#ifndef __GBLIBCPP_BITS_RBTREE__
#define __GBLIBCPP_BITS_RBTREE__

#include "compressed_pair"

#include <cstddef>
#include <functional>
#include <utility>
#include <memory>

namespace std::impl {

template <typename T, typename Compare, typename Allocator>
struct rbtree {
    struct node {
        node* parent;
        node* left;
        node* right;
        T value;
        enum class node_color : unsigned char { RED, BLACK, } color;

        constexpr node(const T& val)
            : parent {}, left {}, right {}
            , value { val } , color {node_color::RED} {}

        constexpr node(T&& val)
            : parent {}, left {}, right {}
            , value { std::move(val) } , color {node_color::RED} {}

        template <typename... Args, std::enable_if_t<
            (sizeof...(Args) > 1)
            || !(... && std::is_same_v<T, std::remove_cvref_t<Args>>)
        , bool> = true>
        constexpr node(Args&&... args)
            : parent {}, left {}, right {}
            , value { std::forward<Args>(args)... }, color { node_color::RED } {}

        constexpr node* grandparent(void) const
        { return this->parent->parent; }

        constexpr node* uncle(void) const
        {
            node* pp = this->grandparent();
            if (this->parent == pp->left)
                return pp->right;
            return pp->left;
        }

        constexpr node* leftmost(void)
        {
            node* nd = this;
            while (nd->left)
                nd = nd->left;
            return nd;
        }

        constexpr node* rightmost(void)
        {
            node* nd = this;
            while (nd->right)
                nd = nd->right;
            return nd;
        }

        constexpr node* next(void)
        {
            if (this->right)
                return this->right->leftmost();
            if (this->is_root())
                return nullptr;
            if (this->is_left_child())
                return this->parent;
            node* ret = this;
            do {
                ret = ret->parent;
            } while (!ret->is_root() && !ret->is_left_child());
            return ret->parent;
        }

        constexpr node* prev(void)
        {
            if (this->left)
                return this->left->rightmost();
            if (this->is_root())
                return nullptr;
            if (this->is_right_child())
                return this->parent;
            node* ret = this;
            do {
                ret = ret->parent;
            } while (!ret->is_root() && !ret->is_right_child());
            return ret->parent;
        }

        static constexpr bool is_red(node* nd)
        { return nd && nd->color == node_color::RED; }
        static constexpr bool is_black(node* nd)
        { return !node::is_red(nd); }

        constexpr bool is_root(void) const
        { return this->parent == nullptr; }
        constexpr bool is_full(void) const
        { return this->left && this->right; }
        constexpr bool has_child(void) const
        { return this->left || this->right; }
        constexpr bool is_leaf(void) const
        { return !this->has_child(); }

        constexpr bool is_left_child(void) const
        { return this == this->parent->left; }
        constexpr bool is_right_child(void) const
        { return this == this->parent->right; }

        constexpr void tored(void)
        { this->color = node_color::RED; }
        constexpr void toblack(void)
        { this->color = node_color::BLACK; }

        static constexpr void swap(node* first, node* second)
        {
            if (node::is_red(first)) {
                first->color = second->color;
                second->color = node_color::RED;
            } else {
                first->color = second->color;
                second->color = node_color::BLACK;
            }

            if (first->parent == second) {
                node* tmp = first;
                first = second;
                second = tmp;
            }

            bool f_is_left_child = first->parent ? first->is_left_child() : false;
            bool s_is_left_child = second->parent ? second->is_left_child() : false;

            node* fp = first->parent;
            node* fl = first->left;
            node* fr = first->right;

            node* sp = second->parent;
            node* sl = second->left;
            node* sr = second->right;

            if (second->parent != first) {
                first->parent = sp;
                if (sp) {
                    if (s_is_left_child)
                        sp->left = first;
                    else
                        sp->right = first;
                }
                first->left = sl;
                if (sl)
                    sl->parent = first;
                first->right = sr;
                if (sr)
                    sr->parent = first;

                second->parent = fp;
                if (fp) {
                    if (f_is_left_child)
                        fp->left = second;
                    else
                        fp->right = second;
                }

                second->left = fl;
                if (fl)
                    fl->parent = second;
                second->right = fr;
                if (fr)
                    fr->parent = second;
            } else {
                first->left = sl;
                if (sl)
                    sl->parent = first;
                first->right = sr;
                if (sr)
                    sr->parent = first;

                second->parent = fp;
                if (fp) {
                    if (f_is_left_child)
                        fp->left = second;
                    else
                        fp->right = second;
                }
                first->parent = second;

                if (s_is_left_child) {
                    second->left = first;
                    second->right = fr;
                    if (fr)
                        fr->parent = second;
                } else {
                    second->right = first;
                    second->left = fl;
                    if (fl)
                        fl->parent = second;
                }
            }
        }
    };

    template <bool Const>
    class _iterator {
    public:
        using node_pointer = node*;
        using value_type = std::conditional_t<Const, const T, T>;
        using pointer = std::add_pointer_t<value_type>;
        using reference = std::add_lvalue_reference_t<value_type>;

        friend rbtree;

    private:
        node_pointer p;

    public:
        constexpr _iterator() = default;
        explicit constexpr _iterator(node_pointer ptr)
            : p { ptr } {}
        constexpr _iterator(const _iterator& iter) = default;
        constexpr _iterator(_iterator&& iter) = default;
        constexpr ~_iterator() = default;
        constexpr _iterator& operator=(const _iterator& iter) = default;
        constexpr _iterator& operator=(_iterator&& iter) = default;
        constexpr bool operator==(const _iterator& iter) const = default;

        constexpr reference operator*(void) const { return p->value; }
        constexpr pointer operator&(void) const { return std::addressof(p->value); }
        constexpr pointer operator->(void) const { return this->operator&(); }
        constexpr _iterator& operator++(void)
        { p = p->next(); return *this; }
        constexpr _iterator operator++(int)
        { _iterator ret(p); (void)this->operator++(); return ret; }
        constexpr _iterator& operator--(void)
        { p = p->prev(); return *this; }
        constexpr _iterator operator--(int)
        { _iterator ret(p); (void)this->operator--(); return ret; }
        constexpr operator bool() const
        { return p; }
        constexpr operator _iterator<true>() const
        { return _iterator<true> { p }; }
    };

    using iterator = _iterator<false>;
    using const_iterator = _iterator<true>;

    using node_allocator = typename
        std::allocator_traits<Allocator>::template rebind_alloc<node>;
    using node_alloc_traits = std::allocator_traits<node_allocator>;

    compressed_pair<node*, node_allocator> root_data;
    compressed_pair<std::size_t, Compare> size_data;

private:
    constexpr node*& _root() noexcept { return root_data.first(); }
    constexpr node* const& _root() const noexcept { return root_data.first(); }

    constexpr std::size_t& _size() noexcept { return size_data.first(); }
    constexpr const std::size_t& _size() const noexcept { return size_data.first(); }

    constexpr node_allocator& _alloc() noexcept { return root_data.second(); }
    constexpr const node_allocator& _alloc() const noexcept { return root_data.second(); }

    constexpr Compare& _comp() noexcept { return size_data.second(); }
    constexpr const Compare& _comp() const noexcept { return size_data.second(); }

    template <typename... Args>
    constexpr node* newnode(Args&&... key)
    {
        node* ptr = node_alloc_traits::allocate(_alloc(), 1);
        node_alloc_traits::construct(_alloc(), ptr, std::forward<Args>(key)...);
        return ptr;
    }

    constexpr void delnode(node* nd)
    {
        node_alloc_traits::destroy(_alloc(), nd);
        node_alloc_traits::deallocate(_alloc(), nd, 1);
    }

    constexpr void do_insertion(node* parent,
        node*& child_inserted, node* nd)
    {
        nd->parent = parent;
        child_inserted = nd;
        this->balance(nd);
        ++_size();
    }

public:
    constexpr iterator end(void) noexcept
    { return iterator(nullptr); }
    constexpr const_iterator end(void) const noexcept
    { return const_iterator(nullptr); }
    constexpr const_iterator cend(void) const noexcept
    { return const_iterator(nullptr); }

    constexpr iterator begin(void) noexcept
    { return _root() ? iterator(_root()->leftmost()) : end(); }
    constexpr const_iterator begin(void) const noexcept
    { return _root() ? const_iterator(_root()->leftmost()) : end(); }
    constexpr const_iterator cbegin(void) const noexcept
    { return _root() ? const_iterator(_root()->leftmost()) : end(); }

    constexpr void destroy(node* nd)
    {
        if (!nd)
            return;
        destroy(nd->left);
        destroy(nd->right);
        delnode(nd);
    }

    constexpr void destroy() { destroy(_root()); _root() = nullptr; _size() = 0; }

    constexpr node* copy(node* nd)
    {
        if (!nd)
            return nullptr;

        node* newnd = newnode(nd->value);
        newnd->color = nd->color;
        ++_size();

        newnd->left = copy(nd->left);
        if (newnd->left)
            newnd->left->parent = newnd;

        newnd->right = copy(nd->right);
        if (newnd->right)
            newnd->right->parent = newnd;

        return newnd;
    }

    explicit constexpr rbtree(const Compare& comp, const node_allocator& alloc)
        : root_data{nullptr, alloc}, size_data{0, comp} { }

    constexpr rbtree(const rbtree& other)
        : rbtree(other._comp(), other._alloc())
    {
        _root() = copy(other._root());
        if (_root())
            _root()->parent = nullptr;
    }

    constexpr rbtree(const rbtree& other, const node_allocator& alloc)
        : rbtree(other._comp(), alloc)
    {
        _root() = copy(other._root());
        if (_root())
            _root()->parent = nullptr;
    }

    constexpr rbtree(rbtree&& other) noexcept
        : root_data{std::exchange(other._root(), nullptr), std::move(other._alloc())}
        , size_data{std::exchange(other._size(), 0), std::move(other._comp())} { }

    constexpr rbtree(rbtree&& other, const node_allocator& alloc) noexcept
        : root_data{std::exchange(other._root(), nullptr), alloc}
        , size_data{std::exchange(other._size(), 0), std::move(other._comp())} { }

    constexpr ~rbtree() { destroy(); }

    constexpr rbtree& operator=(const rbtree& other)
    {
        destroy(_root());

        _comp() = other._comp();
        if constexpr (node_alloc_traits::
            propagate_on_container_copy_assignment::value)
            _alloc() = other._alloc();

        _root() = copy(other._root());
        if (_root())
            _root()->parent = nullptr;

        return *this;
    }

    constexpr rbtree& operator=(rbtree&& other) noexcept
    {
        destroy(_root());
        _root() = std::exchange(other._root(), nullptr);
        _size() = std::exchange(other._size(), 0);
        _comp() = std::move(other._comp());
        if constexpr (node_alloc_traits::
            propagate_on_container_move_assignment::value)
            _alloc() = std::move(other._alloc());

        return *this;
    }

    constexpr void rotateleft(node* rt)
    {
        node* nrt = rt->right;

        if (!rt->is_root()) {
            if (rt->is_left_child())
                rt->parent->left = nrt;
            else
                rt->parent->right = nrt;
        } else {
            _root() = nrt;
        }

        nrt->parent = rt->parent;
        rt->parent = nrt;

        rt->right = nrt->left;
        if (rt->right)
            rt->right->parent = rt;

        nrt->left = rt;
    }

    constexpr void rotateright(node* rt)
    {
        node* nrt = rt->left;

        if (!rt->is_root()) {
            if (rt->is_left_child())
                rt->parent->left = nrt;
            else
                rt->parent->right = nrt;
        } else {
            _root() = nrt;
        }

        nrt->parent = rt->parent;
        rt->parent = nrt;

        rt->left = nrt->right;
        if (rt->left)
            rt->left->parent = rt;
        nrt->right = rt;
    }

    constexpr void balance(node* nd)
    {
        if (nd->is_root()) {
            nd->toblack();
            return;
        }

        if (node::is_black(nd->parent))
            return;

        node* p = nd->parent;
        node* pp = nd->grandparent();
        node* uncle = nd->uncle();

        if (node::is_red(uncle)) {
            p->toblack();
            uncle->toblack();
            pp->tored();
            this->balance(pp);
            return;
        }

        if (p->is_left_child()) {
            if (nd->is_left_child()) {
                p->toblack();
                pp->tored();
                this->rotateright(pp);
            } else {
                this->rotateleft(p);
                this->balance(p);
            }
        } else {
            if (nd->is_right_child()) {
                p->toblack();
                pp->tored();
                this->rotateleft(pp);
            } else {
                this->rotateright(p);
                this->balance(p);
            }
        }
    }

    template <typename U>
    constexpr node* _find(const U& key) const
    {
        for (node* cur = _root(); cur; ) {
            if (_comp()(key, cur->value))
                cur = cur->left;
            else if (_comp()(cur->value, key))
                cur = cur->right;
            else
                return cur;
        }

        return nullptr;
    }

    template <typename U>
    constexpr iterator find(const U& key) const
    { return iterator { _find(key) }; }

    // RBTREE RECURSIVE DELETE
    // THIS FUNCTION DOES NOT DELLOCATE THE NODE
    // CALLER IS RESPONSIBLE FOR FREEING THE MEMORY
    // @param: nd is guaranteed to be a leaf node
    constexpr void _erase(node* nd)
    {
        if (nd->is_root())
            return;

        if (node::is_black(nd)) {
            node* p = nd->parent;
            node* s = nullptr;
            if (nd->is_left_child())
                s = p->right;
            else
                s = p->left;

            if (node::is_red(s)) {
                p->tored();
                s->toblack();
                if (nd->is_right_child()) {
                    this->rotateright(p);
                    s = p->left;
                } else {
                    this->rotateleft(p);
                    s = p->right;
                }
            }

            node* r = nullptr;
            if (node::is_red(s->left)) {
                r = s->left;
                if (s->is_left_child()) {
                    r->toblack();
                    s->color = p->color;
                    this->rotateright(p);
                    p->toblack();
                } else {
                    r->color = p->color;
                    this->rotateright(s);
                    this->rotateleft(p);
                    p->toblack();
                }
            } else if (node::is_red(s->right)) {
                r = s->right;
                if (s->is_left_child()) {
                    r->color = p->color;
                    this->rotateleft(s);
                    this->rotateright(p);
                    p->toblack();
                } else {
                    r->toblack();
                    s->color = p->color;
                    this->rotateleft(p);
                    p->toblack();
                }
            } else {
                s->tored();
                if (node::is_black(p))
                    this->_erase(p);
                else
                    p->toblack();
            }
        }
    }

    // delete nd from the tree. make nd safe to deallocate
    // THIS FUNCTION DOES NOT DELLOCATE THE NODE
    // CALLER IS RESPONSIBLE FOR FREEING THE MEMORY
    constexpr node* erase(node* nd)
    {
        if (nd->is_root() && nd->is_leaf()) {
            _root() = nullptr;
            return nullptr;
        }

        node* next = nd->next();

        while (!nd->is_leaf()) {
            node* alt = nd->right ? nd->right->leftmost() : nd->left;
            if (nd->is_root())
                _root() = alt;
            node::swap(nd, alt);
        }

        this->_erase(nd);

        if (nd->is_left_child())
            nd->parent->left = nullptr;
        else
            nd->parent->right = nullptr;

        return next;
    }

    constexpr iterator erase(iterator pos) noexcept
    {
        node* nextpos = erase(pos.p);
        delnode(pos.p);
        --_size();
        return iterator { nextpos };
    }

    constexpr iterator erase(const_iterator pos) noexcept
    {
        node* nextpos = erase(pos.p);
        delnode(pos.p);
        --_size();
        return iterator { nextpos };
    }

    template <typename U>
    constexpr iterator lower_bound(U&& val) const
    {
        node* cur = _root();
        node* result = nullptr;

        while (cur) {
            if (!_comp()(cur->value, val)) {
                result = cur;
                cur = cur->left;
            }
            else {
                cur = cur->right;
            }
        }

        return iterator { result };
    }

    template <typename U>
    constexpr iterator upper_bound(U&& val) const
    {
        iterator iter = lower_bound(std::forward<U>(val));
        if (iter && !_comp()(*iter, val) && !_comp()(val, *iter))
            return ++iter;
        return iter;
    }

    // value in nd MUST NOT exist in the rbtree,
    // that is, if a < b, then a > b
    constexpr void insert(node* nd)
    {
        node* cur = _root();

        while (cur) {
            if (_comp()(nd->value, cur->value)) {
                if (!cur->left) {
                    do_insertion(cur, cur->left, nd);
                    return;
                }
                cur = cur->left;
            } else {
                if (!cur->right) {
                    do_insertion(cur, cur->right, nd);
                    return;
                }
                cur = cur->right;
            }
        }
        do_insertion(cur, _root(), nd);
    }

    template <typename U>
    constexpr std::pair<iterator, bool> insert(U&& value)
    {
        auto iter = find(value);
        if (iter)
            return { iter, false };

        node* ptr = newnode(std::forward<U>(value));
        insert(ptr);

        return { iterator { ptr }, true };
    }

    template <typename... Args>
    constexpr std::pair<iterator, bool> emplace(Args&&... args)
    {
        node* nd = newnode(std::forward<Args>(args)...);
        node* exist_nd = _find(nd->value);
        if (exist_nd) {
            delnode(nd);
            return { iterator { exist_nd }, false };
        }
        insert(nd);
        return { iterator { nd }, true };
    }

    constexpr bool empty() const noexcept { return !_root(); }
    constexpr std::size_t size() const noexcept { return _size(); }

    constexpr void swap(rbtree& other)
    {
        std::swap(_root(), other._root());
        std::swap(_size(), other._size());
        std::swap(_comp(), other._comp());
        if constexpr (node_alloc_traits::propagate_on_container_swap::value)
            std::swap(_alloc(), other._alloc());
    }
};

} // namespace std::impl

#endif