// commenting everything out when I commit so all commits my code technically
// compiles
#include <algorithm>
#include <cassert>
#include <cstddef>
#include <initializer_list>
#include <optional>
#include <stdexcept>
#include <utility>
#include <vector>

// everything is super interconnected so some forward declarations are needed at
// various points
namespace cs440 {

template <typename Key_T, typename Mapped_T> class Map;

namespace {
enum class Color { Red, Black };
enum class Direction { Left, Right };
Direction operator!(Direction dir) {
  switch (dir) {
  case Direction::Left:
    return Direction::Right;
  case Direction::Right:
    return Direction::Left;
  default:
    // unreachable the only directions are left and right
    assert(false);
  }
}
template <typename Key_T, typename Mapped_T> struct BookKeeping {
  using Self = BookKeeping<Key_T, Mapped_T>;
  using ValueType = std::pair<Key_T, Mapped_T>;
  using Ptr = typename std::vector<Self>::iterator;
  friend class Map<Key_T, Mapped_T>;
  Map<Key_T, Mapped_T> &container;
  ValueType value;
  // Ptr self;
  Color color;
  // nullptr indicates empty
  std::optional<std::size_t> parent;
  std::optional<std::size_t> left;
  std::optional<std::size_t> right;
  std::optional<std::size_t> prev;
  std::optional<std::size_t> next;
  BookKeeping(Map<Key_T, Mapped_T> &container) : container{container} {}
  BookKeeping(BookKeeping const &rhs)
      : container{rhs.container}, value{rhs.value}, // self{rhs.self},
        color{rhs.color}, parent{rhs.parent}, left{rhs.left}, right{rhs.right},
        prev{rhs.prev}, next{rhs.next} {}
  // if pointing to different containers throws
  BookKeeping &operator=(BookKeeping const &rhs) {
    if (&this->container != &rhs.container) {
      throw std::invalid_argument{"can only reassign Bookkeeping "
                                  "values/iterators from the same map object"};
    }
    this->value = rhs.value;
    // this->self = rhs.self;
    this->color = rhs.color;
    this->parent = rhs.parent;
    this->left = rhs.left;
    this->right = rhs.right;
    this->prev = rhs.prev;
    this->next = rhs.next;
    return *this;
  }
  // reference to a pointer because the alternatives were worse
  inline Self *child(Direction dir) {
    auto ret = c_select(dir);
    return ret.has_value() ? &container.nodes[ret.value()] : nullptr;
  }
  inline std::optional<std::size_t> c_select(Direction dir) {
    switch (dir) {
    case Direction::Left:
      return left;
      break;
    case Direction::Right:
      return right;
      break;
    default:
      assert(false);
    }
  }
  inline void c_trans(Direction dir, Self *v) {
    switch (dir) {
    case Direction::Left:
      this->set_l(v);
      break;
    case Direction::Right:
      this->set_r(v);
      break;
    default:
      assert(false);
    }
  }

  inline Self *n() {
    return next.has_value() ? &container.nodes[next.value()] : nullptr;
  }
  inline void set_n(Self *ptr) {
    this->next = ptr == nullptr
                     ? std::nullopt
                     : std::optional<std::size_t>{static_cast<std::size_t>(
                           ptr - &this->container.nodes[0])};
  }
  inline Self *p() {
    return prev.has_value() ? &container.nodes[prev.value()] : nullptr;
  }
  inline void set_p(Self *ptr) {
    this->prev = ptr == nullptr
                     ? std::nullopt
                     : std::optional<std::size_t>{static_cast<std::size_t>(
                           ptr - &this->container.nodes[0])};
  }
  inline Self *r() {
    return right.has_value() ? &container.nodes[right.value()] : nullptr;
  }
  inline void set_r(Self *ptr) {
    this->right = ptr == nullptr
                      ? std::nullopt
                      : std::optional<std::size_t>{static_cast<std::size_t>(
                            ptr - &this->container.nodes[0])};
  }
  inline Self *l() {
    return left.has_value() ? &container.nodes[left.value()] : nullptr;
  }
  inline void set_l(Self *ptr) {
    this->left = ptr == nullptr
                     ? std::nullopt
                     : std::optional<std::size_t>{static_cast<std::size_t>(
                           ptr - &this->container.nodes[0])};
  }
  inline Self *par() {
    return parent.has_value() ? &container.nodes[parent.value()] : nullptr;
  }
  inline void set_par(Self *ptr) {
    this->parent = ptr == nullptr
                       ? std::nullopt
                       : std::optional<std::size_t>{static_cast<std::size_t>(
                             ptr - &this->container.nodes[0])};
  }
  // this is root/P for this method
  // copying from wikipedia RotateDirRoot with translation into my own idioms
  // https://en.wikipedia.org/wiki/Red%E2%80%93black_tree#Operations
  inline void rotate(Direction dir) {
    // wikipedia version uses alphabet soup, might fix later
    Self *P = this;
    auto &T = container;
    Self *G = P->par();
    Self *S = P->child(!dir);
    Self *C;

    // this tidbit is wrong and wikipedia is wrong to have this assert it seems
    // this method shouldn't be called in cases where this assert will trip
    // assert(S != nullptr);

    C = S->child(dir);
    P->c_trans(!dir, C);

    if (C != nullptr) {
      C->set_par(P);
    }
    S->c_trans(dir, P);
    P->set_par(S);
    S->set_par(G);
    if (G != nullptr) {
      if (P == G->r()) {
        G->set_r(S);
      } else {
        G->set_l(S);
      }
    } else {
      T.root = S - &T.nodes[0];
    }
  }
};
} // namespace
// https://en.wikipedia.org/wiki/Red%E2%80%93black_tree
template <typename Key_T, typename Mapped_T> class Map {
private:
  using ValueType = std::pair<Key_T, Mapped_T>;
  using Node = BookKeeping<Key_T, Mapped_T>;
  using Map_T = Map<Key_T, Mapped_T>;

public:
  class Iterator;
  class ConstIterator;
  class ReverseIterator;

  friend class Iterator;
  friend class ConstIterator;
  friend class ReverseIterator;
  friend Node;
  class Iterator {
    friend Map_T;
    friend Node;

  private:
    using Ref_T = std::optional<std::size_t>;
    Map<Key_T, Mapped_T> &parent;
    Ref_T ref;
    Ref_T escape;
    Iterator(Map<Key_T, Mapped_T> &parent, Ref_T ref,
             Ref_T escape = std::nullopt)
        : parent{parent}, ref{ref}, escape{escape} {}

  public:
    Iterator() = delete;
    Iterator &operator++() {
      if (ref == std::nullopt) {
        ref = escape;
        return *this;
      }
      if (parent.nodes[ref.value()].next == std::nullopt) {
        escape = ref;
      }
      ref = parent.nodes[ref.value()].next;
      return *this;
    }
    Iterator operator++(int) {
      Iterator tmp = *this;
      ++(*this);
      return tmp;
    }
    Iterator &operator--() {
      if (ref == std::nullopt) {
        ref = escape;
        return *this;
      }
      if (parent.nodes[ref.value()].prev == std::nullopt) {
        escape = ref;
      }
      ref = parent.nodes[ref.value()].prev;
      return *this;
    }
    Iterator operator--(int) {
      Iterator tmp = *this;
      --(*this);
      return tmp;
    }
    ValueType &operator*() const {
      return this->parent.nodes[this->ref.value()].value;
    }
    ValueType *operator->() const { return &this->operator*(); }
    friend bool operator==(Iterator const &lhs, Iterator const &rhs) {
      return lhs.ref == rhs.ref;
    }
    friend bool operator!=(Iterator const &lhs, Iterator const &rhs) {
      return lhs.ref != rhs.ref;
    }
    friend bool operator==(ConstIterator const &lhs, Iterator const &rhs) {
      return lhs.store_iter.ref == rhs.ref;
    }
    friend bool operator!=(ConstIterator const &lhs, Iterator const &rhs) {
      return lhs.store_iter.ref != rhs.ref;
    }
    friend bool operator==(Iterator const &lhs, ConstIterator const &rhs) {
      return lhs.ref == rhs.store_iter.ref;
    }
    friend bool operator!=(Iterator const &lhs, ConstIterator const &rhs) {
      return lhs.ref != rhs.store_iter.ref;
    }
  };
  class ConstIterator {
  public:
    friend class Map<Key_T, Mapped_T>;
    friend class Iterator;
    using underlying = Iterator;

  private:
    underlying store_iter;
    ConstIterator(underlying iter) : store_iter{iter} {}

  public:
    ConstIterator() = delete;
    friend bool operator==(ConstIterator const &lhs, ConstIterator const &rhs) {
      return lhs.store_iter == rhs.store_iter;
    }
    ConstIterator &operator++() {
      ++this->store_iter;
      return *this;
    }
    ConstIterator operator++(int) {
      ConstIterator tmp = *this;
      this->store_iter++;
      return tmp;
    }
    ConstIterator &operator--() {
      --this->store_iter;
      return *this;
    }
    ConstIterator operator--(int) {
      ConstIterator tmp = *this;
      this->store_iter--;
      return tmp;
    }
    const ValueType &operator*() const { return *this->store_iter; }
    const ValueType *operator->() const {
      return this->store_iter.operator->();
    }
    friend bool operator!=(ConstIterator const &lhs, ConstIterator const &rhs) {
      return lhs.store_iter != rhs.store_iter;
    }
  };
  class ReverseIterator {
  public:
    friend class Map<Key_T, Mapped_T>;
    friend class Iterator;
    using underlying = Iterator;

  private:
    underlying store_iter;

  public:
    ReverseIterator() = delete;
    ReverseIterator(underlying store_iter) : store_iter{store_iter} {}
    ReverseIterator &operator++() {
      --store_iter;
      return *this;
    }
    ReverseIterator operator++(int) {
      ReverseIterator ret = *this;
      ++(*this);
      return ret;
    }
    ReverseIterator &operator--() {
      ++store_iter;
      return *this;
    }
    ReverseIterator operator--(int) {
      ReverseIterator ret = *this;
      --(*this);
      return ret;
    }
    ValueType &operator*() const { return this->store_iter.ref->value; }
    ValueType *operator->() const { return &this->store_iter.ref->value; }
    friend bool operator==(ReverseIterator const &lhs,
                           ReverseIterator const &rhs) {
      return lhs.store_iter == rhs.store_iter;
    }
    friend bool operator!=(ConstIterator const &lhs, ConstIterator const &rhs) {
      return lhs.store_iter != rhs.store_iter;
    }
  };

private:
  std::optional<std::size_t> root;
  std::optional<std::size_t> min;
  std::optional<std::size_t> max;
  std::vector<Node> nodes;
  std::size_t size_diff;

  std::optional<std::size_t> pred(std::size_t node) {
    if (this->nodes[node].left.has_value()) {
      std::size_t store = this->nodes[node].left.value();
      while (this->nodes[store].right.has_value()) {
        store = this->nodes[node].right.value();
      }
      return store;
    } else {
      if (!this->nodes[node].parent.has_value()) {
        return std::nullopt;
      }

      std::size_t prev_store = node;
      std::size_t store = this->nodes[node].parent.value();
      while (this->nodes[store].parent.has_value()) {
        if (this->nodes[store].right == prev_store) {
          return store;
        }
        prev_store = store;
        store = this->nodes[store].parent.value();
      }
      return std::nullopt;
    }
  }
  std::optional<std::size_t> succ(std::size_t node) {
    if (this->nodes[node].right.has_value()) {
      std::size_t store = this->nodes[node].right.value();
      while (this->nodes[store].left.has_value()) {
        store = this->nodes[node].left.value();
      }
      return store;
    } else {
      if (!this->nodes[node].parent.has_value()) {
        return std::nullopt;
      }

      std::size_t prev_store = node;
      std::size_t store = this->nodes[prev_store].parent.value();
      while (this->nodes[store].parent.has_value()) {
        if (this->nodes[store].left == prev_store) {
          return store;
        }
        prev_store = store;
        store = this->nodes[store].parent.value();
      }
      return std::nullopt;
    }
  }

public:
  Map()
      : root{std::nullopt}, min{std::nullopt}, max{std::nullopt}, nodes{},
        size_diff{0} {}
  Map(const Map &rhs)
      : root{rhs.root}, min{rhs.min}, max{rhs.max}, nodes{rhs.nodes},
        size_diff{0} {}
  Map &operator=(const Map &rhs) {
    this->root = rhs.root;
    this->min = rhs.min;
    this->max = rhs.max;
    this->nodes = rhs.nodes;
  }
  Map(std::initializer_list<ValueType> elems)
      : root{std::nullopt}, min{std::nullopt}, max{std::nullopt}, nodes{} {
    this->insert(elems.begin(), elems.end());
  }

  ~Map() {}

  size_t size() const { return this->nodes.size() - this->size_diff; }
  bool empty() const { return this->size() == 0; }

  Iterator begin() { return Iterator{*this, min}; }
  Iterator end() { return Iterator{*this, std::nullopt, max}; }
  ConstIterator begin() const { return ConstIterator{*this, this->begin()}; }
  ConstIterator end() const { return ConstIterator{*this, this->end()}; }
  ConstIterator cbegin() const { return this->begin(); }
  ConstIterator cend() const { return this->end(); }
  ReverseIterator rbegin() {
    return ReverseIterator{Iterator{*this, this->max}};
  }
  ReverseIterator rend() {
    return ReverseIterator{Iterator{*this, nullptr, min}};
  }
  Iterator find(const Key_T &key) {
    // we need a locate slot function for insert regardless so might as well use
    // it here
    auto [parent, dir] = this->locate_slot(key);
    if (!parent.has_value()) {
      if (this->root.has_value() &&
          this->nodes[this->root.value()].value.first == key) {
        return Iterator{*this, root};
      } else {
        return this->end();
      }
    }
    if (!this->nodes[parent.value()].c_select(dir).has_value()) {
      return this->end();
    }
    return Iterator{*this, this->nodes[parent.value()].c_select(dir)};
  }
  // implicit cast to ConstIterator from Iterator
  ConstIterator find(const Key_T &key) const { return this->find(key); }

  Mapped_T &at(const Key_T &key) {
    auto ret = this->find(key);
    if (ret == this->end()) {
      throw std::out_of_range{"Key not in map"};
    }
    return ret->second;
  }
  const Mapped_T &at(const Key_T &key) const {
    auto ret = this->find(key);
    if (ret == this->end()) {
      throw std::out_of_range{"Key not in map"};
    }
    return ret->second;
  }
  Mapped_T &operator[](const Key_T &key) {
    Mapped_T v;
    auto insert_val = std::make_pair(key, v);
    auto [iter, key_no_exist] = this->insert(insert_val);
    return iter->second;
  }

private:
  void handle_root_rotation(std::optional<std::size_t> g,
                            std::optional<std::size_t> p,
                            std::optional<std::size_t> i, Direction dir) {
    handle_root_rotation(g.has_value() ? &this->nodes[g.value()] : nullptr,
                         p.has_value() ? &this->nodes[p.value()] : nullptr,
                         i.has_value() ? &this->nodes[i.value()] : nullptr,
                         dir);
  }
  void handle_root_rotation(Node *grandparent, Node *parent, Node *inserting,
                            Direction dir) {
    // making inner grandchild into outer grandchild

    if (inserting == parent->child(!dir)) {
      parent->rotate(dir);
      inserting = parent;
      parent = grandparent->child(dir);
    }
    grandparent->rotate(!dir);

    parent->color = Color::Black;
    grandparent->color = Color::Red;
  }
  using Ref_T = std::optional<std::size_t>;
  // heavily referencing the wikipedia implementation for this
  // https://en.wikipedia.org/wiki/Red%E2%80%93black_tree#Insertion
  void insert_helper(Ref_T to_insert, Ref_T parent, Direction dir) {
    // initialize the element we're inserting
    this->nodes[to_insert.value()].color = Color::Red;
    this->nodes[to_insert.value()].left = std::nullopt;
    this->nodes[to_insert.value()].right = std::nullopt;
    this->nodes[to_insert.value()].next = std::nullopt;
    this->nodes[to_insert.value()].prev = std::nullopt;
    this->nodes[to_insert.value()].parent = parent;

    // if this is the first element to be inserted it's root
    if (!this->nodes[to_insert.value()].parent.has_value()) {
      this->root = to_insert;
      this->nodes[to_insert.value()].color = Color::Black;
      return;
    }

    switch (dir) {
    case Direction::Left:
      this->nodes[parent.value()].left = to_insert;
      break;
    case Direction::Right:
      this->nodes[parent.value()].right = to_insert;
      break;
    }

    do {
      // don't need to keep track of these in between loops they get
      // recalculated
      std::optional<std::size_t> grandparent;
      std::optional<std::size_t> uncle;
      if (this->nodes[parent.value()].color == Color::Black) {
        // black parent means invariants definitely hold
        return;
      }

      grandparent = this->nodes[parent.value()].parent;

      if (!grandparent.has_value()) {
        // parent is root, just need to recolor it to black
        this->nodes[parent.value()].color = Color::Black;
        return;
      }

      Direction parent_direction;
      if (this->nodes[grandparent.value()].left == parent) {
        parent_direction = Direction::Left;
        uncle = this->nodes[grandparent.value()].right;
      } else {
        parent_direction = Direction::Right;
        uncle = this->nodes[grandparent.value()].left;
      }

      if (!uncle.has_value() ||
          this->nodes[uncle.value()].color == Color::Black) {
        if (to_insert == this->nodes[parent.value()].c_select(!dir)) {
          // case 5
          this->nodes[parent.value()].rotate(dir);
          to_insert = parent;
          parent = this->nodes[grandparent.value()].c_select(dir);
        }
        // case 6
        this->handle_root_rotation(grandparent, parent, to_insert,
                                   parent_direction);
        return;
      }

      // now we know parent and uncle are both red so red-black coloring can be
      // pushed down from grandparent
      this->nodes[parent.value()].color = Color::Black;
      this->nodes[uncle.value()].color = Color::Black;
      this->nodes[grandparent.value()].color = Color::Red;

      to_insert = grandparent;
      parent = this->nodes[to_insert.value()].parent;
    } while (parent.has_value());

    // case 3: current node is red root so we're done
  }
  // returns nullptr iff map is empty
  std::pair<std::optional<std::size_t>, Direction>
  locate_slot(const Key_T &key) {
    using Ref_T = std::optional<std::size_t>;
    Ref_T current = this->root;
    Ref_T parent = std::nullopt;
    Direction dir;
    while (current.has_value() &&
           this->nodes[current.value()].value.first != key) {
      parent = current;
      if (key < this->nodes[current.value()].value.first) {
        dir = Direction::Left;
        current = this->nodes[current.value()].left;
      } else {
        dir = Direction::Right;
        current = this->nodes[current.value()].right;
      }
    }
    return std::make_pair(parent, dir);
  }

public:
  // If the key does not already exist in the map, it returns an iterator
  // pointing to the new element, and true. If the key already exists, no
  // insertion is performed nor is the mapped object changed, and it returns
  // an iterator pointing to the element with the same key, and false.
  std::pair<Iterator, bool> insert(const ValueType &val) {
    auto [parent, dir] = locate_slot(val.first);
    bool ret = !parent.has_value() ||
               !this->nodes[parent.value()].c_select(dir).has_value();
    if (!ret) {
      return std::make_pair(
          Iterator{*this, this->nodes[parent.value()].c_select(dir)}, ret);
    }
    Node to_insert{*this};
    to_insert.value = val;
    this->nodes.push_back(std::move(to_insert));
    // this->nodes.back().self = (--this->nodes.end());
    insert_helper(nodes.size() - 1, parent, dir);

    if (min == std::nullopt ||
        val.first < this->nodes[min.value()].value.first) {
      min = nodes.size() - 1;
    }
    if (max == std::nullopt ||
        val.first > this->nodes[max.value()].value.first) {
      max = nodes.size() - 1;
    }
    Ref_T successor = this->succ(this->nodes.size() - 1);
    Ref_T predessor = this->pred(this->nodes.size() - 1);
    if (successor.has_value()) {
      this->nodes[successor.value()].prev = this->nodes.size() - 1;
    }
    this->nodes[this->nodes.size() - 1].next = successor;
    if (predessor.has_value()) {
      this->nodes[predessor.value()].next = this->nodes.size() - 1;
    }
    this->nodes[this->nodes.size() - 1].prev = successor;
    return std::make_pair(Iterator(*this, nodes.size() - 1), ret);
  }
  template <typename IT_T> void insert(IT_T range_beg, IT_T range_end) {
    std::for_each(range_beg, range_end,
                  [&](ValueType &val) { this->insert(val); });
  }

private:
  void case5(Node *parent, Node *sibling, Node *close_nephew,
             Node *distant_nephew, Direction dir) {
    sibling->rotate(!dir);
    sibling->color = Color::Red;
    close_nephew->color = Color::Black;
    distant_nephew = sibling;
    sibling = close_nephew;
    case6(parent, sibling, distant_nephew, dir);
  }
  void case6(Node *parent, Node *sibling, Node *distant_nephew, Direction dir) {
    parent->rotate(dir);
    sibling->color = parent->color;
    parent->color = Color::Black;
    distant_nephew->color = Color::Black;
  }
  // heavily referring to
  // https://en.wikipedia.org/wiki/Red%E2%80%93black_tree#Removal_of_a_black_non-root_leaf
  void complex_erase(Iterator pos) {

    Node *to_delete = &this->nodes[pos.ref.value()];
    Node *parent = to_delete->par();
    assert(parent != nullptr);

    Direction dir =
        parent->r() == to_delete ? Direction::Right : Direction::Left;

    Node *sibling;
    ;
    Node *close_nephew;
    Node *distant_nephew;

    parent->c_trans(dir, nullptr);

    do {
      dir = parent->r() == to_delete ? Direction::Right : Direction::Left;

      sibling = parent->child(!dir);
      distant_nephew = sibling->child(!dir);
      close_nephew = sibling->child(dir);

      if (sibling->color == Color::Red) {
        // case 3
        parent->rotate(dir);
        parent->color = Color::Red;
        sibling->color = Color::Black;
        sibling = close_nephew;
        // redundant?
        distant_nephew = sibling->child(!dir);
        if (distant_nephew != nullptr && distant_nephew->color == Color::Red) {
          case6(parent, sibling, distant_nephew, dir);
          return;
        }
        close_nephew = sibling->child(dir);
        if (close_nephew != nullptr && close_nephew->color == Color::Red) {
          case5(parent, sibling, close_nephew, distant_nephew, dir);
          return;
        }
        sibling->color = Color::Red;
        parent->color = Color::Black;
        return;
      }

      if (distant_nephew != nullptr && distant_nephew->color == Color::Red) {
        case6(parent, sibling, distant_nephew, dir);
        return;
      }

      if (close_nephew != nullptr && close_nephew->color == Color::Red) {
        case5(parent, sibling, close_nephew, distant_nephew, dir);
        return;
      }

      if (parent->color == Color::Red) {
        // case 4
        sibling->color = Color::Red;
        parent->color = Color::Black;
        return;
      }

      // case 2
      sibling->color = Color::Red;
      to_delete = parent;
      parent = to_delete->par();
    } while (parent != nullptr);
  }

public:
  void erase(Iterator pos) {
    this->size_diff++;
    // simple cases
    Node *ref = &this->nodes[pos.ref.value()];
    if (ref ==
        (this->min.has_value() ? &this->nodes[this->min.value()] : nullptr)) {
      this->min = ref->next;
    }
    if (ref ==
        (this->max.has_value() ? &this->nodes[this->max.value()] : nullptr)) {
      this->max = ref->prev;
    }
    // 2 children
    if (ref->l() != nullptr && ref->r() != nullptr) {
      Ref_T next = ref->next;
      *ref = this->nodes[next.value()];
      this->erase(Iterator{*this, next});
    }
    // single child which is left
    else if (ref->l() != nullptr && ref->r() == nullptr) {
      if (ref->par()->l() == ref) {
        ref->par()->set_l(ref->l());
      } else {
        ref->par()->set_r(ref->l());
      }
      if (ref->color == Color::Black) {
        ref->l()->color = Color::Black;
      }
    }
    // single child which is right
    else if (ref->l() == nullptr && ref->r() != nullptr) {
      if (ref->par()->l() == ref) {
        ref->par()->set_l(ref->r());
      } else {
        ref->par()->set_r(ref->r());
      }
      if (ref->color == Color::Black) {
        ref->r()->color = Color::Black;
      }
    }
    // no children and root
    else if (this->root == pos.ref && ref->l() == nullptr &&
             ref->r() == nullptr) {
      this->root = std::nullopt;
    }
    // no children and red
    else if (ref->color == Color::Red && ref->l() == nullptr &&
             ref->r() == nullptr) {
      if (ref->parent.has_value()) {
        if (this->nodes[ref->parent.value()].right == pos.ref.value()) {
          this->nodes[ref->parent.value()].right = std::nullopt;
        } else {
          this->nodes[ref->parent.value()].left = std::nullopt;
        }
      }
    }
    // complicated case of black node with no kids
    else {
      this->complex_erase(pos);
    }
    if (ref->next.has_value()) {
      this->nodes[ref->next.value()].prev = this->pred(ref->next.value());
    }
    if (ref->prev.has_value()) {
      this->nodes[ref->next.value()].next = this->succ(ref->next.value());
    }
  }
  void erase(const Key_T &key) { this->erase(this->find(key)); }
  void clear() {
    this->root = std::nullopt;
    this->nodes.clear();
  }
  friend bool operator==(const Map &lhs, const Map &rhs) {
    if (lhs.nodes.size() != rhs.nodes.size()) {
      return false;
    }
    auto liter = lhs.cbegin();
    auto riter = rhs.cbegin();
    // both must be the same length so this is fine
    while (liter != lhs.cend()) {
      if (*liter != *riter) {
        return false;
      }
      liter++;
      riter++;
    }
    return true;
  }
  friend bool operator!=(const Map &lhs, const Map &rhs) {
    return !(lhs == rhs);
  }
  friend bool operator<(const Map &lhs, const Map &rhs) {
    auto l_iter = lhs.cbegin();
    auto r_iter = rhs.cbegin();
    for (; l_iter != lhs.cend() && r_iter != rhs.cend(); l_iter++, r_iter++) {
      if (*l_iter < *r_iter) {
        return true;
      }
    }
    return lhs.size() < rhs.size();
  }
};
} // namespace cs440