#include <initializer_list>
namespace std {
  template<class T, class Container = deque<T>> class queue;
  template<class T, class Container = vector<T>,
           class Compare = less<typename Container::value_type>>
    class priority_queue;
  template<class T, class Container>
    bool operator==(const queue<T, Container>& x, const queue<T, Container>& y);
  template<class T, class Container>
    bool operator!=(const queue<T, Container>& x, const queue<T, Container>& y);
  template<class T, class Container>
    bool operator< (const queue<T, Container>& x, const queue<T, Container>& y);
  template<class T, class Container>
    bool operator> (const queue<T, Container>& x, const queue<T, Container>& y);
  template<class T, class Container>
    bool operator<=(const queue<T, Container>& x, const queue<T, Container>& y);
  template<class T, class Container>
    bool operator>=(const queue<T, Container>& x, const queue<T, Container>& y);
  template<class T, class Container>
    void swap(queue<T, Container>& x, queue<T, Container>& y) noexcept(noexcept(x.swap(y)));
  template<class T, class Container, class Compare>
    void swap(priority_queue<T, Container, Compare>& x,
              priority_queue<T, Container, Compare>& y) noexcept(noexcept(x.swap(y)));
}
#include <initializer_list>
namespace std {
  template<class T, class Container = deque<T>> class stack;
  template<class T, class Container>
    bool operator==(const stack<T, Container>& x, const stack<T, Container>& y);
  template<class T, class Container>
    bool operator!=(const stack<T, Container>& x, const stack<T, Container>& y);
  template<class T, class Container>
    bool operator< (const stack<T, Container>& x, const stack<T, Container>& y);
  template<class T, class Container>
    bool operator> (const stack<T, Container>& x, const stack<T, Container>& y);
  template<class T, class Container>
    bool operator<=(const stack<T, Container>& x, const stack<T, Container>& y);
  template<class T, class Container>
    bool operator>=(const stack<T, Container>& x, const stack<T, Container>& y);
  template<class T, class Container>
    void swap(stack<T, Container>& x, stack<T, Container>& y) noexcept(noexcept(x.swap(y)));
}
namespace std {
  template<class T, class Container = deque<T>>
  class queue {
  public:
    using value_type      = typename Container::value_type;
    using reference       = typename Container::reference;
    using const_reference = typename Container::const_reference;
    using size_type       = typename Container::size_type;
    using container_type  =          Container;
  protected:
    Container c;
  public:
    queue() : queue(Container()) {}
    explicit queue(const Container&);
    explicit queue(Container&&);
    template<class Alloc> explicit queue(const Alloc&);
    template<class Alloc> queue(const Container&, const Alloc&);
    template<class Alloc> queue(Container&&, const Alloc&);
    template<class Alloc> queue(const queue&, const Alloc&);
    template<class Alloc> queue(queue&&, const Alloc&);
    [[nodiscard]] bool empty() const    { return c.empty(); }
    size_type         size()  const     { return c.size(); }
    reference         front()           { return c.front(); }
    const_reference   front() const     { return c.front(); }
    reference         back()            { return c.back(); }
    const_reference   back() const      { return c.back(); }
    void push(const value_type& x)      { c.push_back(x); }
    void push(value_type&& x)           { c.push_back(std::move(x)); }
    template<class... Args>
      decltype(auto) emplace(Args&&... args)
        { return c.emplace_back(std::forward<Args>(args)...); }
    void pop()                          { c.pop_front(); }
    void swap(queue& q) noexcept(is_nothrow_swappable_v<Container>)
      { using std::swap; swap(c, q.c); }
  };
  template<class Container>
    queue(Container) -> queue<typename Container::value_type, Container>;
  template<class Container, class Allocator>
    queue(Container, Allocator) -> queue<typename Container::value_type, Container>;
  template<class T, class Container>
    void swap(queue<T, Container>& x, queue<T, Container>& y) noexcept(noexcept(x.swap(y)));
  template<class T, class Container, class Alloc>
    struct uses_allocator<queue<T, Container>, Alloc>
      : uses_allocator<Container, Alloc>::type { };
}explicit queue(const Container& cont);
explicit queue(Container&& cont);
template<class Alloc> explicit queue(const Alloc& a);
template<class Alloc> queue(const container_type& cont, const Alloc& a);
template<class Alloc> queue(container_type&& cont, const Alloc& a);
template<class Alloc> queue(const queue& q, const Alloc& a);
template<class Alloc> queue(queue&& q, const Alloc& a);
template<class T, class Container>
  bool operator==(const queue<T, Container>& x, const queue<T, Container>& y);
template<class T, class Container>
  bool operator!=(const queue<T, Container>& x,  const queue<T, Container>& y);
template<class T, class Container>
  bool operator< (const queue<T, Container>& x, const queue<T, Container>& y);
template<class T, class Container>
  bool operator> (const queue<T, Container>& x, const queue<T, Container>& y);
template<class T, class Container>
  bool operator<=(const queue<T, Container>& x, const queue<T, Container>& y);
template<class T, class Container>
    bool operator>=(const queue<T, Container>& x,
                    const queue<T, Container>& y);
template<class T, class Container>
  void swap(queue<T, Container>& x, queue<T, Container>& y) noexcept(noexcept(x.swap(y)));
namespace std {
  template<class T, class Container = vector<T>,
           class Compare = less<typename Container::value_type>>
  class priority_queue {
  public:
    using value_type      = typename Container::value_type;
    using reference       = typename Container::reference;
    using const_reference = typename Container::const_reference;
    using size_type       = typename Container::size_type;
    using container_type  = Container;
    using value_compare   = Compare;
  protected:
    Container c;
    Compare comp;
  public:
    priority_queue() : priority_queue(Compare()) {}
    explicit priority_queue(const Compare& x) : priority_queue(x, Container()) {}
    priority_queue(const Compare& x, const Container&);
    priority_queue(const Compare& x, Container&&);
    template<class InputIterator>
      priority_queue(InputIterator first, InputIterator last, const Compare& x,
                     const Container&);
    template<class InputIterator>
      priority_queue(InputIterator first, InputIterator last,
                     const Compare& x = Compare(), Container&& = Container());
    template<class Alloc> explicit priority_queue(const Alloc&);
    template<class Alloc> priority_queue(const Compare&, const Alloc&);
    template<class Alloc> priority_queue(const Compare&, const Container&, const Alloc&);
    template<class Alloc> priority_queue(const Compare&, Container&&, const Alloc&);
    template<class Alloc> priority_queue(const priority_queue&, const Alloc&);
    template<class Alloc> priority_queue(priority_queue&&, const Alloc&);
    [[nodiscard]] bool empty() const { return c.empty(); }
    size_type size()  const          { return c.size(); }
    const_reference   top() const    { return c.front(); }
    void push(const value_type& x);
    void push(value_type&& x);
    template<class... Args> void emplace(Args&&... args);
    void pop();
    void swap(priority_queue& q) noexcept(is_nothrow_swappable_v<Container> &&
                                          is_nothrow_swappable_v<Compare>)
      { using std::swap; swap(c, q.c); swap(comp, q.comp); }
  };
  template<class Compare, class Container>
    priority_queue(Compare, Container)
      -> priority_queue<typename Container::value_type, Container, Compare>;
  template<class InputIterator,
           class Compare = less<typename iterator_traits<InputIterator>::value_type>,
           class Container = vector<typename iterator_traits<InputIterator>::value_type>>
    priority_queue(InputIterator, InputIterator, Compare = Compare(), Container = Container())
      -> priority_queue<typename iterator_traits<InputIterator>::value_type, Container, Compare>;
  template<class Compare, class Container, class Allocator>
    priority_queue(Compare, Container, Allocator)
      -> priority_queue<typename Container::value_type, Container, Compare>;
  // no equality is provided
  template<class T, class Container, class Compare>
    void swap(priority_queue<T, Container, Compare>& x,
              priority_queue<T, Container, Compare>& y) noexcept(noexcept(x.swap(y)));
  template<class T, class Container, class Compare, class Alloc>
    struct uses_allocator<priority_queue<T, Container, Compare>, Alloc>
      : uses_allocator<Container, Alloc>::type { };
}priority_queue(const Compare& x, const Container& y);
priority_queue(const Compare& x, Container&& y);
template<class InputIterator>
  priority_queue(InputIterator first, InputIterator last, const Compare& x, const Container& y);
template<class InputIterator>
  priority_queue(InputIterator first, InputIterator last, const Compare& x = Compare(),
                 Container&& y = Container());
template<class Alloc> explicit priority_queue(const Alloc& a);
template<class Alloc> priority_queue(const Compare& compare, const Alloc& a);
template<class Alloc>
  priority_queue(const Compare& compare, const Container& cont, const Alloc& a);
template<class Alloc>
  priority_queue(const Compare& compare, Container&& cont, const Alloc& a);
template<class Alloc> priority_queue(const priority_queue& q, const Alloc& a);
template<class Alloc> priority_queue(priority_queue&& q, const Alloc& a);
void push(const value_type& x);
void push(value_type&& x);
template<class... Args> void emplace(Args&&... args)
c.emplace_back(std::forward<Args>(args)...); push_heap(c.begin(), c.end(), comp);
void pop();
template<class T, class Container, class Compare>
  void swap(priority_queue<T, Container, Compare>& x,
            priority_queue<T, Container, Compare>& y) noexcept(noexcept(x.swap(y)));
namespace std {
  template<class T, class Container = deque<T>>
  class stack {
  public:
    using value_type      = typename Container::value_type;
    using reference       = typename Container::reference;
    using const_reference = typename Container::const_reference;
    using size_type       = typename Container::size_type;
    using container_type  = Container;
  protected:
    Container c;
  public:
    stack() : stack(Container()) {}
    explicit stack(const Container&);
    explicit stack(Container&&);
    template<class Alloc> explicit stack(const Alloc&);
    template<class Alloc> stack(const Container&, const Alloc&);
    template<class Alloc> stack(Container&&, const Alloc&);
    template<class Alloc> stack(const stack&, const Alloc&);
    template<class Alloc> stack(stack&&, const Alloc&);
    [[nodiscard]] bool empty() const    { return c.empty(); }
    size_type size()  const             { return c.size(); }
    reference         top()             { return c.back(); }
    const_reference   top() const       { return c.back(); }
    void push(const value_type& x)      { c.push_back(x); }
    void push(value_type&& x)           { c.push_back(std::move(x)); }
    template<class... Args>
      decltype(auto) emplace(Args&&... args)
        { return c.emplace_back(std::forward<Args>(args)...); }
    void pop()                          { c.pop_back(); }
    void swap(stack& s) noexcept(is_nothrow_swappable_v<Container>)
      { using std::swap; swap(c, s.c); }
  };
  template<class Container>
    stack(Container) -> stack<typename Container::value_type, Container>;
  template<class Container, class Allocator>
    stack(Container, Allocator) -> stack<typename Container::value_type, Container>;
  template<class T, class Container, class Alloc>
    struct uses_allocator<stack<T, Container>, Alloc>
      : uses_allocator<Container, Alloc>::type { };
}explicit stack(const Container& cont);
explicit stack(Container&& cont);
template<class Alloc> explicit stack(const Alloc& a);
template<class Alloc> stack(const container_type& cont, const Alloc& a);
template<class Alloc> stack(container_type&& cont, const Alloc& a);
template<class Alloc> stack(const stack& s, const Alloc& a);
template<class Alloc> stack(stack&& s, const Alloc& a);
template<class T, class Container>
  bool operator==(const stack<T, Container>& x, const stack<T, Container>& y);
template<class T, class Container>
  bool operator!=(const stack<T, Container>& x, const stack<T, Container>& y);
template<class T, class Container>
  bool operator< (const stack<T, Container>& x, const stack<T, Container>& y);
template<class T, class Container>
  bool operator> (const stack<T, Container>& x, const stack<T, Container>& y);
template<class T, class Container>
  bool operator<=(const stack<T, Container>& x, const stack<T, Container>& y);
template<class T, class Container>
    bool operator>=(const stack<T, Container>& x, const stack<T, Container>& y);
template<class T, class Container>
  void swap(stack<T, Container>& x, stack<T, Container>& y) noexcept(noexcept(x.swap(y)));