//RTree code taken from http://superliminal.com/sources/sources.htm
//RTree LICENSE: Entirely free for all uses.Enjoy!

#include <cstdio>
#include <cmath>
#include <cassert>
#include <cstdlib>
#include <algorithm>

using std::min;
using std::max;
using std::sort;

#define ASSERT assert // RTree uses ASSERT( condition )
#ifndef Min
#define Min min 
#endif //Min
#ifndef Max
#define Max max 
#endif //Max

//
// RTree.h
//

#define RTREE_TEMPLATE template<class DATATYPE, class ELEMTYPE, int NUMDIMS, class ELEMTYPEREAL, int TMAXNODES, int TMINNODES>
#define RTREE_QUAL RTree<DATATYPE, ELEMTYPE, NUMDIMS, ELEMTYPEREAL, TMAXNODES, TMINNODES>

#define RTREE_DONT_USE_MEMPOOLS // This version does not contain a fixed memory allocator, fill in lines with EXAMPLE to implement one.
#define RTREE_USE_SPHERICAL_VOLUME // Better split classification, may be slower on some systems


/// \class RTree
/// Implementation of RTree, a multidimensional bounding rectangle tree.
/// Example usage: For a 3-dimensional tree use RTree<Object*, float, 3> myTree;
///
/// This modified, templated C++ version by Greg Douglas at Auran (http://www.auran.com)
///
/// DATATYPE Referenced data, should be int, void*, obj* etc. no larger than sizeof<void*> and simple type
/// ELEMTYPE Type of element such as int or float
/// NUMDIMS Number of dimensions such as 2 or 3
/// ELEMTYPEREAL Type of element that allows fractional and large values such as float or double, for use in volume calcs
///
/// NOTES: Inserting and removing data requires the knowledge of its constant Minimal Bounding Rectangle.
///        This version uses new/delete for nodes, I recommend using a fixed size allocator for efficiency.
///        Instead of using a callback function for returned results, I recommend and efficient pre-sized, grow-only memory
///        array similar to MFC CArray or STL Vector for returning search query result.
///
template<class DATATYPE, class ELEMTYPE, int NUMDIMS,
class ELEMTYPEREAL = ELEMTYPE, int TMAXNODES = 8, int TMINNODES = TMAXNODES / 2>
class RTree
{
protected:

  struct Node;  // Fwd decl.  Used by other internal structs and iterator

public:

  // These constant must be declared after Branch and before Node struct
  // Stuck up here for MSVC 6 compiler.  NSVC .NET 2003 is much happier.
  enum
  {
    MAXNODES = TMAXNODES,                         ///< Max elements in node
    MINNODES = TMINNODES,                         ///< Min elements in node
  };


public:

  RTree();
  virtual ~RTree();

  /// Insert entry
  /// \param a_min Min of bounding rect
  /// \param a_max Max of bounding rect
  /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
  void Insert(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId);

  /// Remove entry
  /// \param a_min Min of bounding rect
  /// \param a_max Max of bounding rect
  /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
  void Remove(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId);

  /// Find all within search rectangle
  /// \param a_min Min of search bounding rect
  /// \param a_max Max of search bounding rect
  /// \param a_searchResult Search result array.  Caller should set grow size. Function will reset, not append to array.
  /// \param a_resultCallback Callback function to return result.  Callback should return 'true' to continue searching
  /// \param a_context User context to pass as parameter to a_resultCallback
  /// \return Returns the number of entries found
  int Search(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context);

  /// Remove all entries from tree
  void RemoveAll();

  /// Count the data elements in this container.  This is slow as no internal counter is maintained.
  int Count();

  /// Iterator is not remove safe.
  class Iterator
  {
  private:

    enum { MAX_STACK = 32 }; //  Max stack size. Allows almost n^32 where n is number of branches in node

    struct StackElement
    {
      Node* m_node;
      int m_branchIndex;
    };

  public:

    Iterator()                                    { Init(); }

    ~Iterator()                                   { }

    /// Is iterator invalid
    bool IsNull()                                 { return (m_tos <= 0); }

    /// Is iterator pointing to valid data
    bool IsNotNull()                              { return (m_tos > 0); }

    /// Access the current data element. Caller must be sure iterator is not NULL first.
    DATATYPE& operator*()
    {
      ASSERT(IsNotNull());
      StackElement& curTos = m_stack[m_tos - 1];
      return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
    }

    /// Access the current data element. Caller must be sure iterator is not NULL first.
    const DATATYPE& operator*() const
    {
      ASSERT(IsNotNull());
      StackElement& curTos = m_stack[m_tos - 1];
      return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
    }

    /// Find the next data element
    bool operator++()                             { return FindNextData(); }

    /// Get the bounds for this node
    void GetBounds(ELEMTYPE a_min[NUMDIMS], ELEMTYPE a_max[NUMDIMS])
    {
      ASSERT(IsNotNull());
      StackElement& curTos = m_stack[m_tos - 1];
      Branch& curBranch = curTos.m_node->m_branch[curTos.m_branchIndex];

      for (int index = 0; index < NUMDIMS; ++index)
      {
        a_min[index] = curBranch.m_rect.m_min[index];
        a_max[index] = curBranch.m_rect.m_max[index];
      }
    }

  private:

    /// Reset iterator
    void Init()                                   { m_tos = 0; }

    /// Find the next data element in the tree (For internal use only)
    bool FindNextData()
    {
      for (;;)
      {
        if (m_tos <= 0)
        {
          return false;
        }
        StackElement curTos = Pop(); // Copy stack top cause it may change as we use it

        if (curTos.m_node->IsLeaf())
        {
          // Keep walking through data while we can
          if (curTos.m_branchIndex + 1 < curTos.m_node->m_count)
          {
            // There is more data, just point to the next one
            Push(curTos.m_node, curTos.m_branchIndex + 1);
            return true;
          }
          // No more data, so it will fall back to previous level
        }
        else
        {
          if (curTos.m_branchIndex + 1 < curTos.m_node->m_count)
          {
            // Push sibling on for future tree walk
            // This is the 'fall back' node when we finish with the current level
            Push(curTos.m_node, curTos.m_branchIndex + 1);
          }
          // Since cur node is not a leaf, push first of next level to get deeper into the tree
          Node* nextLevelnode = curTos.m_node->m_branch[curTos.m_branchIndex].m_child;
          Push(nextLevelnode, 0);

          // If we pushed on a new leaf, exit as the data is ready at TOS
          if (nextLevelnode->IsLeaf())
          {
            return true;
          }
        }
      }
    }

    /// Push node and branch onto iteration stack (For internal use only)
    void Push(Node* a_node, int a_branchIndex)
    {
      m_stack[m_tos].m_node = a_node;
      m_stack[m_tos].m_branchIndex = a_branchIndex;
      ++m_tos;
      ASSERT(m_tos <= MAX_STACK);
    }

    /// Pop element off iteration stack (For internal use only)
    StackElement& Pop()
    {
      ASSERT(m_tos > 0);
      --m_tos;
      return m_stack[m_tos];
    }

    StackElement m_stack[MAX_STACK];              ///< Stack as we are doing iteration instead of recursion
    int m_tos;                                    ///< Top Of Stack index

    friend class RTree; // Allow hiding of non-public functions while allowing manipulation by logical owner
  };

  /// Get 'first' for iteration
  void GetFirst(Iterator& a_it)
  {
    a_it.Init();
    Node* first = m_root;
    while (first)
    {
      if (first->IsInternalNode() && first->m_count > 1)
      {
        a_it.Push(first, 1); // Descend sibling branch later
      }
      else if (first->IsLeaf())
      {
        if (first->m_count)
        {
          a_it.Push(first, 0);
        }
        break;
      }
      first = first->m_branch[0].m_child;
    }
  }

  /// Get Next for iteration
  void GetNext(Iterator& a_it)                    { ++a_it; }

  /// Is iterator NULL, or at end?
  bool IsNull(Iterator& a_it)                     { return a_it.IsNull(); }

  /// Get object at iterator position
  DATATYPE& GetAt(Iterator& a_it)                 { return *a_it; }

protected:

  /// Minimal bounding rectangle (n-dimensional)
  struct Rect
  {
    ELEMTYPE m_min[NUMDIMS];                      ///< Min dimensions of bounding box 
    ELEMTYPE m_max[NUMDIMS];                      ///< Max dimensions of bounding box 
  };

  /// May be data or may be another subtree
  /// The parents level determines this.
  /// If the parents level is 0, then this is data
  struct Branch
  {
    Rect m_rect;                                  ///< Bounds
    union
    {
      Node* m_child;                              ///< Child node
      DATATYPE m_data;                            ///< Data Id or Ptr
    };
  };

  /// Node for each branch level
  struct Node
  {
    bool IsInternalNode()                         { return (m_level > 0); } // Not a leaf, but a internal node
    bool IsLeaf()                                 { return (m_level == 0); } // A leaf, contains data

    int m_count;                                  ///< Count
    int m_level;                                  ///< Leaf is zero, others positive
    Branch m_branch[MAXNODES];                    ///< Branch
  };

  /// A link list of nodes for reinsertion after a delete operation
  struct ListNode
  {
    ListNode* m_next;                             ///< Next in list
    Node* m_node;                                 ///< Node
  };

  /// Variables for finding a split partition
  struct PartitionVars
  {
    int m_partition[MAXNODES + 1];
    int m_total;
    int m_minFill;
    int m_taken[MAXNODES + 1];
    int m_count[2];
    Rect m_cover[2];
    ELEMTYPEREAL m_area[2];

    Branch m_branchBuf[MAXNODES + 1];
    int m_branchCount;
    Rect m_coverSplit;
    ELEMTYPEREAL m_coverSplitArea;
  };

  Node* AllocNode();
  void FreeNode(Node* a_node);
  void InitNode(Node* a_node);
  void InitRect(Rect* a_rect);
  bool InsertRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, Node** a_newNode, int a_level);
  bool InsertRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level);
  Rect NodeCover(Node* a_node);
  bool AddBranch(Branch* a_branch, Node* a_node, Node** a_newNode);
  void DisconnectBranch(Node* a_node, int a_index);
  int PickBranch(Rect* a_rect, Node* a_node);
  Rect CombineRect(Rect* a_rectA, Rect* a_rectB);
  void SplitNode(Node* a_node, Branch* a_branch, Node** a_newNode);
  ELEMTYPEREAL RectSphericalVolume(Rect* a_rect);
  ELEMTYPEREAL RectVolume(Rect* a_rect);
  ELEMTYPEREAL CalcRectVolume(Rect* a_rect);
  void GetBranches(Node* a_node, Branch* a_branch, PartitionVars* a_parVars);
  void ChoosePartition(PartitionVars* a_parVars, int a_minFill);
  void LoadNodes(Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars);
  void InitParVars(PartitionVars* a_parVars, int a_maxRects, int a_minFill);
  void PickSeeds(PartitionVars* a_parVars);
  void Classify(int a_index, int a_group, PartitionVars* a_parVars);
  bool RemoveRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root);
  bool RemoveRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, ListNode** a_listNode);
  ListNode* AllocListNode();
  void FreeListNode(ListNode* a_listNode);
  bool Overlap(Rect* a_rectA, Rect* a_rectB);
  void ReInsert(Node* a_node, ListNode** a_listNode);
  bool Search(Node* a_node, Rect* a_rect, int& a_foundCount, bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context);
  void RemoveAllRec(Node* a_node);
  void Reset();
  void CountRec(Node* a_node, int& a_count);

  Node* m_root;                                    ///< Root of tree
  ELEMTYPEREAL m_unitSphereVolume;                 ///< Unit sphere constant for required number of dimensions
};


RTREE_TEMPLATE
RTREE_QUAL::RTree()
{
  ASSERT(MAXNODES > MINNODES);
  ASSERT(MINNODES > 0);


  // We only support machine word size simple data type eg. integer index or object pointer.
  // Since we are storing as union with non data branch
  ASSERT(sizeof(DATATYPE) == sizeof(void*) || sizeof(DATATYPE) == sizeof(int));

  // Precomputed volumes of the unit spheres for the first few dimensions
  const float UNIT_SPHERE_VOLUMES[] = {
    0.000000f, 2.000000f, 3.141593f, // Dimension  0,1,2
    4.188790f, 4.934802f, 5.263789f, // Dimension  3,4,5
    5.167713f, 4.724766f, 4.058712f, // Dimension  6,7,8
    3.298509f, 2.550164f, 1.884104f, // Dimension  9,10,11
    1.335263f, 0.910629f, 0.599265f, // Dimension  12,13,14
    0.381443f, 0.235331f, 0.140981f, // Dimension  15,16,17
    0.082146f, 0.046622f, 0.025807f, // Dimension  18,19,20 
  };

  m_root = AllocNode();
  m_root->m_level = 0;
  m_unitSphereVolume = (ELEMTYPEREAL)UNIT_SPHERE_VOLUMES[NUMDIMS];
}


RTREE_TEMPLATE
RTREE_QUAL::~RTree()
{
  Reset(); // Free, or reset node memory
}


RTREE_TEMPLATE
void RTREE_QUAL::Insert(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId)
{
#ifdef _DEBUG
  for (int index = 0; index<NUMDIMS; ++index)
  {
    ASSERT(a_min[index] <= a_max[index]);
  }
#endif //_DEBUG

  Rect rect;

  for (int axis = 0; axis<NUMDIMS; ++axis)
  {
    rect.m_min[axis] = a_min[axis];
    rect.m_max[axis] = a_max[axis];
  }

  InsertRect(&rect, a_dataId, &m_root, 0);
}


RTREE_TEMPLATE
void RTREE_QUAL::Remove(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId)
{
#ifdef _DEBUG
  for (int index = 0; index<NUMDIMS; ++index)
  {
    ASSERT(a_min[index] <= a_max[index]);
  }
#endif //_DEBUG

  Rect rect;

  for (int axis = 0; axis<NUMDIMS; ++axis)
  {
    rect.m_min[axis] = a_min[axis];
    rect.m_max[axis] = a_max[axis];
  }

  RemoveRect(&rect, a_dataId, &m_root);
}


RTREE_TEMPLATE
int RTREE_QUAL::Search(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context)
{
#ifdef _DEBUG
  for (int index = 0; index<NUMDIMS; ++index)
  {
    ASSERT(a_min[index] <= a_max[index]);
  }
#endif //_DEBUG

  Rect rect;

  for (int axis = 0; axis<NUMDIMS; ++axis)
  {
    rect.m_min[axis] = a_min[axis];
    rect.m_max[axis] = a_max[axis];
  }

  // NOTE: May want to return search result another way, perhaps returning the number of found elements here.

  int foundCount = 0;
  Search(m_root, &rect, foundCount, a_resultCallback, a_context);

  return foundCount;
}


RTREE_TEMPLATE
int RTREE_QUAL::Count()
{
  int count = 0;
  CountRec(m_root, count);

  return count;
}



RTREE_TEMPLATE
void RTREE_QUAL::CountRec(Node* a_node, int& a_count)
{
  if (a_node->IsInternalNode())  // not a leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      CountRec(a_node->m_branch[index].m_child, a_count);
    }
  }
  else // A leaf node
  {
    a_count += a_node->m_count;
  }
}

RTREE_TEMPLATE
void RTREE_QUAL::RemoveAll()
{
  // Delete all existing nodes
  Reset();

  m_root = AllocNode();
  m_root->m_level = 0;
}


RTREE_TEMPLATE
void RTREE_QUAL::Reset()
{
#ifdef RTREE_DONT_USE_MEMPOOLS
  // Delete all existing nodes
  RemoveAllRec(m_root);
#else // RTREE_DONT_USE_MEMPOOLS
  // Just reset memory pools.  We are not using complex types
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::RemoveAllRec(Node* a_node)
{
  ASSERT(a_node);
  ASSERT(a_node->m_level >= 0);

  if (a_node->IsInternalNode()) // This is an internal node in the tree
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      RemoveAllRec(a_node->m_branch[index].m_child);
    }
  }
  FreeNode(a_node);
}


RTREE_TEMPLATE
typename RTREE_QUAL::Node* RTREE_QUAL::AllocNode()
{
  Node* newNode;
#ifdef RTREE_DONT_USE_MEMPOOLS
  newNode = new Node;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
  InitNode(newNode);
  return newNode;
}


RTREE_TEMPLATE
void RTREE_QUAL::FreeNode(Node* a_node)
{
  ASSERT(a_node);

#ifdef RTREE_DONT_USE_MEMPOOLS
  delete a_node;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


// Allocate space for a node in the list used in DeletRect to
// store Nodes that are too empty.
RTREE_TEMPLATE
typename RTREE_QUAL::ListNode* RTREE_QUAL::AllocListNode()
{
#ifdef RTREE_DONT_USE_MEMPOOLS
  return new ListNode;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::FreeListNode(ListNode* a_listNode)
{
#ifdef RTREE_DONT_USE_MEMPOOLS
  delete a_listNode;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::InitNode(Node* a_node)
{
  a_node->m_count = 0;
  a_node->m_level = -1;
}


RTREE_TEMPLATE
void RTREE_QUAL::InitRect(Rect* a_rect)
{
  for (int index = 0; index < NUMDIMS; ++index)
  {
    a_rect->m_min[index] = (ELEMTYPE)0;
    a_rect->m_max[index] = (ELEMTYPE)0;
  }
}


// Inserts a new data rectangle into the index structure.
// Recursively descends tree, propagates splits back up.
// Returns 0 if node was not split.  Old node updated.
// If node was split, returns 1 and sets the pointer pointed to by
// new_node to point to the new node.  Old node updated to become one of two.
// The level argument specifies the number of steps up from the leaf
// level to insert; e.g. a data rectangle goes in at level = 0.
RTREE_TEMPLATE
bool RTREE_QUAL::InsertRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, Node** a_newNode, int a_level)
{
  ASSERT(a_rect && a_node && a_newNode);
  ASSERT(a_level >= 0 && a_level <= a_node->m_level);

  int index;
  Branch branch;
  Node* otherNode;

  // Still above level for insertion, go down tree recursively
  if (a_node->m_level > a_level)
  {
    index = PickBranch(a_rect, a_node);
    if (!InsertRectRec(a_rect, a_id, a_node->m_branch[index].m_child, &otherNode, a_level))
    {
      // Child was not split
      a_node->m_branch[index].m_rect = CombineRect(a_rect, &(a_node->m_branch[index].m_rect));
      return false;
    }
    else // Child was split
    {
      a_node->m_branch[index].m_rect = NodeCover(a_node->m_branch[index].m_child);
      branch.m_child = otherNode;
      branch.m_rect = NodeCover(otherNode);
      return AddBranch(&branch, a_node, a_newNode);
    }
  }
  else if (a_node->m_level == a_level) // Have reached level for insertion. Add rect, split if necessary
  {
    branch.m_rect = *a_rect;
    branch.m_child = (Node*)a_id;
    // Child field of leaves contains id of data record
    return AddBranch(&branch, a_node, a_newNode);
  }
  else
  {
    // Should never occur
    ASSERT(0);
    return false;
  }
}


// Insert a data rectangle into an index structure.
// InsertRect provides for splitting the root;
// returns 1 if root was split, 0 if it was not.
// The level argument specifies the number of steps up from the leaf
// level to insert; e.g. a data rectangle goes in at level = 0.
// InsertRect2 does the recursion.
//
RTREE_TEMPLATE
bool RTREE_QUAL::InsertRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level)
{
  ASSERT(a_rect && a_root);
  ASSERT(a_level >= 0 && a_level <= (*a_root)->m_level);
#ifdef _DEBUG
  for (int index = 0; index < NUMDIMS; ++index)
  {
    ASSERT(a_rect->m_min[index] <= a_rect->m_max[index]);
  }
#endif //_DEBUG  

  Node* newRoot;
  Node* newNode;
  Branch branch;

  if (InsertRectRec(a_rect, a_id, *a_root, &newNode, a_level))  // Root split
  {
    newRoot = AllocNode();  // Grow tree taller and new root
    newRoot->m_level = (*a_root)->m_level + 1;
    branch.m_rect = NodeCover(*a_root);
    branch.m_child = *a_root;
    AddBranch(&branch, newRoot, NULL);
    branch.m_rect = NodeCover(newNode);
    branch.m_child = newNode;
    AddBranch(&branch, newRoot, NULL);
    *a_root = newRoot;
    return true;
  }

  return false;
}


// Find the smallest rectangle that includes all rectangles in branches of a node.
RTREE_TEMPLATE
typename RTREE_QUAL::Rect RTREE_QUAL::NodeCover(Node* a_node)
{
  ASSERT(a_node);

  int firstTime = true;
  Rect rect;
  InitRect(&rect);

  for (int index = 0; index < a_node->m_count; ++index)
  {
    if (firstTime)
    {
      rect = a_node->m_branch[index].m_rect;
      firstTime = false;
    }
    else
    {
      rect = CombineRect(&rect, &(a_node->m_branch[index].m_rect));
    }
  }

  return rect;
}


// Add a branch to a node.  Split the node if necessary.
// Returns 0 if node not split.  Old node updated.
// Returns 1 if node split, sets *new_node to address of new node.
// Old node updated, becomes one of two.
RTREE_TEMPLATE
bool RTREE_QUAL::AddBranch(Branch* a_branch, Node* a_node, Node** a_newNode)
{
  ASSERT(a_branch);
  ASSERT(a_node);

  if (a_node->m_count < MAXNODES)  // Split won't be necessary
  {
    a_node->m_branch[a_node->m_count] = *a_branch;
    ++a_node->m_count;

    return false;
  }
  else
  {
    ASSERT(a_newNode);

    SplitNode(a_node, a_branch, a_newNode);
    return true;
  }
}


// Disconnect a dependent node.
// Caller must return (or stop using iteration index) after this as count has changed
RTREE_TEMPLATE
void RTREE_QUAL::DisconnectBranch(Node* a_node, int a_index)
{
  ASSERT(a_node && (a_index >= 0) && (a_index < MAXNODES));
  ASSERT(a_node->m_count > 0);

  // Remove element by swapping with the last element to prevent gaps in array
  a_node->m_branch[a_index] = a_node->m_branch[a_node->m_count - 1];

  --a_node->m_count;
}


// Pick a branch.  Pick the one that will need the smallest increase
// in area to accomodate the new rectangle.  This will result in the
// least total area for the covering rectangles in the current node.
// In case of a tie, pick the one which was smaller before, to get
// the best resolution when searching.
RTREE_TEMPLATE
int RTREE_QUAL::PickBranch(Rect* a_rect, Node* a_node)
{
  ASSERT(a_rect && a_node);

  bool firstTime = true;
  ELEMTYPEREAL increase;
  ELEMTYPEREAL bestIncr = (ELEMTYPEREAL)-1;
  ELEMTYPEREAL area;
  ELEMTYPEREAL bestArea;
  int best;
  Rect tempRect;

  for (int index = 0; index < a_node->m_count; ++index)
  {
    Rect* curRect = &a_node->m_branch[index].m_rect;
    area = CalcRectVolume(curRect);
    tempRect = CombineRect(a_rect, curRect);
    increase = CalcRectVolume(&tempRect) - area;
    if ((increase < bestIncr) || firstTime)
    {
      best = index;
      bestArea = area;
      bestIncr = increase;
      firstTime = false;
    }
    else if ((increase == bestIncr) && (area < bestArea))
    {
      best = index;
      bestArea = area;
      bestIncr = increase;
    }
  }
  return best;
}


// Combine two rectangles into larger one containing both
RTREE_TEMPLATE
typename RTREE_QUAL::Rect RTREE_QUAL::CombineRect(Rect* a_rectA, Rect* a_rectB)
{
  ASSERT(a_rectA && a_rectB);

  Rect newRect;

  for (int index = 0; index < NUMDIMS; ++index)
  {
    newRect.m_min[index] = Min(a_rectA->m_min[index], a_rectB->m_min[index]);
    newRect.m_max[index] = Max(a_rectA->m_max[index], a_rectB->m_max[index]);
  }

  return newRect;
}



// Split a node.
// Divides the nodes branches and the extra one between two nodes.
// Old node is one of the new ones, and one really new one is created.
// Tries more than one method for choosing a partition, uses best result.
RTREE_TEMPLATE
void RTREE_QUAL::SplitNode(Node* a_node, Branch* a_branch, Node** a_newNode)
{
  ASSERT(a_node);
  ASSERT(a_branch);

  // Could just use local here, but member or external is faster since it is reused
  PartitionVars localVars;
  PartitionVars* parVars = &localVars;
  int level;

  // Load all the branches into a buffer, initialize old node
  level = a_node->m_level;
  GetBranches(a_node, a_branch, parVars);

  // Find partition
  ChoosePartition(parVars, MINNODES);

  // Put branches from buffer into 2 nodes according to chosen partition
  *a_newNode = AllocNode();
  (*a_newNode)->m_level = a_node->m_level = level;
  LoadNodes(a_node, *a_newNode, parVars);

  ASSERT((a_node->m_count + (*a_newNode)->m_count) == parVars->m_total);
}


// Calculate the n-dimensional volume of a rectangle
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::RectVolume(Rect* a_rect)
{
  ASSERT(a_rect);

  ELEMTYPEREAL volume = (ELEMTYPEREAL)1;

  for (int index = 0; index<NUMDIMS; ++index)
  {
    volume *= a_rect->m_max[index] - a_rect->m_min[index];
  }

  ASSERT(volume >= (ELEMTYPEREAL)0);

  return volume;
}


// The exact volume of the bounding sphere for the given Rect
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::RectSphericalVolume(Rect* a_rect)
{
  ASSERT(a_rect);

  ELEMTYPEREAL sumOfSquares = (ELEMTYPEREAL)0;
  ELEMTYPEREAL radius;

  for (int index = 0; index < NUMDIMS; ++index)
  {
    ELEMTYPEREAL halfExtent = ((ELEMTYPEREAL)a_rect->m_max[index] - (ELEMTYPEREAL)a_rect->m_min[index]) * 0.5f;
    sumOfSquares += halfExtent * halfExtent;
  }

  radius = (ELEMTYPEREAL)sqrt(sumOfSquares);

  // Pow maybe slow, so test for common dims like 2,3 and just use x*x, x*x*x.
  if (NUMDIMS == 3)
  {
    return (radius * radius * radius * m_unitSphereVolume);
  }
  else if (NUMDIMS == 2)
  {
    return (radius * radius * m_unitSphereVolume);
  }
  else
  {
    return (ELEMTYPEREAL)(pow(radius, NUMDIMS) * m_unitSphereVolume);
  }
}


// Use one of the methods to calculate retangle volume
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::CalcRectVolume(Rect* a_rect)
{
#ifdef RTREE_USE_SPHERICAL_VOLUME
  return RectSphericalVolume(a_rect); // Slower but helps certain merge cases
#else // RTREE_USE_SPHERICAL_VOLUME
  return RectVolume(a_rect); // Faster but can cause poor merges
#endif // RTREE_USE_SPHERICAL_VOLUME  
}


// Load branch buffer with branches from full node plus the extra branch.
RTREE_TEMPLATE
void RTREE_QUAL::GetBranches(Node* a_node, Branch* a_branch, PartitionVars* a_parVars)
{
  ASSERT(a_node);
  ASSERT(a_branch);

  ASSERT(a_node->m_count == MAXNODES);

  // Load the branch buffer
  for (int index = 0; index < MAXNODES; ++index)
  {
    a_parVars->m_branchBuf[index] = a_node->m_branch[index];
  }
  a_parVars->m_branchBuf[MAXNODES] = *a_branch;
  a_parVars->m_branchCount = MAXNODES + 1;

  // Calculate rect containing all in the set
  a_parVars->m_coverSplit = a_parVars->m_branchBuf[0].m_rect;
  for (int index = 1; index < MAXNODES + 1; ++index)
  {
    a_parVars->m_coverSplit = CombineRect(&a_parVars->m_coverSplit, &a_parVars->m_branchBuf[index].m_rect);
  }
  a_parVars->m_coverSplitArea = CalcRectVolume(&a_parVars->m_coverSplit);

  InitNode(a_node);
}


// Method #0 for choosing a partition:
// As the seeds for the two groups, pick the two rects that would waste the
// most area if covered by a single rectangle, i.e. evidently the worst pair
// to have in the same group.
// Of the remaining, one at a time is chosen to be put in one of the two groups.
// The one chosen is the one with the greatest difference in area expansion
// depending on which group - the rect most strongly attracted to one group
// and repelled from the other.
// If one group gets too full (more would force other group to violate min
// fill requirement) then other group gets the rest.
// These last are the ones that can go in either group most easily.
RTREE_TEMPLATE
void RTREE_QUAL::ChoosePartition(PartitionVars* a_parVars, int a_minFill)
{
  ASSERT(a_parVars);

  ELEMTYPEREAL biggestDiff;
  int group, chosen, betterGroup;

  InitParVars(a_parVars, a_parVars->m_branchCount, a_minFill);
  PickSeeds(a_parVars);

  while (((a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total)
    && (a_parVars->m_count[0] < (a_parVars->m_total - a_parVars->m_minFill))
    && (a_parVars->m_count[1] < (a_parVars->m_total - a_parVars->m_minFill)))
  {
    biggestDiff = (ELEMTYPEREAL)-1;
    for (int index = 0; index<a_parVars->m_total; ++index)
    {
      if (!a_parVars->m_taken[index])
      {
        Rect* curRect = &a_parVars->m_branchBuf[index].m_rect;
        Rect rect0 = CombineRect(curRect, &a_parVars->m_cover[0]);
        Rect rect1 = CombineRect(curRect, &a_parVars->m_cover[1]);
        ELEMTYPEREAL growth0 = CalcRectVolume(&rect0) - a_parVars->m_area[0];
        ELEMTYPEREAL growth1 = CalcRectVolume(&rect1) - a_parVars->m_area[1];
        ELEMTYPEREAL diff = growth1 - growth0;
        if (diff >= 0)
        {
          group = 0;
        }
        else
        {
          group = 1;
          diff = -diff;
        }

        if (diff > biggestDiff)
        {
          biggestDiff = diff;
          chosen = index;
          betterGroup = group;
        }
        else if ((diff == biggestDiff) && (a_parVars->m_count[group] < a_parVars->m_count[betterGroup]))
        {
          chosen = index;
          betterGroup = group;
        }
      }
    }
    Classify(chosen, betterGroup, a_parVars);
  }

  // If one group too full, put remaining rects in the other
  if ((a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total)
  {
    if (a_parVars->m_count[0] >= a_parVars->m_total - a_parVars->m_minFill)
    {
      group = 1;
    }
    else
    {
      group = 0;
    }
    for (int index = 0; index<a_parVars->m_total; ++index)
    {
      if (!a_parVars->m_taken[index])
      {
        Classify(index, group, a_parVars);
      }
    }
  }

  ASSERT((a_parVars->m_count[0] + a_parVars->m_count[1]) == a_parVars->m_total);
  ASSERT((a_parVars->m_count[0] >= a_parVars->m_minFill) &&
    (a_parVars->m_count[1] >= a_parVars->m_minFill));
}


// Copy branches from the buffer into two nodes according to the partition.
RTREE_TEMPLATE
void RTREE_QUAL::LoadNodes(Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars)
{
  ASSERT(a_nodeA);
  ASSERT(a_nodeB);
  ASSERT(a_parVars);

  for (int index = 0; index < a_parVars->m_total; ++index)
  {
    ASSERT(a_parVars->m_partition[index] == 0 || a_parVars->m_partition[index] == 1);

    if (a_parVars->m_partition[index] == 0)
    {
      AddBranch(&a_parVars->m_branchBuf[index], a_nodeA, NULL);
    }
    else if (a_parVars->m_partition[index] == 1)
    {
      AddBranch(&a_parVars->m_branchBuf[index], a_nodeB, NULL);
    }
  }
}


// Initialize a PartitionVars structure.
RTREE_TEMPLATE
void RTREE_QUAL::InitParVars(PartitionVars* a_parVars, int a_maxRects, int a_minFill)
{
  ASSERT(a_parVars);

  a_parVars->m_count[0] = a_parVars->m_count[1] = 0;
  a_parVars->m_area[0] = a_parVars->m_area[1] = (ELEMTYPEREAL)0;
  a_parVars->m_total = a_maxRects;
  a_parVars->m_minFill = a_minFill;
  for (int index = 0; index < a_maxRects; ++index)
  {
    a_parVars->m_taken[index] = false;
    a_parVars->m_partition[index] = -1;
  }
}


RTREE_TEMPLATE
void RTREE_QUAL::PickSeeds(PartitionVars* a_parVars)
{
  int seed0, seed1;
  ELEMTYPEREAL worst, waste;
  ELEMTYPEREAL area[MAXNODES + 1];

  for (int index = 0; index<a_parVars->m_total; ++index)
  {
    area[index] = CalcRectVolume(&a_parVars->m_branchBuf[index].m_rect);
  }

  worst = -a_parVars->m_coverSplitArea - 1;
  for (int indexA = 0; indexA < a_parVars->m_total - 1; ++indexA)
  {
    for (int indexB = indexA + 1; indexB < a_parVars->m_total; ++indexB)
    {
      Rect oneRect = CombineRect(&a_parVars->m_branchBuf[indexA].m_rect, &a_parVars->m_branchBuf[indexB].m_rect);
      waste = CalcRectVolume(&oneRect) - area[indexA] - area[indexB];
      if (waste > worst)
      {
        worst = waste;
        seed0 = indexA;
        seed1 = indexB;
      }
    }
  }
  Classify(seed0, 0, a_parVars);
  Classify(seed1, 1, a_parVars);
}


// Put a branch in one of the groups.
RTREE_TEMPLATE
void RTREE_QUAL::Classify(int a_index, int a_group, PartitionVars* a_parVars)
{
  ASSERT(a_parVars);
  ASSERT(!a_parVars->m_taken[a_index]);

  a_parVars->m_partition[a_index] = a_group;
  a_parVars->m_taken[a_index] = true;

  if (a_parVars->m_count[a_group] == 0)
  {
    a_parVars->m_cover[a_group] = a_parVars->m_branchBuf[a_index].m_rect;
  }
  else
  {
    a_parVars->m_cover[a_group] = CombineRect(&a_parVars->m_branchBuf[a_index].m_rect, &a_parVars->m_cover[a_group]);
  }
  a_parVars->m_area[a_group] = CalcRectVolume(&a_parVars->m_cover[a_group]);
  ++a_parVars->m_count[a_group];
}


// Delete a data rectangle from an index structure.
// Pass in a pointer to a Rect, the tid of the record, ptr to ptr to root node.
// Returns 1 if record not found, 0 if success.
// RemoveRect provides for eliminating the root.
RTREE_TEMPLATE
bool RTREE_QUAL::RemoveRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root)
{
  ASSERT(a_rect && a_root);
  ASSERT(*a_root);

  Node* tempNode;
  ListNode* reInsertList = NULL;

  if (!RemoveRectRec(a_rect, a_id, *a_root, &reInsertList))
  {
    // Found and deleted a data item
    // Reinsert any branches from eliminated nodes
    while (reInsertList)
    {
      tempNode = reInsertList->m_node;

      for (int index = 0; index < tempNode->m_count; ++index)
      {
        InsertRect(&(tempNode->m_branch[index].m_rect),
          tempNode->m_branch[index].m_data,
          a_root,
          tempNode->m_level);
      }

      ListNode* remLNode = reInsertList;
      reInsertList = reInsertList->m_next;

      FreeNode(remLNode->m_node);
      FreeListNode(remLNode);
    }

    // Check for redundant root (not leaf, 1 child) and eliminate
    if ((*a_root)->m_count == 1 && (*a_root)->IsInternalNode())
    {
      tempNode = (*a_root)->m_branch[0].m_child;

      ASSERT(tempNode);
      FreeNode(*a_root);
      *a_root = tempNode;
    }
    return false;
  }
  else
  {
    return true;
  }
}


// Delete a rectangle from non-root part of an index structure.
// Called by RemoveRect.  Descends tree recursively,
// merges branches on the way back up.
// Returns 1 if record not found, 0 if success.
RTREE_TEMPLATE
bool RTREE_QUAL::RemoveRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, ListNode** a_listNode)
{
  ASSERT(a_rect && a_node && a_listNode);
  ASSERT(a_node->m_level >= 0);

  if (a_node->IsInternalNode())  // not a leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (Overlap(a_rect, &(a_node->m_branch[index].m_rect)))
      {
        if (!RemoveRectRec(a_rect, a_id, a_node->m_branch[index].m_child, a_listNode))
        {
          if (a_node->m_branch[index].m_child->m_count >= MINNODES)
          {
            // child removed, just resize parent rect
            a_node->m_branch[index].m_rect = NodeCover(a_node->m_branch[index].m_child);
          }
          else
          {
            // child removed, not enough entries in node, eliminate node
            ReInsert(a_node->m_branch[index].m_child, a_listNode);
            DisconnectBranch(a_node, index); // Must return after this call as count has changed
          }
          return false;
        }
      }
    }
    return true;
  }
  else // A leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (a_node->m_branch[index].m_child == (Node*)a_id)
      {
        DisconnectBranch(a_node, index); // Must return after this call as count has changed
        return false;
      }
    }
    return true;
  }
}


// Decide whether two rectangles overlap.
RTREE_TEMPLATE
bool RTREE_QUAL::Overlap(Rect* a_rectA, Rect* a_rectB)
{
  ASSERT(a_rectA && a_rectB);

  for (int index = 0; index < NUMDIMS; ++index)
  {
    if (a_rectA->m_min[index] > a_rectB->m_max[index] ||
      a_rectB->m_min[index] > a_rectA->m_max[index])
    {
      return false;
    }
  }
  return true;
}


// Add a node to the reinsertion list.  All its branches will later
// be reinserted into the index structure.
RTREE_TEMPLATE
void RTREE_QUAL::ReInsert(Node* a_node, ListNode** a_listNode)
{
  ListNode* newListNode;

  newListNode = AllocListNode();
  newListNode->m_node = a_node;
  newListNode->m_next = *a_listNode;
  *a_listNode = newListNode;
}


// Search in an index tree or subtree for all data retangles that overlap the argument rectangle.
RTREE_TEMPLATE
bool RTREE_QUAL::Search(Node* a_node, Rect* a_rect, int& a_foundCount, bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context)
{
  ASSERT(a_node);
  ASSERT(a_node->m_level >= 0);
  ASSERT(a_rect);

  if (a_node->IsInternalNode()) // This is an internal node in the tree
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (Overlap(a_rect, &a_node->m_branch[index].m_rect))
      {
        if (!Search(a_node->m_branch[index].m_child, a_rect, a_foundCount, a_resultCallback, a_context))
        {
          return false; // Don't continue searching
        }
      }
    }
  }
  else // This is a leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (Overlap(a_rect, &a_node->m_branch[index].m_rect))
      {
        DATATYPE& id = a_node->m_branch[index].m_data;

        // NOTE: There are different ways to return results.  Here's where to modify
        if (&a_resultCallback)
        {
          ++a_foundCount;
          if (!a_resultCallback(id, a_context))
          {
            return false; // Don't continue searching
          }
        }
      }
    }
  }

  return true; // Continue searching
}


#undef RTREE_TEMPLATE
#undef RTREE_QUAL








//-------------------------------------------------------------


#define MERGE_INFINITY 1000000000



struct Rect
{
  int min[2];
  int max[2];
  bool valid;
};

int n;
Rect rects[100000];
int hits[100000];
int hitsCount;
int answer[100000];
int answerSize;
RTree<int, int, 2, float> spatialIndex;
int searchMin[2];
int searchMax[2];
int mergeMin[2];
int mergeMax[2];

bool searchCallback(int id, void* arg)
{
  hits[hitsCount++] = id;
  return true; // keep going
}

void search(int index)
{
  hitsCount = 0;
  Rect & r = rects[index];
  searchMin[0] = r.min[0] + 1;
  searchMin[1] = r.min[1] + 1;
  searchMax[0] = r.max[0] - 1;
  searchMax[1] = r.max[1] - 1;
  spatialIndex.Search(searchMin, searchMax, searchCallback, NULL);
}

bool answerLessOperator(int i1, int i2)
{
  Rect & r1 = rects[i1];
  Rect & r2 = rects[i2];
  if (r1.min[0] != r2.min[0])
    return r1.min[0] < r2.min[0];
  if (r1.max[0] != r2.max[0])
    return r1.max[0] < r2.max[0];
  if (r1.min[1] != r2.min[1])
    return r1.min[1] < r2.min[1];
  if (r1.max[1] != r2.max[1])
    return r1.max[1] < r2.max[1];
  return true;
}

int main()
{
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++)
  {
    Rect & r = rects[i];
    scanf("%d%d%d%d", r.min, r.max, r.min + 1, r.max + 1);
    r.min[0] <<= 1;
    r.min[1] <<= 1;
    r.max[0] <<= 1;
    r.max[1] <<= 1;
    r.valid = true;
    spatialIndex.Insert(r.min, r.max, i);
  } 

  for (int i = 0; i < n; i++)
  {
    Rect & r = rects[i];
    if (!r.valid)
      continue;

    search(i);
    if (hitsCount <= 1)
      continue;

    mergeMin[0] = MERGE_INFINITY;
    mergeMin[1] = MERGE_INFINITY;
    mergeMax[0] = -1;
    mergeMax[1] = -1;
    for (int si = 0; si < hitsCount; si++)
    {
      Rect & sr = rects[hits[si]];
      if (sr.min[0] < mergeMin[0])
        mergeMin[0] = sr.min[0];
      if (sr.min[1] < mergeMin[1])
        mergeMin[1] = sr.min[1];
      if (sr.max[0] > mergeMax[0])
        mergeMax[0] = sr.max[0];
      if (sr.max[1] > mergeMax[1])
        mergeMax[1] = sr.max[1];

      sr.valid = false;
      spatialIndex.Remove(sr.min, sr.max, hits[si]);
    }

    r.min[0] = mergeMin[0];
    r.min[1] = mergeMin[1];
    r.max[0] = mergeMax[0];
    r.max[1] = mergeMax[1];
    r.valid = true;
    spatialIndex.Insert(r.min, r.max, i);
    i--;
  }

  answerSize = 0;
  for (int i = 0; i < n; i++)
  {
    if (rects[i].valid)
      answer[answerSize++] = i;
  }

  sort(answer, answer + answerSize, answerLessOperator);

  printf("%d\n", answerSize);
  for (int i = 0; i < answerSize; i++)
  {
    Rect & ar = rects[answer[i]];
    printf("%d %d %d %d\n", ar.min[0] >> 1, ar.max[0] >> 1, ar.min[1] >> 1, ar.max[1] >> 1);
  }

  return 0;
}

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//RTree code taken from http://superliminal.com/sources/sources.htm
//RTree LICENSE: Entirely free for all uses.Enjoy!

#include <cstdio>
#include <cmath>
#include <cassert>
#include <cstdlib>
#include <algorithm>

using std::min;
using std::max;
using std::sort;

#define ASSERT assert // RTree uses ASSERT( condition )
#ifndef Min
#define Min min 
#endif //Min
#ifndef Max
#define Max max 
#endif //Max

//
// RTree.h
//

#define RTREE_TEMPLATE template<class DATATYPE, class ELEMTYPE, int NUMDIMS, class ELEMTYPEREAL, int TMAXNODES, int TMINNODES>
#define RTREE_QUAL RTree<DATATYPE, ELEMTYPE, NUMDIMS, ELEMTYPEREAL, TMAXNODES, TMINNODES>

#define RTREE_DONT_USE_MEMPOOLS // This version does not contain a fixed memory allocator, fill in lines with EXAMPLE to implement one.
#define RTREE_USE_SPHERICAL_VOLUME // Better split classification, may be slower on some systems


/// \class RTree
/// Implementation of RTree, a multidimensional bounding rectangle tree.
/// Example usage: For a 3-dimensional tree use RTree<Object*, float, 3> myTree;
///
/// This modified, templated C++ version by Greg Douglas at Auran (http://www.auran.com)
///
/// DATATYPE Referenced data, should be int, void*, obj* etc. no larger than sizeof<void*> and simple type
/// ELEMTYPE Type of element such as int or float
/// NUMDIMS Number of dimensions such as 2 or 3
/// ELEMTYPEREAL Type of element that allows fractional and large values such as float or double, for use in volume calcs
///
/// NOTES: Inserting and removing data requires the knowledge of its constant Minimal Bounding Rectangle.
///        This version uses new/delete for nodes, I recommend using a fixed size allocator for efficiency.
///        Instead of using a callback function for returned results, I recommend and efficient pre-sized, grow-only memory
///        array similar to MFC CArray or STL Vector for returning search query result.
///
template<class DATATYPE, class ELEMTYPE, int NUMDIMS,
class ELEMTYPEREAL = ELEMTYPE, int TMAXNODES = 8, int TMINNODES = TMAXNODES / 2>
class RTree
{
protected:

  struct Node;  // Fwd decl.  Used by other internal structs and iterator

public:

  // These constant must be declared after Branch and before Node struct
  // Stuck up here for MSVC 6 compiler.  NSVC .NET 2003 is much happier.
  enum
  {
    MAXNODES = TMAXNODES,                         ///< Max elements in node
    MINNODES = TMINNODES,                         ///< Min elements in node
  };


public:

  RTree();
  virtual ~RTree();

  /// Insert entry
  /// \param a_min Min of bounding rect
  /// \param a_max Max of bounding rect
  /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
  void Insert(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId);

  /// Remove entry
  /// \param a_min Min of bounding rect
  /// \param a_max Max of bounding rect
  /// \param a_dataId Positive Id of data.  Maybe zero, but negative numbers not allowed.
  void Remove(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId);

  /// Find all within search rectangle
  /// \param a_min Min of search bounding rect
  /// \param a_max Max of search bounding rect
  /// \param a_searchResult Search result array.  Caller should set grow size. Function will reset, not append to array.
  /// \param a_resultCallback Callback function to return result.  Callback should return 'true' to continue searching
  /// \param a_context User context to pass as parameter to a_resultCallback
  /// \return Returns the number of entries found
  int Search(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context);

  /// Remove all entries from tree
  void RemoveAll();

  /// Count the data elements in this container.  This is slow as no internal counter is maintained.
  int Count();

  /// Iterator is not remove safe.
  class Iterator
  {
  private:

    enum { MAX_STACK = 32 }; //  Max stack size. Allows almost n^32 where n is number of branches in node

    struct StackElement
    {
      Node* m_node;
      int m_branchIndex;
    };

  public:

    Iterator()                                    { Init(); }

    ~Iterator()                                   { }

    /// Is iterator invalid
    bool IsNull()                                 { return (m_tos <= 0); }

    /// Is iterator pointing to valid data
    bool IsNotNull()                              { return (m_tos > 0); }

    /// Access the current data element. Caller must be sure iterator is not NULL first.
    DATATYPE& operator*()
    {
      ASSERT(IsNotNull());
      StackElement& curTos = m_stack[m_tos - 1];
      return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
    }

    /// Access the current data element. Caller must be sure iterator is not NULL first.
    const DATATYPE& operator*() const
    {
      ASSERT(IsNotNull());
      StackElement& curTos = m_stack[m_tos - 1];
      return curTos.m_node->m_branch[curTos.m_branchIndex].m_data;
    }

    /// Find the next data element
    bool operator++()                             { return FindNextData(); }

    /// Get the bounds for this node
    void GetBounds(ELEMTYPE a_min[NUMDIMS], ELEMTYPE a_max[NUMDIMS])
    {
      ASSERT(IsNotNull());
      StackElement& curTos = m_stack[m_tos - 1];
      Branch& curBranch = curTos.m_node->m_branch[curTos.m_branchIndex];

      for (int index = 0; index < NUMDIMS; ++index)
      {
        a_min[index] = curBranch.m_rect.m_min[index];
        a_max[index] = curBranch.m_rect.m_max[index];
      }
    }

  private:

    /// Reset iterator
    void Init()                                   { m_tos = 0; }

    /// Find the next data element in the tree (For internal use only)
    bool FindNextData()
    {
      for (;;)
      {
        if (m_tos <= 0)
        {
          return false;
        }
        StackElement curTos = Pop(); // Copy stack top cause it may change as we use it

        if (curTos.m_node->IsLeaf())
        {
          // Keep walking through data while we can
          if (curTos.m_branchIndex + 1 < curTos.m_node->m_count)
          {
            // There is more data, just point to the next one
            Push(curTos.m_node, curTos.m_branchIndex + 1);
            return true;
          }
          // No more data, so it will fall back to previous level
        }
        else
        {
          if (curTos.m_branchIndex + 1 < curTos.m_node->m_count)
          {
            // Push sibling on for future tree walk
            // This is the 'fall back' node when we finish with the current level
            Push(curTos.m_node, curTos.m_branchIndex + 1);
          }
          // Since cur node is not a leaf, push first of next level to get deeper into the tree
          Node* nextLevelnode = curTos.m_node->m_branch[curTos.m_branchIndex].m_child;
          Push(nextLevelnode, 0);

          // If we pushed on a new leaf, exit as the data is ready at TOS
          if (nextLevelnode->IsLeaf())
          {
            return true;
          }
        }
      }
    }

    /// Push node and branch onto iteration stack (For internal use only)
    void Push(Node* a_node, int a_branchIndex)
    {
      m_stack[m_tos].m_node = a_node;
      m_stack[m_tos].m_branchIndex = a_branchIndex;
      ++m_tos;
      ASSERT(m_tos <= MAX_STACK);
    }

    /// Pop element off iteration stack (For internal use only)
    StackElement& Pop()
    {
      ASSERT(m_tos > 0);
      --m_tos;
      return m_stack[m_tos];
    }

    StackElement m_stack[MAX_STACK];              ///< Stack as we are doing iteration instead of recursion
    int m_tos;                                    ///< Top Of Stack index

    friend class RTree; // Allow hiding of non-public functions while allowing manipulation by logical owner
  };

  /// Get 'first' for iteration
  void GetFirst(Iterator& a_it)
  {
    a_it.Init();
    Node* first = m_root;
    while (first)
    {
      if (first->IsInternalNode() && first->m_count > 1)
      {
        a_it.Push(first, 1); // Descend sibling branch later
      }
      else if (first->IsLeaf())
      {
        if (first->m_count)
        {
          a_it.Push(first, 0);
        }
        break;
      }
      first = first->m_branch[0].m_child;
    }
  }

  /// Get Next for iteration
  void GetNext(Iterator& a_it)                    { ++a_it; }

  /// Is iterator NULL, or at end?
  bool IsNull(Iterator& a_it)                     { return a_it.IsNull(); }

  /// Get object at iterator position
  DATATYPE& GetAt(Iterator& a_it)                 { return *a_it; }

protected:

  /// Minimal bounding rectangle (n-dimensional)
  struct Rect
  {
    ELEMTYPE m_min[NUMDIMS];                      ///< Min dimensions of bounding box 
    ELEMTYPE m_max[NUMDIMS];                      ///< Max dimensions of bounding box 
  };

  /// May be data or may be another subtree
  /// The parents level determines this.
  /// If the parents level is 0, then this is data
  struct Branch
  {
    Rect m_rect;                                  ///< Bounds
    union
    {
      Node* m_child;                              ///< Child node
      DATATYPE m_data;                            ///< Data Id or Ptr
    };
  };

  /// Node for each branch level
  struct Node
  {
    bool IsInternalNode()                         { return (m_level > 0); } // Not a leaf, but a internal node
    bool IsLeaf()                                 { return (m_level == 0); } // A leaf, contains data

    int m_count;                                  ///< Count
    int m_level;                                  ///< Leaf is zero, others positive
    Branch m_branch[MAXNODES];                    ///< Branch
  };

  /// A link list of nodes for reinsertion after a delete operation
  struct ListNode
  {
    ListNode* m_next;                             ///< Next in list
    Node* m_node;                                 ///< Node
  };

  /// Variables for finding a split partition
  struct PartitionVars
  {
    int m_partition[MAXNODES + 1];
    int m_total;
    int m_minFill;
    int m_taken[MAXNODES + 1];
    int m_count[2];
    Rect m_cover[2];
    ELEMTYPEREAL m_area[2];

    Branch m_branchBuf[MAXNODES + 1];
    int m_branchCount;
    Rect m_coverSplit;
    ELEMTYPEREAL m_coverSplitArea;
  };

  Node* AllocNode();
  void FreeNode(Node* a_node);
  void InitNode(Node* a_node);
  void InitRect(Rect* a_rect);
  bool InsertRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, Node** a_newNode, int a_level);
  bool InsertRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level);
  Rect NodeCover(Node* a_node);
  bool AddBranch(Branch* a_branch, Node* a_node, Node** a_newNode);
  void DisconnectBranch(Node* a_node, int a_index);
  int PickBranch(Rect* a_rect, Node* a_node);
  Rect CombineRect(Rect* a_rectA, Rect* a_rectB);
  void SplitNode(Node* a_node, Branch* a_branch, Node** a_newNode);
  ELEMTYPEREAL RectSphericalVolume(Rect* a_rect);
  ELEMTYPEREAL RectVolume(Rect* a_rect);
  ELEMTYPEREAL CalcRectVolume(Rect* a_rect);
  void GetBranches(Node* a_node, Branch* a_branch, PartitionVars* a_parVars);
  void ChoosePartition(PartitionVars* a_parVars, int a_minFill);
  void LoadNodes(Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars);
  void InitParVars(PartitionVars* a_parVars, int a_maxRects, int a_minFill);
  void PickSeeds(PartitionVars* a_parVars);
  void Classify(int a_index, int a_group, PartitionVars* a_parVars);
  bool RemoveRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root);
  bool RemoveRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, ListNode** a_listNode);
  ListNode* AllocListNode();
  void FreeListNode(ListNode* a_listNode);
  bool Overlap(Rect* a_rectA, Rect* a_rectB);
  void ReInsert(Node* a_node, ListNode** a_listNode);
  bool Search(Node* a_node, Rect* a_rect, int& a_foundCount, bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context);
  void RemoveAllRec(Node* a_node);
  void Reset();
  void CountRec(Node* a_node, int& a_count);

  Node* m_root;                                    ///< Root of tree
  ELEMTYPEREAL m_unitSphereVolume;                 ///< Unit sphere constant for required number of dimensions
};


RTREE_TEMPLATE
RTREE_QUAL::RTree()
{
  ASSERT(MAXNODES > MINNODES);
  ASSERT(MINNODES > 0);


  // We only support machine word size simple data type eg. integer index or object pointer.
  // Since we are storing as union with non data branch
  ASSERT(sizeof(DATATYPE) == sizeof(void*) || sizeof(DATATYPE) == sizeof(int));

  // Precomputed volumes of the unit spheres for the first few dimensions
  const float UNIT_SPHERE_VOLUMES[] = {
    0.000000f, 2.000000f, 3.141593f, // Dimension  0,1,2
    4.188790f, 4.934802f, 5.263789f, // Dimension  3,4,5
    5.167713f, 4.724766f, 4.058712f, // Dimension  6,7,8
    3.298509f, 2.550164f, 1.884104f, // Dimension  9,10,11
    1.335263f, 0.910629f, 0.599265f, // Dimension  12,13,14
    0.381443f, 0.235331f, 0.140981f, // Dimension  15,16,17
    0.082146f, 0.046622f, 0.025807f, // Dimension  18,19,20 
  };

  m_root = AllocNode();
  m_root->m_level = 0;
  m_unitSphereVolume = (ELEMTYPEREAL)UNIT_SPHERE_VOLUMES[NUMDIMS];
}


RTREE_TEMPLATE
RTREE_QUAL::~RTree()
{
  Reset(); // Free, or reset node memory
}


RTREE_TEMPLATE
void RTREE_QUAL::Insert(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId)
{
#ifdef _DEBUG
  for (int index = 0; index<NUMDIMS; ++index)
  {
    ASSERT(a_min[index] <= a_max[index]);
  }
#endif //_DEBUG

  Rect rect;

  for (int axis = 0; axis<NUMDIMS; ++axis)
  {
    rect.m_min[axis] = a_min[axis];
    rect.m_max[axis] = a_max[axis];
  }

  InsertRect(&rect, a_dataId, &m_root, 0);
}


RTREE_TEMPLATE
void RTREE_QUAL::Remove(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], const DATATYPE& a_dataId)
{
#ifdef _DEBUG
  for (int index = 0; index<NUMDIMS; ++index)
  {
    ASSERT(a_min[index] <= a_max[index]);
  }
#endif //_DEBUG

  Rect rect;

  for (int axis = 0; axis<NUMDIMS; ++axis)
  {
    rect.m_min[axis] = a_min[axis];
    rect.m_max[axis] = a_max[axis];
  }

  RemoveRect(&rect, a_dataId, &m_root);
}


RTREE_TEMPLATE
int RTREE_QUAL::Search(const ELEMTYPE a_min[NUMDIMS], const ELEMTYPE a_max[NUMDIMS], bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context)
{
#ifdef _DEBUG
  for (int index = 0; index<NUMDIMS; ++index)
  {
    ASSERT(a_min[index] <= a_max[index]);
  }
#endif //_DEBUG

  Rect rect;

  for (int axis = 0; axis<NUMDIMS; ++axis)
  {
    rect.m_min[axis] = a_min[axis];
    rect.m_max[axis] = a_max[axis];
  }

  // NOTE: May want to return search result another way, perhaps returning the number of found elements here.

  int foundCount = 0;
  Search(m_root, &rect, foundCount, a_resultCallback, a_context);

  return foundCount;
}


RTREE_TEMPLATE
int RTREE_QUAL::Count()
{
  int count = 0;
  CountRec(m_root, count);

  return count;
}



RTREE_TEMPLATE
void RTREE_QUAL::CountRec(Node* a_node, int& a_count)
{
  if (a_node->IsInternalNode())  // not a leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      CountRec(a_node->m_branch[index].m_child, a_count);
    }
  }
  else // A leaf node
  {
    a_count += a_node->m_count;
  }
}

RTREE_TEMPLATE
void RTREE_QUAL::RemoveAll()
{
  // Delete all existing nodes
  Reset();

  m_root = AllocNode();
  m_root->m_level = 0;
}


RTREE_TEMPLATE
void RTREE_QUAL::Reset()
{
#ifdef RTREE_DONT_USE_MEMPOOLS
  // Delete all existing nodes
  RemoveAllRec(m_root);
#else // RTREE_DONT_USE_MEMPOOLS
  // Just reset memory pools.  We are not using complex types
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::RemoveAllRec(Node* a_node)
{
  ASSERT(a_node);
  ASSERT(a_node->m_level >= 0);

  if (a_node->IsInternalNode()) // This is an internal node in the tree
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      RemoveAllRec(a_node->m_branch[index].m_child);
    }
  }
  FreeNode(a_node);
}


RTREE_TEMPLATE
typename RTREE_QUAL::Node* RTREE_QUAL::AllocNode()
{
  Node* newNode;
#ifdef RTREE_DONT_USE_MEMPOOLS
  newNode = new Node;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
  InitNode(newNode);
  return newNode;
}


RTREE_TEMPLATE
void RTREE_QUAL::FreeNode(Node* a_node)
{
  ASSERT(a_node);

#ifdef RTREE_DONT_USE_MEMPOOLS
  delete a_node;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


// Allocate space for a node in the list used in DeletRect to
// store Nodes that are too empty.
RTREE_TEMPLATE
typename RTREE_QUAL::ListNode* RTREE_QUAL::AllocListNode()
{
#ifdef RTREE_DONT_USE_MEMPOOLS
  return new ListNode;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::FreeListNode(ListNode* a_listNode)
{
#ifdef RTREE_DONT_USE_MEMPOOLS
  delete a_listNode;
#else // RTREE_DONT_USE_MEMPOOLS
  // EXAMPLE
#endif // RTREE_DONT_USE_MEMPOOLS
}


RTREE_TEMPLATE
void RTREE_QUAL::InitNode(Node* a_node)
{
  a_node->m_count = 0;
  a_node->m_level = -1;
}


RTREE_TEMPLATE
void RTREE_QUAL::InitRect(Rect* a_rect)
{
  for (int index = 0; index < NUMDIMS; ++index)
  {
    a_rect->m_min[index] = (ELEMTYPE)0;
    a_rect->m_max[index] = (ELEMTYPE)0;
  }
}


// Inserts a new data rectangle into the index structure.
// Recursively descends tree, propagates splits back up.
// Returns 0 if node was not split.  Old node updated.
// If node was split, returns 1 and sets the pointer pointed to by
// new_node to point to the new node.  Old node updated to become one of two.
// The level argument specifies the number of steps up from the leaf
// level to insert; e.g. a data rectangle goes in at level = 0.
RTREE_TEMPLATE
bool RTREE_QUAL::InsertRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, Node** a_newNode, int a_level)
{
  ASSERT(a_rect && a_node && a_newNode);
  ASSERT(a_level >= 0 && a_level <= a_node->m_level);

  int index;
  Branch branch;
  Node* otherNode;

  // Still above level for insertion, go down tree recursively
  if (a_node->m_level > a_level)
  {
    index = PickBranch(a_rect, a_node);
    if (!InsertRectRec(a_rect, a_id, a_node->m_branch[index].m_child, &otherNode, a_level))
    {
      // Child was not split
      a_node->m_branch[index].m_rect = CombineRect(a_rect, &(a_node->m_branch[index].m_rect));
      return false;
    }
    else // Child was split
    {
      a_node->m_branch[index].m_rect = NodeCover(a_node->m_branch[index].m_child);
      branch.m_child = otherNode;
      branch.m_rect = NodeCover(otherNode);
      return AddBranch(&branch, a_node, a_newNode);
    }
  }
  else if (a_node->m_level == a_level) // Have reached level for insertion. Add rect, split if necessary
  {
    branch.m_rect = *a_rect;
    branch.m_child = (Node*)a_id;
    // Child field of leaves contains id of data record
    return AddBranch(&branch, a_node, a_newNode);
  }
  else
  {
    // Should never occur
    ASSERT(0);
    return false;
  }
}


// Insert a data rectangle into an index structure.
// InsertRect provides for splitting the root;
// returns 1 if root was split, 0 if it was not.
// The level argument specifies the number of steps up from the leaf
// level to insert; e.g. a data rectangle goes in at level = 0.
// InsertRect2 does the recursion.
//
RTREE_TEMPLATE
bool RTREE_QUAL::InsertRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root, int a_level)
{
  ASSERT(a_rect && a_root);
  ASSERT(a_level >= 0 && a_level <= (*a_root)->m_level);
#ifdef _DEBUG
  for (int index = 0; index < NUMDIMS; ++index)
  {
    ASSERT(a_rect->m_min[index] <= a_rect->m_max[index]);
  }
#endif //_DEBUG  

  Node* newRoot;
  Node* newNode;
  Branch branch;

  if (InsertRectRec(a_rect, a_id, *a_root, &newNode, a_level))  // Root split
  {
    newRoot = AllocNode();  // Grow tree taller and new root
    newRoot->m_level = (*a_root)->m_level + 1;
    branch.m_rect = NodeCover(*a_root);
    branch.m_child = *a_root;
    AddBranch(&branch, newRoot, NULL);
    branch.m_rect = NodeCover(newNode);
    branch.m_child = newNode;
    AddBranch(&branch, newRoot, NULL);
    *a_root = newRoot;
    return true;
  }

  return false;
}


// Find the smallest rectangle that includes all rectangles in branches of a node.
RTREE_TEMPLATE
typename RTREE_QUAL::Rect RTREE_QUAL::NodeCover(Node* a_node)
{
  ASSERT(a_node);

  int firstTime = true;
  Rect rect;
  InitRect(&rect);

  for (int index = 0; index < a_node->m_count; ++index)
  {
    if (firstTime)
    {
      rect = a_node->m_branch[index].m_rect;
      firstTime = false;
    }
    else
    {
      rect = CombineRect(&rect, &(a_node->m_branch[index].m_rect));
    }
  }

  return rect;
}


// Add a branch to a node.  Split the node if necessary.
// Returns 0 if node not split.  Old node updated.
// Returns 1 if node split, sets *new_node to address of new node.
// Old node updated, becomes one of two.
RTREE_TEMPLATE
bool RTREE_QUAL::AddBranch(Branch* a_branch, Node* a_node, Node** a_newNode)
{
  ASSERT(a_branch);
  ASSERT(a_node);

  if (a_node->m_count < MAXNODES)  // Split won't be necessary
  {
    a_node->m_branch[a_node->m_count] = *a_branch;
    ++a_node->m_count;

    return false;
  }
  else
  {
    ASSERT(a_newNode);

    SplitNode(a_node, a_branch, a_newNode);
    return true;
  }
}


// Disconnect a dependent node.
// Caller must return (or stop using iteration index) after this as count has changed
RTREE_TEMPLATE
void RTREE_QUAL::DisconnectBranch(Node* a_node, int a_index)
{
  ASSERT(a_node && (a_index >= 0) && (a_index < MAXNODES));
  ASSERT(a_node->m_count > 0);

  // Remove element by swapping with the last element to prevent gaps in array
  a_node->m_branch[a_index] = a_node->m_branch[a_node->m_count - 1];

  --a_node->m_count;
}


// Pick a branch.  Pick the one that will need the smallest increase
// in area to accomodate the new rectangle.  This will result in the
// least total area for the covering rectangles in the current node.
// In case of a tie, pick the one which was smaller before, to get
// the best resolution when searching.
RTREE_TEMPLATE
int RTREE_QUAL::PickBranch(Rect* a_rect, Node* a_node)
{
  ASSERT(a_rect && a_node);

  bool firstTime = true;
  ELEMTYPEREAL increase;
  ELEMTYPEREAL bestIncr = (ELEMTYPEREAL)-1;
  ELEMTYPEREAL area;
  ELEMTYPEREAL bestArea;
  int best;
  Rect tempRect;

  for (int index = 0; index < a_node->m_count; ++index)
  {
    Rect* curRect = &a_node->m_branch[index].m_rect;
    area = CalcRectVolume(curRect);
    tempRect = CombineRect(a_rect, curRect);
    increase = CalcRectVolume(&tempRect) - area;
    if ((increase < bestIncr) || firstTime)
    {
      best = index;
      bestArea = area;
      bestIncr = increase;
      firstTime = false;
    }
    else if ((increase == bestIncr) && (area < bestArea))
    {
      best = index;
      bestArea = area;
      bestIncr = increase;
    }
  }
  return best;
}


// Combine two rectangles into larger one containing both
RTREE_TEMPLATE
typename RTREE_QUAL::Rect RTREE_QUAL::CombineRect(Rect* a_rectA, Rect* a_rectB)
{
  ASSERT(a_rectA && a_rectB);

  Rect newRect;

  for (int index = 0; index < NUMDIMS; ++index)
  {
    newRect.m_min[index] = Min(a_rectA->m_min[index], a_rectB->m_min[index]);
    newRect.m_max[index] = Max(a_rectA->m_max[index], a_rectB->m_max[index]);
  }

  return newRect;
}



// Split a node.
// Divides the nodes branches and the extra one between two nodes.
// Old node is one of the new ones, and one really new one is created.
// Tries more than one method for choosing a partition, uses best result.
RTREE_TEMPLATE
void RTREE_QUAL::SplitNode(Node* a_node, Branch* a_branch, Node** a_newNode)
{
  ASSERT(a_node);
  ASSERT(a_branch);

  // Could just use local here, but member or external is faster since it is reused
  PartitionVars localVars;
  PartitionVars* parVars = &localVars;
  int level;

  // Load all the branches into a buffer, initialize old node
  level = a_node->m_level;
  GetBranches(a_node, a_branch, parVars);

  // Find partition
  ChoosePartition(parVars, MINNODES);

  // Put branches from buffer into 2 nodes according to chosen partition
  *a_newNode = AllocNode();
  (*a_newNode)->m_level = a_node->m_level = level;
  LoadNodes(a_node, *a_newNode, parVars);

  ASSERT((a_node->m_count + (*a_newNode)->m_count) == parVars->m_total);
}


// Calculate the n-dimensional volume of a rectangle
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::RectVolume(Rect* a_rect)
{
  ASSERT(a_rect);

  ELEMTYPEREAL volume = (ELEMTYPEREAL)1;

  for (int index = 0; index<NUMDIMS; ++index)
  {
    volume *= a_rect->m_max[index] - a_rect->m_min[index];
  }

  ASSERT(volume >= (ELEMTYPEREAL)0);

  return volume;
}


// The exact volume of the bounding sphere for the given Rect
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::RectSphericalVolume(Rect* a_rect)
{
  ASSERT(a_rect);

  ELEMTYPEREAL sumOfSquares = (ELEMTYPEREAL)0;
  ELEMTYPEREAL radius;

  for (int index = 0; index < NUMDIMS; ++index)
  {
    ELEMTYPEREAL halfExtent = ((ELEMTYPEREAL)a_rect->m_max[index] - (ELEMTYPEREAL)a_rect->m_min[index]) * 0.5f;
    sumOfSquares += halfExtent * halfExtent;
  }

  radius = (ELEMTYPEREAL)sqrt(sumOfSquares);

  // Pow maybe slow, so test for common dims like 2,3 and just use x*x, x*x*x.
  if (NUMDIMS == 3)
  {
    return (radius * radius * radius * m_unitSphereVolume);
  }
  else if (NUMDIMS == 2)
  {
    return (radius * radius * m_unitSphereVolume);
  }
  else
  {
    return (ELEMTYPEREAL)(pow(radius, NUMDIMS) * m_unitSphereVolume);
  }
}


// Use one of the methods to calculate retangle volume
RTREE_TEMPLATE
ELEMTYPEREAL RTREE_QUAL::CalcRectVolume(Rect* a_rect)
{
#ifdef RTREE_USE_SPHERICAL_VOLUME
  return RectSphericalVolume(a_rect); // Slower but helps certain merge cases
#else // RTREE_USE_SPHERICAL_VOLUME
  return RectVolume(a_rect); // Faster but can cause poor merges
#endif // RTREE_USE_SPHERICAL_VOLUME  
}


// Load branch buffer with branches from full node plus the extra branch.
RTREE_TEMPLATE
void RTREE_QUAL::GetBranches(Node* a_node, Branch* a_branch, PartitionVars* a_parVars)
{
  ASSERT(a_node);
  ASSERT(a_branch);

  ASSERT(a_node->m_count == MAXNODES);

  // Load the branch buffer
  for (int index = 0; index < MAXNODES; ++index)
  {
    a_parVars->m_branchBuf[index] = a_node->m_branch[index];
  }
  a_parVars->m_branchBuf[MAXNODES] = *a_branch;
  a_parVars->m_branchCount = MAXNODES + 1;

  // Calculate rect containing all in the set
  a_parVars->m_coverSplit = a_parVars->m_branchBuf[0].m_rect;
  for (int index = 1; index < MAXNODES + 1; ++index)
  {
    a_parVars->m_coverSplit = CombineRect(&a_parVars->m_coverSplit, &a_parVars->m_branchBuf[index].m_rect);
  }
  a_parVars->m_coverSplitArea = CalcRectVolume(&a_parVars->m_coverSplit);

  InitNode(a_node);
}


// Method #0 for choosing a partition:
// As the seeds for the two groups, pick the two rects that would waste the
// most area if covered by a single rectangle, i.e. evidently the worst pair
// to have in the same group.
// Of the remaining, one at a time is chosen to be put in one of the two groups.
// The one chosen is the one with the greatest difference in area expansion
// depending on which group - the rect most strongly attracted to one group
// and repelled from the other.
// If one group gets too full (more would force other group to violate min
// fill requirement) then other group gets the rest.
// These last are the ones that can go in either group most easily.
RTREE_TEMPLATE
void RTREE_QUAL::ChoosePartition(PartitionVars* a_parVars, int a_minFill)
{
  ASSERT(a_parVars);

  ELEMTYPEREAL biggestDiff;
  int group, chosen, betterGroup;

  InitParVars(a_parVars, a_parVars->m_branchCount, a_minFill);
  PickSeeds(a_parVars);

  while (((a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total)
    && (a_parVars->m_count[0] < (a_parVars->m_total - a_parVars->m_minFill))
    && (a_parVars->m_count[1] < (a_parVars->m_total - a_parVars->m_minFill)))
  {
    biggestDiff = (ELEMTYPEREAL)-1;
    for (int index = 0; index<a_parVars->m_total; ++index)
    {
      if (!a_parVars->m_taken[index])
      {
        Rect* curRect = &a_parVars->m_branchBuf[index].m_rect;
        Rect rect0 = CombineRect(curRect, &a_parVars->m_cover[0]);
        Rect rect1 = CombineRect(curRect, &a_parVars->m_cover[1]);
        ELEMTYPEREAL growth0 = CalcRectVolume(&rect0) - a_parVars->m_area[0];
        ELEMTYPEREAL growth1 = CalcRectVolume(&rect1) - a_parVars->m_area[1];
        ELEMTYPEREAL diff = growth1 - growth0;
        if (diff >= 0)
        {
          group = 0;
        }
        else
        {
          group = 1;
          diff = -diff;
        }

        if (diff > biggestDiff)
        {
          biggestDiff = diff;
          chosen = index;
          betterGroup = group;
        }
        else if ((diff == biggestDiff) && (a_parVars->m_count[group] < a_parVars->m_count[betterGroup]))
        {
          chosen = index;
          betterGroup = group;
        }
      }
    }
    Classify(chosen, betterGroup, a_parVars);
  }

  // If one group too full, put remaining rects in the other
  if ((a_parVars->m_count[0] + a_parVars->m_count[1]) < a_parVars->m_total)
  {
    if (a_parVars->m_count[0] >= a_parVars->m_total - a_parVars->m_minFill)
    {
      group = 1;
    }
    else
    {
      group = 0;
    }
    for (int index = 0; index<a_parVars->m_total; ++index)
    {
      if (!a_parVars->m_taken[index])
      {
        Classify(index, group, a_parVars);
      }
    }
  }

  ASSERT((a_parVars->m_count[0] + a_parVars->m_count[1]) == a_parVars->m_total);
  ASSERT((a_parVars->m_count[0] >= a_parVars->m_minFill) &&
    (a_parVars->m_count[1] >= a_parVars->m_minFill));
}


// Copy branches from the buffer into two nodes according to the partition.
RTREE_TEMPLATE
void RTREE_QUAL::LoadNodes(Node* a_nodeA, Node* a_nodeB, PartitionVars* a_parVars)
{
  ASSERT(a_nodeA);
  ASSERT(a_nodeB);
  ASSERT(a_parVars);

  for (int index = 0; index < a_parVars->m_total; ++index)
  {
    ASSERT(a_parVars->m_partition[index] == 0 || a_parVars->m_partition[index] == 1);

    if (a_parVars->m_partition[index] == 0)
    {
      AddBranch(&a_parVars->m_branchBuf[index], a_nodeA, NULL);
    }
    else if (a_parVars->m_partition[index] == 1)
    {
      AddBranch(&a_parVars->m_branchBuf[index], a_nodeB, NULL);
    }
  }
}


// Initialize a PartitionVars structure.
RTREE_TEMPLATE
void RTREE_QUAL::InitParVars(PartitionVars* a_parVars, int a_maxRects, int a_minFill)
{
  ASSERT(a_parVars);

  a_parVars->m_count[0] = a_parVars->m_count[1] = 0;
  a_parVars->m_area[0] = a_parVars->m_area[1] = (ELEMTYPEREAL)0;
  a_parVars->m_total = a_maxRects;
  a_parVars->m_minFill = a_minFill;
  for (int index = 0; index < a_maxRects; ++index)
  {
    a_parVars->m_taken[index] = false;
    a_parVars->m_partition[index] = -1;
  }
}


RTREE_TEMPLATE
void RTREE_QUAL::PickSeeds(PartitionVars* a_parVars)
{
  int seed0, seed1;
  ELEMTYPEREAL worst, waste;
  ELEMTYPEREAL area[MAXNODES + 1];

  for (int index = 0; index<a_parVars->m_total; ++index)
  {
    area[index] = CalcRectVolume(&a_parVars->m_branchBuf[index].m_rect);
  }

  worst = -a_parVars->m_coverSplitArea - 1;
  for (int indexA = 0; indexA < a_parVars->m_total - 1; ++indexA)
  {
    for (int indexB = indexA + 1; indexB < a_parVars->m_total; ++indexB)
    {
      Rect oneRect = CombineRect(&a_parVars->m_branchBuf[indexA].m_rect, &a_parVars->m_branchBuf[indexB].m_rect);
      waste = CalcRectVolume(&oneRect) - area[indexA] - area[indexB];
      if (waste > worst)
      {
        worst = waste;
        seed0 = indexA;
        seed1 = indexB;
      }
    }
  }
  Classify(seed0, 0, a_parVars);
  Classify(seed1, 1, a_parVars);
}


// Put a branch in one of the groups.
RTREE_TEMPLATE
void RTREE_QUAL::Classify(int a_index, int a_group, PartitionVars* a_parVars)
{
  ASSERT(a_parVars);
  ASSERT(!a_parVars->m_taken[a_index]);

  a_parVars->m_partition[a_index] = a_group;
  a_parVars->m_taken[a_index] = true;

  if (a_parVars->m_count[a_group] == 0)
  {
    a_parVars->m_cover[a_group] = a_parVars->m_branchBuf[a_index].m_rect;
  }
  else
  {
    a_parVars->m_cover[a_group] = CombineRect(&a_parVars->m_branchBuf[a_index].m_rect, &a_parVars->m_cover[a_group]);
  }
  a_parVars->m_area[a_group] = CalcRectVolume(&a_parVars->m_cover[a_group]);
  ++a_parVars->m_count[a_group];
}


// Delete a data rectangle from an index structure.
// Pass in a pointer to a Rect, the tid of the record, ptr to ptr to root node.
// Returns 1 if record not found, 0 if success.
// RemoveRect provides for eliminating the root.
RTREE_TEMPLATE
bool RTREE_QUAL::RemoveRect(Rect* a_rect, const DATATYPE& a_id, Node** a_root)
{
  ASSERT(a_rect && a_root);
  ASSERT(*a_root);

  Node* tempNode;
  ListNode* reInsertList = NULL;

  if (!RemoveRectRec(a_rect, a_id, *a_root, &reInsertList))
  {
    // Found and deleted a data item
    // Reinsert any branches from eliminated nodes
    while (reInsertList)
    {
      tempNode = reInsertList->m_node;

      for (int index = 0; index < tempNode->m_count; ++index)
      {
        InsertRect(&(tempNode->m_branch[index].m_rect),
          tempNode->m_branch[index].m_data,
          a_root,
          tempNode->m_level);
      }

      ListNode* remLNode = reInsertList;
      reInsertList = reInsertList->m_next;

      FreeNode(remLNode->m_node);
      FreeListNode(remLNode);
    }

    // Check for redundant root (not leaf, 1 child) and eliminate
    if ((*a_root)->m_count == 1 && (*a_root)->IsInternalNode())
    {
      tempNode = (*a_root)->m_branch[0].m_child;

      ASSERT(tempNode);
      FreeNode(*a_root);
      *a_root = tempNode;
    }
    return false;
  }
  else
  {
    return true;
  }
}


// Delete a rectangle from non-root part of an index structure.
// Called by RemoveRect.  Descends tree recursively,
// merges branches on the way back up.
// Returns 1 if record not found, 0 if success.
RTREE_TEMPLATE
bool RTREE_QUAL::RemoveRectRec(Rect* a_rect, const DATATYPE& a_id, Node* a_node, ListNode** a_listNode)
{
  ASSERT(a_rect && a_node && a_listNode);
  ASSERT(a_node->m_level >= 0);

  if (a_node->IsInternalNode())  // not a leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (Overlap(a_rect, &(a_node->m_branch[index].m_rect)))
      {
        if (!RemoveRectRec(a_rect, a_id, a_node->m_branch[index].m_child, a_listNode))
        {
          if (a_node->m_branch[index].m_child->m_count >= MINNODES)
          {
            // child removed, just resize parent rect
            a_node->m_branch[index].m_rect = NodeCover(a_node->m_branch[index].m_child);
          }
          else
          {
            // child removed, not enough entries in node, eliminate node
            ReInsert(a_node->m_branch[index].m_child, a_listNode);
            DisconnectBranch(a_node, index); // Must return after this call as count has changed
          }
          return false;
        }
      }
    }
    return true;
  }
  else // A leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (a_node->m_branch[index].m_child == (Node*)a_id)
      {
        DisconnectBranch(a_node, index); // Must return after this call as count has changed
        return false;
      }
    }
    return true;
  }
}


// Decide whether two rectangles overlap.
RTREE_TEMPLATE
bool RTREE_QUAL::Overlap(Rect* a_rectA, Rect* a_rectB)
{
  ASSERT(a_rectA && a_rectB);

  for (int index = 0; index < NUMDIMS; ++index)
  {
    if (a_rectA->m_min[index] > a_rectB->m_max[index] ||
      a_rectB->m_min[index] > a_rectA->m_max[index])
    {
      return false;
    }
  }
  return true;
}


// Add a node to the reinsertion list.  All its branches will later
// be reinserted into the index structure.
RTREE_TEMPLATE
void RTREE_QUAL::ReInsert(Node* a_node, ListNode** a_listNode)
{
  ListNode* newListNode;

  newListNode = AllocListNode();
  newListNode->m_node = a_node;
  newListNode->m_next = *a_listNode;
  *a_listNode = newListNode;
}


// Search in an index tree or subtree for all data retangles that overlap the argument rectangle.
RTREE_TEMPLATE
bool RTREE_QUAL::Search(Node* a_node, Rect* a_rect, int& a_foundCount, bool a_resultCallback(DATATYPE a_data, void* a_context), void* a_context)
{
  ASSERT(a_node);
  ASSERT(a_node->m_level >= 0);
  ASSERT(a_rect);

  if (a_node->IsInternalNode()) // This is an internal node in the tree
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (Overlap(a_rect, &a_node->m_branch[index].m_rect))
      {
        if (!Search(a_node->m_branch[index].m_child, a_rect, a_foundCount, a_resultCallback, a_context))
        {
          return false; // Don't continue searching
        }
      }
    }
  }
  else // This is a leaf node
  {
    for (int index = 0; index < a_node->m_count; ++index)
    {
      if (Overlap(a_rect, &a_node->m_branch[index].m_rect))
      {
        DATATYPE& id = a_node->m_branch[index].m_data;

        // NOTE: There are different ways to return results.  Here's where to modify
        if (&a_resultCallback)
        {
          ++a_foundCount;
          if (!a_resultCallback(id, a_context))
          {
            return false; // Don't continue searching
          }
        }
      }
    }
  }

  return true; // Continue searching
}


#undef RTREE_TEMPLATE
#undef RTREE_QUAL








//-------------------------------------------------------------


#define MERGE_INFINITY 1000000000



struct Rect
{
  int min[2];
  int max[2];
  bool valid;
};

int n;
Rect rects[100000];
int hits[100000];
int hitsCount;
int answer[100000];
int answerSize;
RTree<int, int, 2, float> spatialIndex;
int searchMin[2];
int searchMax[2];
int mergeMin[2];
int mergeMax[2];

bool searchCallback(int id, void* arg)
{
  hits[hitsCount++] = id;
  return true; // keep going
}

void search(int index)
{
  hitsCount = 0;
  Rect & r = rects[index];
  searchMin[0] = r.min[0] + 1;
  searchMin[1] = r.min[1] + 1;
  searchMax[0] = r.max[0] - 1;
  searchMax[1] = r.max[1] - 1;
  spatialIndex.Search(searchMin, searchMax, searchCallback, NULL);
}

bool answerLessOperator(int i1, int i2)
{
  Rect & r1 = rects[i1];
  Rect & r2 = rects[i2];
  if (r1.min[0] != r2.min[0])
    return r1.min[0] < r2.min[0];
  if (r1.max[0] != r2.max[0])
    return r1.max[0] < r2.max[0];
  if (r1.min[1] != r2.min[1])
    return r1.min[1] < r2.min[1];
  if (r1.max[1] != r2.max[1])
    return r1.max[1] < r2.max[1];
  return true;
}

int main()
{
  int n;
  scanf("%d", &n);
  for (int i = 0; i < n; i++)
  {
    Rect & r = rects[i];
    scanf("%d%d%d%d", r.min, r.max, r.min + 1, r.max + 1);
    r.min[0] <<= 1;
    r.min[1] <<= 1;
    r.max[0] <<= 1;
    r.max[1] <<= 1;
    r.valid = true;
    spatialIndex.Insert(r.min, r.max, i);
  } 

  for (int i = 0; i < n; i++)
  {
    Rect & r = rects[i];
    if (!r.valid)
      continue;

    search(i);
    if (hitsCount <= 1)
      continue;

    mergeMin[0] = MERGE_INFINITY;
    mergeMin[1] = MERGE_INFINITY;
    mergeMax[0] = -1;
    mergeMax[1] = -1;
    for (int si = 0; si < hitsCount; si++)
    {
      Rect & sr = rects[hits[si]];
      if (sr.min[0] < mergeMin[0])
        mergeMin[0] = sr.min[0];
      if (sr.min[1] < mergeMin[1])
        mergeMin[1] = sr.min[1];
      if (sr.max[0] > mergeMax[0])
        mergeMax[0] = sr.max[0];
      if (sr.max[1] > mergeMax[1])
        mergeMax[1] = sr.max[1];

      sr.valid = false;
      spatialIndex.Remove(sr.min, sr.max, hits[si]);
    }

    r.min[0] = mergeMin[0];
    r.min[1] = mergeMin[1];
    r.max[0] = mergeMax[0];
    r.max[1] = mergeMax[1];
    r.valid = true;
    spatialIndex.Insert(r.min, r.max, i);
    i--;
  }

  answerSize = 0;
  for (int i = 0; i < n; i++)
  {
    if (rects[i].valid)
      answer[answerSize++] = i;
  }

  sort(answer, answer + answerSize, answerLessOperator);

  printf("%d\n", answerSize);
  for (int i = 0; i < answerSize; i++)
  {
    Rect & ar = rects[answer[i]];
    printf("%d %d %d %d\n", ar.min[0] >> 1, ar.max[0] >> 1, ar.min[1] >> 1, ar.max[1] >> 1);
  }

  return 0;
}