	            node_ptr const w_right(NodeTraits::get_right(w));

	            if((!w_right || NodeTraits::get_color(w_right) == NodeTraits::black()) &&
	               (!w_left  || NodeTraits::get_color(w_left)  == NodeTraits::black())){
	               NodeTraits::set_color(w, NodeTraits::red());
	               x = x_parent;
	               x_parent = NodeTraits::get_parent(x_parent);

	            }

	            else {

	               if(!w_left || NodeTraits::get_color(w_left) == NodeTraits::black()){

	                  NodeTraits::set_color(w_right, NodeTraits::black());
	                  NodeTraits::set_color(w, NodeTraits::red());
	                  bstree_algo::rotate_left(w, w_right, NodeTraits::get_parent(w), header);
	                  w = NodeTraits::get_left(x_parent);
	                  BOOST_INTRUSIVE_INVARIANT_ASSERT(w);
	               }
	               NodeTraits::set_color(w, NodeTraits::get_color(x_parent));
	               NodeTraits::set_color(x_parent, NodeTraits::black());
	               const node_ptr new_wleft(NodeTraits::get_left(w));
	               if(new_wleft)
	                  NodeTraits::set_color(new_wleft, NodeTraits::black());
	               bstree_algo::rotate_right(x_parent, NodeTraits::get_left(x_parent), NodeTraits::get_parent(x_parent), header);
	               break;

	            }

	         }

	      }
	      if(x)
	         NodeTraits::set_color(x, NodeTraits::black());
	   }
	
	   static void rebalance_after_insertion(const node_ptr & header, node_ptr p)
	   {
	      NodeTraits::set_color(p, NodeTraits::red());
	      while(1){
	         node_ptr p_parent(NodeTraits::get_parent(p));
	         const node_ptr p_grandparent(NodeTraits::get_parent(p_parent));
	         if(p_parent == header || NodeTraits::get_color(p_parent) == NodeTraits::black() || p_grandparent == header){
	            break;
	         }
	
	         NodeTraits::set_color(p_grandparent, NodeTraits::red());
	         node_ptr const p_grandparent_left (NodeTraits::get_left (p_grandparent));
	         bool const p_parent_is_left_child = p_parent == p_grandparent_left;
	         node_ptr const x(p_parent_is_left_child ? NodeTraits::get_right(p_grandparent) : p_grandparent_left);
	
	         if(x && NodeTraits::get_color(x) == NodeTraits::red()){
	            NodeTraits::set_color(x, NodeTraits::black());
	            NodeTraits::set_color(p_parent, NodeTraits::black());
	            p = p_grandparent;
	         }
	         else{ //Final step
	            const bool p_is_left_child(NodeTraits::get_left(p_parent) == p);
	            if(p_parent_is_left_child){ //p_parent is left child
	               if(!p_is_left_child){ //p is right child
	                  bstree_algo::rotate_left_no_parent_fix(p_parent, p);
	                  //No need to link p and p_grandparent:
	                  //    [NodeTraits::set_parent(p, p_grandparent) + NodeTraits::set_left(p_grandparent, p)]
	                  //as p_grandparent is not the header, another rotation is coming and p_parent
	                  //will be the left child of p_grandparent
	                  p_parent = p;
	               }
	               bstree_algo::rotate_right(p_grandparent, p_parent, NodeTraits::get_parent(p_grandparent), header);
	            }
	            else{  //p_parent is right child
	               if(p_is_left_child){ //p is left child
	                  bstree_algo::rotate_right_no_parent_fix(p_parent, p);
	                  //No need to link p and p_grandparent:
	                  //    [NodeTraits::set_parent(p, p_grandparent) + NodeTraits::set_right(p_grandparent, p)]
	                  //as p_grandparent is not the header, another rotation is coming and p_parent
	                  //will be the right child of p_grandparent
	                  p_parent = p;
	               }
	               bstree_algo::rotate_left(p_grandparent, p_parent, NodeTraits::get_parent(p_grandparent), header);
	            }
	            NodeTraits::set_color(p_parent, NodeTraits::black());
	            break;
	         }
	      }
	      NodeTraits::set_color(NodeTraits::get_parent(header), NodeTraits::black());
	   }
	   /// @endcond
	};
	
	/// @cond
	
	template<class NodeTraits>
	struct get_algo<RbTreeAlgorithms, NodeTraits>
	{
	   typedef rbtree_algorithms<NodeTraits> type;
	};
	
	template <class ValueTraits, class NodePtrCompare, class ExtraChecker>
	struct get_node_checker<RbTreeAlgorithms, ValueTraits, NodePtrCompare, ExtraChecker>
	{
	    typedef detail::rbtree_node_checker<ValueTraits, NodePtrCompare, ExtraChecker> type;
	};
	
	/// @endcond
	
	} //namespace intrusive
	} //namespace boost
	
	#include <boost/intrusive/detail/config_end.hpp>
	
	#endif //BOOST_INTRUSIVE_RBTREE_ALGORITHMS_HPP