typedef unsigned long size_t;






















#include "type_traits.h"

namespace std
{
	template<class T> constexpr T&& forward(remove_reference_t<T>& t) noexcept;
	template<class T> constexpr T&& forward(remove_reference_t<T>&& t) noexcept;
}

// --- iterator ---

namespace std {
	struct ptrdiff_t;

	template<class I> struct iterator_traits;

	template <class Category,
			  class value_type,
			  class difference_type = ptrdiff_t,
			  class pointer_type = value_type*,
			  class reference_type = value_type&>
	struct iterator {
		typedef Category iterator_category;

		iterator();
		iterator(iterator<Category, remove_const_t<value_type> > const &other); // non-const -> const conversion constructor

		iterator &operator++();
		iterator operator++(int);
		iterator &operator--();
		iterator operator--(int);
		bool operator==(iterator other) const;
		bool operator!=(iterator other) const;
		reference_type operator*() const;
		pointer_type operator->() const;
		iterator operator+(int);
		iterator operator-(int);
		iterator &operator+=(int);
		iterator &operator-=(int);
		int operator-(iterator);
		reference_type operator[](int);
	};

	struct input_iterator_tag {};
	struct forward_iterator_tag : public input_iterator_tag {};
	struct bidirectional_iterator_tag : public forward_iterator_tag {};
	struct random_access_iterator_tag : public bidirectional_iterator_tag {};

	struct output_iterator_tag {};

	template<class Container>
	class back_insert_iterator {
	protected:
		Container* container = nullptr;
	public:
		using iterator_category = output_iterator_tag;
		using value_type = void;
		using difference_type = ptrdiff_t;
		using pointer = void;
		using reference = void;
		using container_type = Container;
		constexpr back_insert_iterator() noexcept = default;
		constexpr explicit back_insert_iterator(Container& x);
		back_insert_iterator& operator=(const typename Container::value_type& value);
		back_insert_iterator& operator=(typename Container::value_type&& value);
		back_insert_iterator& operator*();
		back_insert_iterator& operator++();
		back_insert_iterator operator++(int);
	};

	template<class Container>
	constexpr back_insert_iterator<Container> back_inserter(Container& x) {
		return back_insert_iterator<Container>(x);
	}

	template<class Container>
	class front_insert_iterator {
	protected:
		Container* container = nullptr;
	public:
		using iterator_category = output_iterator_tag;
		using value_type = void;
		using difference_type = ptrdiff_t;
		using pointer = void;
		using reference = void;
		using container_type = Container;
		constexpr front_insert_iterator() noexcept = default;
		constexpr explicit front_insert_iterator(Container& x);
		constexpr front_insert_iterator& operator=(const typename Container::value_type& value);
		constexpr front_insert_iterator& operator=(typename Container::value_type&& value);
		constexpr front_insert_iterator& operator*();
		constexpr front_insert_iterator& operator++();
		constexpr front_insert_iterator operator++(int);
	};
	template<class Container>
	constexpr front_insert_iterator<Container> front_inserter(Container& x) {
		return front_insert_iterator<Container>(x);
	}
}

// --- string ---

namespace std
{
	template<class charT> struct char_traits;

	typedef size_t streamsize;

	template <class T> class allocator {
	public:
		allocator() throw();
		typedef size_t size_type;
	};

	template<class charT, class traits = char_traits<charT>, class Allocator = allocator<charT> >
	class basic_string {
	public:
		using value_type = charT;
		using reference = value_type&;
		using const_reference = const value_type&;
		typedef typename Allocator::size_type size_type;
		static const size_type npos = -1;

		explicit basic_string(const Allocator& a = Allocator());
		basic_string(const charT* s, const Allocator& a = Allocator());
		template<class InputIterator> basic_string(InputIterator begin, InputIterator end, const Allocator& a = Allocator());

		const charT* c_str() const;
		charT* data() noexcept;
		size_t length() const;

		typedef std::iterator<random_access_iterator_tag, charT> iterator;
		typedef std::iterator<random_access_iterator_tag, const charT> const_iterator;

		iterator begin();
		iterator end();
		const_iterator begin() const;
		const_iterator end() const;
		const_iterator cbegin() const;
		const_iterator cend() const;

		void push_back(charT c);

		const charT& front() const;
		charT& front();
		const charT& back() const;
		charT& back();

		const_reference operator[](size_type pos) const;
		reference operator[](size_type pos);
		const_reference at(size_type n) const;
		reference at(size_type n);
		template<class T> basic_string& operator+=(const T& t);
		basic_string& operator+=(const charT* s);
		basic_string& append(const basic_string& str);
		basic_string& append(const charT* s);
		basic_string& append(size_type n, charT c);
		template<class InputIterator> basic_string& append(InputIterator first, InputIterator last); 
		basic_string& assign(const basic_string& str);
		basic_string& assign(size_type n, charT c);
		template<class InputIterator> basic_string& assign(InputIterator first, InputIterator last);
		basic_string& insert(size_type pos, const basic_string& str);
		basic_string& insert(size_type pos, size_type n, charT c);
		basic_string& insert(size_type pos, const charT* s);
		iterator insert(const_iterator p, size_type n, charT c);
		template<class InputIterator> iterator insert(const_iterator p, InputIterator first, InputIterator last); 
		basic_string& replace(size_type pos1, size_type n1, const basic_string& str);
		basic_string& replace(size_type pos1, size_type n1, size_type n2, charT c);
		size_type copy(charT* s, size_type n, size_type pos = 0) const;
		void clear() noexcept;
		basic_string substr(size_type pos = 0, size_type n = npos) const;
		void swap(basic_string& s) noexcept/*(allocator_traits<Allocator>::propagate_on_container_swap::value || allocator_traits<Allocator>::is_always_equal::value)*/;
	};

	template<class charT, class traits, class Allocator> basic_string<charT, traits, Allocator> operator+(const basic_string<charT, traits, Allocator>& lhs, const basic_string<charT, traits, Allocator>& rhs);
	template<class charT, class traits, class Allocator> basic_string<charT, traits, Allocator> operator+(const basic_string<charT, traits, Allocator>& lhs, const charT* rhs);

	typedef basic_string<char> string;
}

// --- istring / ostream / stringstream ---

namespace std
{
	template <class charT, class traits = char_traits<charT> >
	class basic_istream /*: virtual public basic_ios<charT,traits> - not needed for this test */ {
	public:
		using char_type = charT;
		using int_type = int; //typename traits::int_type;

		basic_istream<charT, traits>& operator>>(int& n);

		int_type get();
		basic_istream<charT, traits>& get(char_type& c);
		basic_istream<charT, traits>& get(char_type* s, streamsize n);
		int_type peek();
		basic_istream<charT, traits>& read (char_type* s, streamsize n);
		streamsize readsome(char_type* s, streamsize n);
		basic_istream<charT, traits>& putback(char_type c);
		basic_istream<charT,traits>& unget();

		basic_istream<charT,traits>& getline(char_type* s, streamsize n);
		basic_istream<charT,traits>& getline(char_type* s, streamsize n, char_type delim);
 	};

	template<class charT, class traits> basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>&, charT*);
	template<class charT, class traits, class Allocator> basic_istream<charT, traits>& operator>>(basic_istream<charT, traits>& is, basic_string<charT, traits, Allocator>& str); 

	template<class charT, class traits, class Allocator> basic_istream<charT,traits>& getline(basic_istream<charT,traits>& is, basic_string<charT,traits,Allocator>& str, charT delim);
	template<class charT, class traits, class Allocator> basic_istream<charT,traits>& getline(basic_istream<charT,traits>& is, basic_string<charT,traits,Allocator>& str);

	template <class charT, class traits = char_traits<charT> >
	class basic_ostream /*: virtual public basic_ios<charT,traits> - not needed for this test */ {
	public:
		typedef charT char_type;

		basic_ostream<charT, traits>& operator<<(int n);

		basic_ostream<charT, traits>& put(char_type c);
		basic_ostream<charT, traits>& write(const char_type* s, streamsize n);
		basic_ostream<charT,traits>& flush();
	};

	template<class charT, class traits> basic_ostream<charT,traits>& operator<<(basic_ostream<charT,traits>&, const charT*);
	template<class charT, class traits, class Allocator> basic_ostream<charT, traits>& operator<<(basic_ostream<charT, traits>& os, const basic_string<charT, traits, Allocator>& str); 

	template<class charT, class traits = char_traits<charT>>
	class basic_iostream : public basic_istream<charT, traits>, public basic_ostream<charT, traits> {
	public:
	};

	template<class charT, class traits = char_traits<charT>, class Allocator = allocator<charT>>
	class basic_stringstream : public basic_iostream<charT, traits> {
	public:
		explicit basic_stringstream(/*ios_base::openmode which = ios_base::out|ios_base::in - not needed for this test*/);
		explicit basic_stringstream( const basic_string<charT, traits, Allocator>& str/*, ios_base::openmode which = ios_base::out | ios_base::in*/);
		basic_stringstream(const basic_stringstream& rhs) = delete;
		basic_stringstream(basic_stringstream&& rhs);
		basic_stringstream& operator=(const basic_stringstream& rhs) = delete;
		basic_stringstream& operator=(basic_stringstream&& rhs);

		void swap(basic_stringstream& rhs);

		basic_string<charT, traits, Allocator> str() const;
		void str(const basic_string<charT, traits, Allocator>& str);
	};

	typedef basic_istream<char> istream;
	typedef basic_ostream<char> ostream;
	extern istream cin;
	extern ostream cout;

	using stringstream = basic_stringstream<char>;
}

// --- vector ---

namespace std {
	template<class T, class Allocator = allocator<T>>
	class vector { 
	public:
		using value_type = T;
		using reference = value_type&;
		using const_reference = const value_type&; 
		using size_type = unsigned int;
		using iterator = std::iterator<random_access_iterator_tag, T>;
		using const_iterator = std::iterator<random_access_iterator_tag, const T>;

		vector() noexcept(noexcept(Allocator())) : vector(Allocator()) { }
		explicit vector(const Allocator&) noexcept;
		explicit vector(size_type n, const Allocator& = Allocator());
		vector(size_type n, const T& value, const Allocator& = Allocator());
		template<class InputIterator, class IteratorCategory = typename InputIterator::iterator_category> vector(InputIterator first, InputIterator last, const Allocator& = Allocator());
			// use of `iterator_category` makes sure InputIterator is (probably) an iterator, and not an `int` or
			// similar that should match a different overload (SFINAE).
		~vector();

		vector& operator=(const vector& x);
		vector& operator=(vector&& x) noexcept/*(allocator_traits<Allocator>::propagate_on_container_move_assignment::value || allocator_traits<Allocator>::is_always_equal::value)*/;
		template<class InputIterator, class IteratorCategory = typename InputIterator::iterator_category> void assign(InputIterator first, InputIterator last);
			// use of `iterator_category` makes sure InputIterator is (probably) an iterator, and not an `int` or
			// similar that should match a different overload (SFINAE).
		void assign(size_type n, const T& u);

		iterator begin() noexcept;
		const_iterator begin() const noexcept;
		iterator end() noexcept;
		const_iterator end() const noexcept;

		size_type size() const noexcept;

		reference operator[](size_type n);
		const_reference operator[](size_type n) const;
		const_reference at(size_type n) const;
		reference at(size_type n);
		reference front();
		const_reference front() const;
		reference back();
		const_reference back() const;

		T* data() noexcept;
		const T* data() const noexcept;

		void push_back(const T& x);
		void push_back(T&& x);

		iterator insert(const_iterator position, const T& x);
		iterator insert(const_iterator position, T&& x);
		iterator insert(const_iterator position, size_type n, const T& x);
		template<class InputIterator> iterator insert(const_iterator position, InputIterator first, InputIterator last);

		template <class... Args> iterator emplace (const_iterator position, Args&&... args);
		template <class... Args> void emplace_back (Args&&... args);

		void swap(vector&) noexcept/*(allocator_traits<Allocator>::propagate_on_container_swap::value || allocator_traits<Allocator>::is_always_equal::value)*/;

		void clear() noexcept;
	};
}

// --- make_shared / make_unique ---

namespace std {
	template<typename T>
	class shared_ptr {
	public:
		shared_ptr() noexcept;
		explicit shared_ptr(T*);
		shared_ptr(const shared_ptr&) noexcept;
		template<class U> shared_ptr(const shared_ptr<U>&) noexcept;
		template<class U> shared_ptr(shared_ptr<U>&&) noexcept;

		shared_ptr<T>& operator=(const shared_ptr<T>&) noexcept;
		shared_ptr<T>& operator=(shared_ptr<T>&&) noexcept;

		T& operator*() const noexcept;
		T* operator->() const noexcept;

		T* get() const noexcept;
	};

	template<typename T>
	class unique_ptr {
	public:
		constexpr unique_ptr() noexcept;
		explicit unique_ptr(T*) noexcept;
		unique_ptr(unique_ptr<T>&&) noexcept;

		unique_ptr<T>& operator=(unique_ptr<T>&&) noexcept;

		T& operator*() const;
		T* operator->() const noexcept;

		T* get() const noexcept;
	};

	template<typename T, class... Args> unique_ptr<T> make_unique(Args&&...);

	template<typename T, class... Args> shared_ptr<T> make_shared(Args&&...);
}

// --- pair ---

namespace std {
	template <class T1, class T2>
	struct pair {
		typedef T1 first_type;
		typedef T2 second_type;

		T1 first;
		T2 second;
		pair();
		pair(const T1& x, const T2& y) : first(x), second(y) {};
		template<class U, class V> pair(const pair<U, V> &p);

		void swap(pair& p) /*noexcept(...)*/;
	};

	template<class T1, class T2> constexpr pair<decay_t<T1>, decay_t<T2>> make_pair(T1&& x, T2&& y) {
		return pair<decay_t<T1>, decay_t<T2>>(std::forward<T1>(x), std::forward<T2>(y));
	}
}

// --- map ---

namespace std {
	template<class T = void> struct less;

	template<class Key, class T, class Compare = less<Key>, class Allocator = allocator<pair<const Key, T>>>
	class map {
	public:
		using key_type = Key;
		using mapped_type = T;
		using value_type = pair<const Key, T>;
		using iterator = std::iterator<random_access_iterator_tag, value_type >;
		using const_iterator = std::iterator<random_access_iterator_tag, const value_type >;

		map() /*: map(Compare()) { }*/;
		map(const map& x);
		map(map&& x);
		~map();

		map& operator=(const map& x);
		map& operator=(map&& x) /*noexcept(allocator_traits<Allocator>::is_always_equal::value && is_nothrow_move_assignable_v<Compare>)*/;

		iterator begin() noexcept;
		const_iterator begin() const noexcept;
		iterator end() noexcept;
		const_iterator end() const noexcept;

		T& operator[](const key_type& x);
		T& operator[](key_type&& x);
		T& at(const key_type& x);
		const T& at(const key_type& x) const;

		template<class... Args> pair<iterator, bool> emplace(Args&&... args);
		template<class... Args> iterator emplace_hint(const_iterator position, Args&&... args);

		pair<iterator, bool> insert(const value_type& x);
		pair<iterator, bool> insert(value_type&& x);
		iterator insert(const_iterator position, const value_type& x);
		iterator insert(const_iterator position, value_type&& x);

		template<class... Args> pair<iterator, bool> try_emplace(const key_type& k, Args&&... args);
		template<class... Args> pair<iterator, bool> try_emplace(key_type&& k, Args&&... args);
		template<class... Args> iterator try_emplace(const_iterator hint, const key_type& k, Args&&... args);
		template<class... Args> iterator try_emplace(const_iterator hint, key_type&& k, Args&&... args);
		template<class M> pair<iterator, bool> insert_or_assign(const key_type& k, M&& obj);
		template<class M> pair<iterator, bool> insert_or_assign(key_type&& k, M&& obj);
		template<class M> iterator insert_or_assign(const_iterator hint, const key_type& k, M&& obj);
		template<class M> iterator insert_or_assign(const_iterator hint, key_type&& k, M&& obj);

		iterator erase(iterator position);
		iterator erase(const_iterator position);
		iterator erase(const_iterator first, const_iterator last);
		void swap(map&) /*noexcept(/*==allocator_traits<Allocator>::is_always_equal::value && is_nothrow_swappable_v<Compare>)*/;
		void clear() noexcept;

		template<class C2> void merge(map<Key, T, C2, Allocator>& source);
		template<class C2> void merge(map<Key, T, C2, Allocator>&& source);

		iterator find(const key_type& x);
		const_iterator find(const key_type& x) const;

		iterator lower_bound(const key_type& x);
		const_iterator lower_bound(const key_type& x) const;
		iterator upper_bound(const key_type& x);
		const_iterator upper_bound(const key_type& x) const;

		pair<iterator, iterator> equal_range(const key_type& x);
		pair<const_iterator, const_iterator> equal_range(const key_type& x) const;
	};

	template<class T> struct hash;
	template<class T = void> struct equal_to;

	template<class Key, class T, class Hash = hash<Key>, class Pred = equal_to<Key>, class Allocator = allocator<pair<const Key, T>>>
	class unordered_map {
	public:
		using key_type = Key;
		using mapped_type = T;
		using value_type = pair<const Key, T>;
		using iterator = std::iterator<random_access_iterator_tag, value_type >;
		using const_iterator = std::iterator<random_access_iterator_tag, const value_type >;

		unordered_map();
		unordered_map(const unordered_map&);
		unordered_map(unordered_map&&);
		~unordered_map();

		unordered_map& operator=(const unordered_map&);
		unordered_map& operator=(unordered_map&&) /*noexcept(allocator_traits<Allocator>::is_always_equal::value && is_nothrow_move_assignable_v<Hash> && is_nothrow_move_assignable_v<Pred>)*/;

		iterator begin() noexcept;
		const_iterator begin() const noexcept;
		iterator end() noexcept;
		const_iterator end() const noexcept;

		mapped_type& operator[](const key_type& k);
		mapped_type& operator[](key_type&& k);
		mapped_type& at(const key_type& k);
		const mapped_type& at(const key_type& k) const;
		
		template<class... Args> pair<iterator, bool> emplace(Args&&... args);
		template<class... Args> iterator emplace_hint(const_iterator position, Args&&... args);

		pair<iterator, bool> insert(const value_type& obj);
		pair<iterator, bool> insert(value_type&& obj);
		iterator insert(const_iterator hint, const value_type& obj);
		iterator insert(const_iterator hint, value_type&& obj);

		template<class... Args> pair<iterator, bool> try_emplace(const key_type& k, Args&&... args);
		template<class... Args> pair<iterator, bool> try_emplace(key_type&& k, Args&&... args);
		template<class... Args> iterator try_emplace(const_iterator hint, const key_type& k, Args&&... args);
		template<class... Args> iterator try_emplace(const_iterator hint, key_type&& k, Args&&... args);
		template<class M> pair<iterator, bool> insert_or_assign(const key_type& k, M&& obj);
		template<class M> pair<iterator, bool> insert_or_assign(key_type&& k, M&& obj);
		template<class M> iterator insert_or_assign(const_iterator hint, const key_type& k, M&& obj);
		template<class M> iterator insert_or_assign(const_iterator hint, key_type&& k, M&& obj);

		iterator erase(iterator position);
		iterator erase(const_iterator position);
		iterator erase(const_iterator first, const_iterator last);
		void swap(unordered_map&) /*noexcept(allocator_traits<Allocator>::is_always_equal::value && is_nothrow_swappable_v<Hash> && is_nothrow_swappable_v<Pred>)*/;
		void clear() noexcept;

		template<class H2, class P2> void merge(unordered_map<Key, T, H2, P2, Allocator>& source);
		template<class H2, class P2> void merge(unordered_map<Key, T, H2, P2, Allocator>&& source);

		iterator find(const key_type& k);
		const_iterator find(const key_type& k) const;

		pair<iterator, iterator> equal_range(const key_type& k);
		pair<const_iterator, const_iterator> equal_range(const key_type& k) const;
	};
};

// --- set ---

namespace std {
	template<class Key, class Compare = less<Key>, class Allocator = allocator<Key>>
	class set {
	public:
		using key_type = Key;
		using value_type = Key;
		using size_type = size_t;
		using allocator_type = Allocator;
		using iterator = std::iterator<random_access_iterator_tag, value_type >;
		using const_iterator = std::iterator<random_access_iterator_tag, const value_type >;

		set() /*: set(Compare())*/ { }
		set(const set& x);
		set(set&& x);
		template<class InputIterator> set(InputIterator first, InputIterator last/*, const Compare& comp = Compare(), const Allocator& = Allocator()*/);
		~set();
		
		set& operator=(const set& x);
		set& operator=(set&& x) noexcept/*(allocator_traits<Allocator>::is_always_equal::value && is_nothrow_move_assignable_v<Compare>)*/;

		iterator begin() noexcept;
		const_iterator begin() const noexcept;
		iterator end() noexcept;
		const_iterator end() const noexcept;

		template<class... Args> pair<iterator, bool> emplace(Args&&... args);
		template<class... Args> iterator emplace_hint(const_iterator position, Args&&... args);
		pair<iterator,bool> insert(const value_type& x);
		pair<iterator,bool> insert(value_type&& x);
		iterator insert(const_iterator position, const value_type& x);
		iterator insert(const_iterator position, value_type&& x);
		template<class InputIterator> void insert(InputIterator first, InputIterator last); 
		
		iterator erase(iterator position);
		iterator erase(const_iterator position);
		iterator erase(const_iterator first, const_iterator last); 
		void swap(set&) noexcept/*(allocator_traits<Allocator>::is_always_equal::value && is_nothrow_swappable_v<Compare>)*/;
		void clear() noexcept;

		template<class C2> void merge(set<Key, C2, Allocator>& source);
		template<class C2> void merge(set<Key, C2, Allocator>&& source);

		iterator find(const key_type& x);
		const_iterator find(const key_type& x) const;
		
		iterator lower_bound(const key_type& x);
		const_iterator lower_bound(const key_type& x) const;
		iterator upper_bound(const key_type& x);
		const_iterator upper_bound(const key_type& x) const;
		pair<iterator, iterator> equal_range(const key_type& x);
		pair<const_iterator, const_iterator> equal_range(const key_type& x) const;
	};

	template<class Key, class Hash = hash<Key>, class Pred = equal_to<Key>, class Allocator = allocator<Key>>
	class unordered_set { 
	public:
		using key_type = Key;
		using value_type = Key;
		using hasher = Hash;
		using key_equal = Pred;
		using allocator_type = Allocator;
		using size_type = size_t;
		using iterator = std::iterator<random_access_iterator_tag, value_type >;
		using const_iterator = std::iterator<random_access_iterator_tag, const value_type >;

		unordered_set();
		unordered_set(const unordered_set&);
		unordered_set(unordered_set&&);
		template<class InputIterator> unordered_set(InputIterator f, InputIterator l, size_type n = 0/*, const hasher& hf = hasher(), const key_equal& eql = key_equal(), const allocator_type& a = allocator_type()*/);
		~unordered_set();

		unordered_set& operator=(const unordered_set&);
		unordered_set& operator=(unordered_set&&) noexcept/*(allocator_traits<Allocator>::is_always_equal::value && is_nothrow_move_assignable_v<Hash> && is_nothrow_move_assignable_v<Pred>)*/;
		
		iterator begin() noexcept;
		const_iterator begin() const noexcept;
		iterator end() noexcept;
		const_iterator end() const noexcept;

		template<class... Args> pair<iterator, bool> emplace(Args&&... args);
		template<class... Args> iterator emplace_hint(const_iterator position, Args&&... args);
		pair<iterator, bool> insert(const value_type& obj);
		pair<iterator, bool> insert(value_type&& obj);
		iterator insert(const_iterator hint, const value_type& obj);
		iterator insert(const_iterator hint, value_type&& obj);
		template<class InputIterator> void insert(InputIterator first, InputIterator last); 

		iterator erase(iterator position);
		iterator erase(const_iterator position);
		iterator erase(const_iterator first, const_iterator last);
		void swap(unordered_set&) noexcept/*(allocator_traits<Allocator>::is_always_equal::value && is_nothrow_swappable_v<Hash> && is_nothrow_swappable_v<Pred>)*/;
		void clear() noexcept;

		template<class H2, class P2> void merge(unordered_set<Key, H2, P2, Allocator>& source);
		template<class H2, class P2> void merge(unordered_set<Key, H2, P2, Allocator>&& source);

		iterator find(const key_type& k);
		const_iterator find(const key_type& k) const;
		pair<iterator, iterator> equal_range(const key_type& k);
		pair<const_iterator, const_iterator> equal_range(const key_type& k) const;
	};
}