#line 2 "library/KowerKoint/base.hpp"

#include <bits/stdc++.h>
using namespace std;

#line 4 "library/KowerKoint/stl-wrapper/pair.hpp"

template <typename T1, typename T2>
struct Pair : public std::pair<T1, T2> {
    constexpr Pair() : std::pair<T1, T2>() {}
    constexpr Pair(const T1& first, const T2& second) : std::pair<T1, T2>(first, second) {}
    template <typename U1, typename U2>
    constexpr Pair(U1&& first, U2&& second) : std::pair<T1, T2>(std::forward<U1>(first), std::forward<U2>(second)) {}
    template <typename U1, typename U2>
    constexpr Pair(const std::pair<U1, U2>& other) : std::pair<T1, T2>(other) {}
    template <typename U1, typename U2>
    constexpr Pair(std::pair<U1, U2>&& other) : std::pair<T1, T2>(std::move(other)) {}
    template <typename... Args1, typename... Args2>
    Pair(std::piecewise_construct_t, std::tuple<Args1...> first_args, std::tuple<Args2...> second_args) : std::pair<T1, T2>(std::piecewise_construct, first_args, second_args) {}
    friend std::istream& operator>>(std::istream& is, Pair& p) {
        return is >> p.first >> p.second;
    }
    friend std::ostream& operator<<(std::ostream& os, const Pair& p) {
        return os << p.first << ' ' << p.second;
    }
};
namespace std {
    template <typename T1, typename T2>
    struct hash<Pair<T1, T2>> {
        size_t operator()(const Pair<T1, T2>& p) const {
            size_t seed = 0;
            seed ^= hash<T1>()(p.first) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
            seed ^= hash<T2>()(p.second) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
            return seed;
        }
    };
}
#line 5 "library/KowerKoint/stl-wrapper/vector.hpp"

template <typename T>
struct Vector : std::vector<T> {
    Vector() noexcept : std::vector<T>() {}
    explicit Vector(size_t count) : std::vector<T>(count, T()) {}
    Vector(size_t count, const T& value) : std::vector<T>(count, value) {}
    template <typename InputIt>
    Vector(InputIt first, InputIt last) : std::vector<T>(first, last) {}
    Vector(const std::vector<T>& other) : std::vector<T>(other) {}
    Vector(std::vector<T>&& other) noexcept : std::vector<T>(std::move(other)) {}
    Vector(std::initializer_list<T> init) : std::vector<T>(init) {}
    const T& operator[](size_t i) const {
        assert(i < this->size());
        return std::vector<T>::operator[](i);
    }
    T& operator[](size_t i) {
        assert(i < this->size());
        return std::vector<T>::operator[](i);
    }
    const T& front() const {
        assert(!this->empty());
        return std::vector<T>::front();
    }
    T& front() {
        assert(!this->empty());
        return std::vector<T>::front();
    }
    const T& back() const {
        assert(!this->empty());
        return std::vector<T>::back();
    }
    T& back() {
        assert(!this->empty());
        return std::vector<T>::back();
    }
    friend std::istream& operator>>(std::istream& is, Vector& v) {
        for (auto& x : v) is >> x;
        return is;
    }
    friend std::ostream& operator<<(std::ostream& os, const Vector& v) {
        for (size_t i = 0; i < v.size(); ++i) {
            if (i) os << ' ';
            os << v[i];
        }
        return os;
    }
};
namespace std {
    template <typename T>
    struct hash<Vector<T>> {
        size_t operator()(const Vector<T>& v) const {
            size_t seed = 0;
            for (const auto& x : v) seed ^= hash<T>{}(x) + 0x9e3779b9 + (seed << 6) + (seed >> 2);
            return seed;
        }
    };
};
#line 4 "library/KowerKoint/stl-wrapper/set.hpp"
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#line 7 "library/KowerKoint/stl-wrapper/set.hpp"


template <typename T, typename Compare = std::less<T>>
using pbds_set = __gnu_pbds::tree<T, __gnu_pbds::null_type, Compare, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

template <typename T, typename Compare = std::less<T>>
struct Set : public pbds_set<T, Compare> {
    Set() : pbds_set<T, Compare>() {}
    explicit Set(const Compare& comp) : pbds_set<T, Compare>(comp) {}
    template <typename It>
    Set(It first, It last, const Compare& comp = Compare()) : pbds_set<T, Compare>(first, last, comp) {}
    Set(const pbds_set<T, Compare>& other) : pbds_set<T, Compare>(other) {}
    Set(const std::set<T, Compare>& other) : pbds_set<T, Compare>(other.begin(), other.end()) {}
    Set(pbds_set<T, Compare>&& other) : pbds_set<T, Compare>(std::move(other)) {}
    Set(std::initializer_list<T> init, const Compare& comp = Compare()) : pbds_set<T, Compare>(init, comp) {}
    typename Set::const_iterator cbegin() const { return this->begin(); }
    typename Set::const_iterator cend() const { return this->end(); }
    typename Set::const_reverse_iterator crbegin() const { return this->rbegin(); }
    typename Set::const_reverse_iterator crend() const { return this->rend(); }
    template <typename K>
    std::pair<typename Set::iterator, typename Set::iterator> equal_range(const K& value) {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    template <typename K>
    std::pair<typename Set::const_iterator, typename Set::const_iterator> equal_range(const K& value) const {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    template <typename K>
    size_t count(const K& x) const { return this->find(x) != this->end(); }
    decltype(Compare()) key_comp() const { return Compare(); }
    template <typename... Args>
    std::pair<typename Set::iterator, bool> emplace(Args&&... args) {
        return this->insert(T(std::forward<Args>(args)...));
    }
    template <typename... Args>
    typename Set::iterator emplace_hint(typename Set::const_iterator hint, Args&&... args) {
        return this->insert(hint, T(std::forward<Args>(args)...));
    }
    friend std::ostream& operator<<(std::ostream& os, const Set& set) {
        Vector<T> vector(set.begin(), set.end());
        return os << vector;
    }
};

namespace _set_util {
    template <typename T, typename Compare>
    struct CompareEqual {
        bool operator()(const T& lhs, const T& rhs) const {
            return !Compare()(rhs, lhs);
        }
    };
}
template <typename T, typename Compare = std::less<T>>
using pbds_multiset = __gnu_pbds::tree<T, __gnu_pbds::null_type, _set_util::CompareEqual<T, Compare>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

template <typename T, typename Compare = std::less<T>>
struct MultiSet : public pbds_multiset<T, Compare> {
    MultiSet() : pbds_multiset<T, Compare>() {}
    explicit MultiSet(const Compare& comp) : pbds_multiset<T, Compare>(comp) {}
    template <typename It>
    MultiSet(It first, It last, const Compare& comp = Compare()) : pbds_multiset<T, Compare>(first, last, comp) {}
    MultiSet(const pbds_multiset<T, Compare>& other) : pbds_multiset<T, Compare>(other) {}
    MultiSet(const std::multiset<T, Compare>& other) : pbds_multiset<T, Compare>(other.begin(), other.end()) {}
    MultiSet(pbds_multiset<T, Compare>&& other) : pbds_multiset<T, Compare>(std::move(other)) {}
    MultiSet(std::initializer_list<T> init, const Compare& comp = Compare()) : pbds_multiset<T, Compare>(init, comp) {}
    typename MultiSet::const_iterator cbegin() const { return this->begin(); }
    typename MultiSet::const_iterator cend() const { return this->end(); }
    typename MultiSet::const_reverse_iterator crbegin() const { return this->rbegin(); }
    typename MultiSet::const_reverse_iterator crend() const { return this->rend(); }
    template <typename K>
    std::pair<typename MultiSet::iterator, typename MultiSet::iterator> equal_range(const K& value) {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    template <typename K>
    std::pair<typename MultiSet::const_iterator, typename MultiSet::const_iterator> equal_range(const K& value) const {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    template <typename K>
    size_t count(const K& x) const {
        auto range = equal_range(x);
        return std::distance(range.first, range.second);
    }
    decltype(Compare()) key_comp() const { return Compare(); }
    template <typename... Args>
    typename MultiSet::iterator emplace(Args&&... args) {
        return this->insert(T(std::forward<Args>(args)...));
    }
    template <typename... Args>
    typename MultiSet::iterator emplace_hint(typename MultiSet::const_iterator hint, Args&&... args) {
        return this->insert(hint, T(std::forward<Args>(args)...));
    }
    friend std::ostream& operator<<(std::ostream& os, const MultiSet& set) {
        Vector<T> vector(set.begin(), set.end());
        return os << vector;
    }
};
namespace std {
    template <typename T, typename Compare>
    struct hash<Set<T, Compare>> {
        size_t operator()(const Set<T, Compare>& set) const {
            Vector<T> vec(set.begin(), set.end());
            return hash<Vector<T>>()(vec);
        }
    };
    template <typename T, typename Compare>
    struct hash<MultiSet<T, Compare>> {
        size_t operator()(const MultiSet<T, Compare>& set) const {
            Vector<T> vec(set.begin(), set.end());
            return hash<Vector<T>>()(vec);
        }
    };
};
#line 7 "library/KowerKoint/stl-wrapper/map.hpp"

template <typename Key, typename Value, typename Compare>
using pbds_map = __gnu_pbds::tree<Key, Value, Compare, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

template <typename Key, typename Value, typename Compare = std::less<Key>>
struct Map : pbds_map<Key, Value, Compare> {
    Map() : pbds_map<Key, Value, Compare>() {}
    explicit Map(const Compare& comp) : pbds_map<Key, Value, Compare>(comp) {}
    template <typename It>
    Map(It first, It last, const Compare& comp = Compare()) : pbds_map<Key, Value, Compare>(first, last, comp) {}
    Map(const pbds_map<Key, Value, Compare>& other) : pbds_map<Key, Value, Compare>(other) {}
    Map(const std::map<Key, Value, Compare>& other) : pbds_map<Key, Value, Compare>(other.begin(), other.end()) {}
    Map(pbds_map<Key, Value, Compare>&& other) : pbds_map<Key, Value, Compare>(std::move(other)) {}
    Map(std::initializer_list<std::pair<Key, Value>> init, const Compare& comp = Compare()) : pbds_map<Key, Value, Compare>(init, comp) {}
    typename Map::const_iterator cbegin() const { return this->begin(); }
    typename Map::const_iterator cend() const { return this->end(); }
    typename Map::const_reverse_iterator crbegin() const { return this->rbegin(); }
    typename Map::const_reverse_iterator crend() const { return this->rend(); }
    template <typename K>
    std::pair<typename Map::iterator, typename Map::iterator> equal_range(const K& value) {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    template <typename K>
    std::pair<typename Map::const_iterator, typename Map::const_iterator> equal_range(const K& value) const {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    Value& at(const Key& key) {
        auto it = find(key);
        assert(it != this->end());
        return it->second;
    }
    const Value& at(const Key& key) const {
        auto it = find(key);
        assert(it != this->end());
        return it->second;
    }
    template <typename K>
    size_t count(const K& x) const { return this->find(x) != this->end(); }
    decltype(Compare()) key_comp() const { return Compare(); }
    template <typename... Args>
    std::pair<typename Map::iterator, bool> emplace(Args&&... args) {
        return this->insert(std::make_pair(std::forward<Args>(args)...));
    }
    template <typename... Args>
    typename Map::iterator emplace_hint(typename Map::const_iterator hint, Args&&... args) {
        return this->insert(hint, std::make_pair(std::forward<Args>(args)...));
    }
    friend std::ostream& operator<<(std::ostream& out, const Map& map) {
        for (auto it = map.begin(); it != map.end(); ++it) {
            out << it->first << ' ' << it->second << '\n';
        }
        return out;
    }
};

namespace _map_util {
    template <typename T, typename Compare>
    struct CompareEqual {
        bool operator()(const T& lhs, const T& rhs) const {
            return !Compare()(rhs, lhs);
        }
    };
}
template <typename Key, typename Value, typename Compare = std::less<Key>>
using pbds_multimap = __gnu_pbds::tree<Key, Value, _map_util::CompareEqual<Key, Compare>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

template <typename Key, typename Value, typename Compare = std::less<Key>>
struct MultiMap : pbds_multimap<Key, Value, Compare> {
    MultiMap() : pbds_multimap<Key, Value, Compare>() {}
    explicit MultiMap(const Compare& comp) : pbds_multimap<Key, Value, Compare>(comp) {}
    template <typename It>
    MultiMap(It first, It last, const Compare& comp = Compare()) : pbds_multimap<Key, Value, Compare>(first, last, comp) {}
    MultiMap(const pbds_multimap<Key, Value, Compare>& other) : pbds_multimap<Key, Value, Compare>(other) {}
    MultiMap(const std::multimap<Key, Value, Compare>& other) : pbds_multimap<Key, Value, Compare>(other.begin(), other.end()) {}
    MultiMap(pbds_multimap<Key, Value, Compare>&& other) : pbds_multimap<Key, Value, Compare>(std::move(other)) {}
    MultiMap(std::initializer_list<std::pair<Key, Value>> init, const Compare& comp = Compare()) : pbds_multimap<Key, Value, Compare>(init, comp) {}
    typename MultiMap::const_iterator cbegin() const { return this->begin(); }
    typename MultiMap::const_iterator cend() const { return this->end(); }
    typename MultiMap::const_reverse_iterator crbegin() const { return this->rbegin(); }
    typename MultiMap::const_reverse_iterator crend() const { return this->rend(); }
    template <typename K>
    std::pair<typename MultiMap::iterator, typename MultiMap::iterator> equal_range(const K& value) {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    template <typename K>
    std::pair<typename MultiMap::const_iterator, typename MultiMap::const_iterator> equal_range(const K& value) const {
        return std::make_pair(lower_bound(value), upper_bound(value));
    }
    Value& at(const Key& key) {
        auto it = find(key);
        assert(it != this->end());
        return it->second;
    }
    const Value& at(const Key& key) const {
        auto it = find(key);
        assert(it != this->end());
        return it->second;
    }
    template <typename K>
    size_t count(const K& x) const {
        auto range = equal_range(x);
        return std::distance(range.first, range.second);
    }
    decltype(Compare())key_comp() const { return Compare(); }
    template <typename... Args>
    typename MultiMap::iterator emplace(Args&&... args) {
        return this->insert(std::make_pair(std::forward<Args>(args)...));
    }
    template <typename... Args>
    typename MultiMap::iterator emplace_hint(typename MultiMap::const_iterator hint, Args&&... args) {
        return this->insert(hint, std::make_pair(std::forward<Args>(args)...));
    }
    friend std::ostream& operator<<(std::ostream& out, const MultiMap& map) {
        for (auto it = map.begin(); it != map.end(); ++it) {
            out << it->first << ' ' << it->second << '\n';
        }
        return out;
    }
};

namespace std {
    template <typename Key, typename Value, typename Compare>
    struct hash<Map<Key, Value, Compare>> {
        size_t operator()(const Map<Key, Value, Compare>& map) const {
            Vector<pair<Key, Value>> v(map.begin(), map.end());
            return hash<Vector<pair<Key, Value>>>()(v);
        }
    };
    template <typename Key, typename Value, typename Compare>
    struct hash<MultiMap<Key, Value, Compare>> {
        size_t operator()(const Map<Key, Value, Compare>& map) const {
            Vector<pair<Key, Value>> v(map.begin(), map.end());
            return hash<Vector<pair<Key, Value>>>()(v);
        }
    };
}
#line 9 "library/KowerKoint/stl-wrapper/unordered_set.hpp"

template <typename T, typename Hash = std::hash<T>, typename KeyEqual = std::equal_to<T>>
using pbds_unordered_set = __gnu_pbds::gp_hash_table<T, __gnu_pbds::null_type, Hash, KeyEqual>;

template <typename T, typename Hash = std::hash<T>, typename KeyEqual = std::equal_to<T>>
struct UnorderedSet : public pbds_unordered_set<T, Hash, KeyEqual> {
    UnorderedSet() : pbds_unordered_set<T, Hash, KeyEqual>() {}
    explicit UnorderedSet(std::size_t bucket_count, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : pbds_unordered_set<T, Hash, KeyEqual>(bucket_count, hash, equal) {}
    template <typename InputIt>
    UnorderedSet(InputIt first, InputIt last, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : pbds_unordered_set<T, Hash, KeyEqual>(first, last, bucket_count, hash, equal) {}
    UnorderedSet(const pbds_unordered_set<T, Hash, KeyEqual>& other) : pbds_unordered_set<T, Hash, KeyEqual>(other) {}
    UnorderedSet(const std::unordered_set<T, Hash, KeyEqual>& other) : pbds_unordered_set<T, Hash, KeyEqual>(other.begin(), other.end()) {}
    UnorderedSet(pbds_unordered_set<T, Hash, KeyEqual>&& other) : pbds_unordered_set<T, Hash, KeyEqual>(std::move(other)) {}
    UnorderedSet(std::initializer_list<T> init, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : pbds_unordered_set<T, Hash, KeyEqual>(init, bucket_count, hash, equal) {}
    typename UnorderedSet::const_iterator cbegin() const { return this->begin(); }
    typename UnorderedSet::const_iterator cend() const { return this->end(); }
    KeyEqual key_eq() const { return KeyEqual(); }
    std::size_t count(const T& value) const { return this->find(value) != this->end(); }
    template <typename... Args>
    std::pair<typename UnorderedSet::iterator, bool> emplace(Args&&... args) { return this->insert(T(std::forward<Args>(args)...)); }
    template <typename... Args>
    typename UnorderedSet::iterator emplace_hint(typename UnorderedSet::const_iterator hint, Args&&... args) { return this->insert(hint, T(std::forward<Args>(args)...)); }
    friend std::ostream& operator<<(std::ostream& os, const UnorderedSet& set) {
        for (auto it = set.begin(); it != set.end(); ++it) {
            if(it != set.begin()) os << " ";
            os << *it;
        }
        return os;
    }
};
template <typename T, typename Hash = std::hash<T>, typename KeyEqual = std::equal_to<T>>
struct UnorderedMultiSet : std::unordered_multiset<T, Hash, KeyEqual> {
    UnorderedMultiSet() : std::unordered_multiset<T, Hash, KeyEqual>() {}
    explicit UnorderedMultiSet(std::size_t bucket_count, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : std::unordered_multiset<T, Hash, KeyEqual>(bucket_count, hash, equal) {}
    template <typename InputIt>
    UnorderedMultiSet(InputIt first, InputIt last, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : std::unordered_multiset<T, Hash, KeyEqual>(first, last, bucket_count, hash, equal) {}
    UnorderedMultiSet(const std::unordered_set<T, Hash, KeyEqual>& other) : std::unordered_multiset<T, Hash, KeyEqual>(other) {}
    UnorderedMultiSet(std::unordered_set<T, Hash, KeyEqual>&& other) : std::unordered_multiset<T, Hash, KeyEqual>(std::move(other)) {}
    UnorderedMultiSet(std::initializer_list<T> init, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : std::unordered_multiset<T, Hash, KeyEqual>(init, bucket_count, hash, equal) {}
    friend std::ostream& operator<<(std::ostream& os, const UnorderedMultiSet& set) {
        for (auto it = set.begin(); it != set.end(); ++it) {
            if(it != set.begin()) os << " ";
            os << *it;
        }
        return os;
    }
};
namespace std {
    template<typename T, typename Hash, typename KeyEqual>
    struct hash<UnorderedSet<T, Hash, KeyEqual>> {
        size_t operator()(const UnorderedSet<T, Hash, KeyEqual>& set) const {
            Vector<T> vec(set.begin(), set.end());
            sort(vec.begin(), vec.end());
            return hash<Vector<T>>()(vec);
        }
    };
    template<typename T, typename Hash, typename KeyEqual>
    struct hash<UnorderedMultiSet<T, Hash, KeyEqual>> {
        size_t operator()(const UnorderedMultiSet<T, Hash, KeyEqual>& set) const {
            Vector<T> vec(set.begin(), set.end());
            sort(vec.begin(), vec.end());
            return hash<Vector<T>>()(vec);
        }
    };
}
#line 9 "library/KowerKoint/stl-wrapper/unordered_map.hpp"

template <typename Key, typename Value, typename Hash = std::hash<Key>, typename KeyEqual = std::equal_to<Key>>
using pbds_unordered_map = __gnu_pbds::gp_hash_table<Key, Value, Hash, KeyEqual>;

template <typename Key, typename Value, typename Hash = std::hash<Key>, typename KeyEqual = std::equal_to<Key>>
struct UnorderedMap : public pbds_unordered_map<Key, Value, Hash, KeyEqual> {
    UnorderedMap() : pbds_unordered_map<Key, Value, Hash, KeyEqual>() {}
    explicit UnorderedMap(std::size_t bucket_count, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : pbds_unordered_map<Key, Value, Hash, KeyEqual>(bucket_count, hash, equal) {}
    template <typename InputIt>
    UnorderedMap(InputIt first, InputIt last, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : pbds_unordered_map<Key, Value, Hash, KeyEqual>(first, last, bucket_count, hash, equal) {}
    UnorderedMap(const pbds_unordered_map<Key, Value, Hash, KeyEqual>& other) : pbds_unordered_map<Key, Value, Hash, KeyEqual>(other) {}
    UnorderedMap(const std::unordered_map<Key, Value, Hash, KeyEqual>& other) : pbds_unordered_map<Key, Value, Hash, KeyEqual>(other.begin(), other.end()) {}
    UnorderedMap(pbds_unordered_map<Key, Value, Hash, KeyEqual>&& other) noexcept : pbds_unordered_map<Key, Value, Hash, KeyEqual>(std::move(other)) {}
    UnorderedMap(std::initializer_list<std::pair<Key, Value>> init, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : pbds_unordered_map<Key, Value, Hash, KeyEqual>(init, bucket_count, hash, equal) {}
    friend std::ostream& operator<<(std::ostream& os, const UnorderedMap& set) {
        for (auto it = set.begin(); it != set.end(); ++it) {
            os << it->first << ' ' << it->second << '\n';
        }
        return os;
    }
};

template <typename Key, typename Value, typename Hash = std::hash<Key>, typename KeyEqual = std::equal_to<Key>>
struct UnorderedMultiMap : std::unordered_multimap<Key, Value, Hash, KeyEqual> {
    UnorderedMultiMap() : std::unordered_multimap<Key, Value, Hash, KeyEqual>() {}
    explicit UnorderedMultiMap(std::size_t bucket_count, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : std::unordered_multimap<Key, Value, Hash, KeyEqual>(bucket_count, hash, equal) {}
    template <typename InputIt>
    UnorderedMultiMap(InputIt first, InputIt last, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : std::unordered_multimap<Key, Value, Hash, KeyEqual>(first, last, bucket_count, hash, equal) {}
    UnorderedMultiMap(const std::unordered_map<Key, Value, Hash, KeyEqual>& other) : std::unordered_multimap<Key, Value, Hash, KeyEqual>(other) {}
    UnorderedMultiMap(std::unordered_map<Key, Value, Hash, KeyEqual>&& other) noexcept : std::unordered_multimap<Key, Value, Hash, KeyEqual>(std::move(other)) {}
    UnorderedMultiMap(std::initializer_list<std::pair<Key, Value>> init, std::size_t bucket_count = 1, const Hash& hash = Hash(), const KeyEqual& equal = KeyEqual()) : std::unordered_multimap<Key, Value, Hash, KeyEqual>(init, bucket_count, hash, equal) {}
    friend std::ostream& operator<<(std::ostream& os, const UnorderedMultiMap& map) {
        for (auto it = map.begin(); it != map.end(); ++it) {
            os << it->first << ' ' << it->second << '\n';
        }
        return os;
    }
};
namespace std {
    template<typename T, typename Hash, typename KeyEqual>
    struct hash<UnorderedMap<T, Hash, KeyEqual>> {
        size_t operator()(const UnorderedMap<T, Hash, KeyEqual>& map) const {
            Vector<T> vec(map.begin(), map.end());
            sort(vec.begin(), vec.end());
            return hash<Vector<T>>()(vec);
        }
    };
    template<typename T, typename Hash, typename KeyEqual>
    struct hash<UnorderedMultiMap<T, Hash, KeyEqual>> {
        size_t operator()(const UnorderedMultiMap<T, Hash, KeyEqual>& map) const {
            Vector<T> vec(map.begin(), map.end());
            sort(vec.begin(), vec.end());
            return hash<Vector<T>>()(vec);
        }
    };
}
#line 7 "library/KowerKoint/base.hpp"

#define REP(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, a, b) for(ll i = a; i < (ll)(b); i++)
#define ALL(a) (a).begin(),(a).end()
#define RALL(a) (a).rbegin(),(a).rend()
#define END(...) { print(__VA_ARGS__); return; }

using VI = Vector<int>;
using VVI = Vector<VI>;
using VVVI = Vector<VVI>;
using ll = long long;
using VL = Vector<ll>;
using VVL = Vector<VL>;
using VVVL = Vector<VVL>;
using ull = unsigned long long;
using VUL = Vector<ull>;
using VVUL = Vector<VUL>;
using VVVUL = Vector<VVUL>;
using VD = Vector<double>;
using VVD = Vector<VD>;
using VVVD = Vector<VVD>;
using VS = Vector<string>;
using VVS = Vector<VS>;
using VVVS = Vector<VVS>;
using VC = Vector<char>;
using VVC = Vector<VC>;
using VVVC = Vector<VVC>;
using P = Pair<int, int>;
using VP = Vector<P>;
using VVP = Vector<VP>;
using VVVP = Vector<VVP>;
using LP = Pair<ll, ll>;
using VLP = Vector<LP>;
using VVLP = Vector<VLP>;
using VVVLP = Vector<VVLP>;

template <typename T>
using PQ = priority_queue<T>;
template <typename T>
using GPQ = priority_queue<T, vector<T>, greater<T>>;

constexpr int INF = 1001001001;
constexpr ll LINF = 1001001001001001001ll;
constexpr int DX[] = {1, 0, -1, 0};
constexpr int DY[] = {0, 1, 0, -1};

void print() { cout << '\n'; }
template<typename T>
void print(const T &t) { cout << t << '\n'; }
template<typename Head, typename... Tail>
void print(const Head &head, const Tail &... tail) {
    cout << head << ' ';
    print(tail...);
}

#ifdef DEBUG
void dbg() { cerr << '\n'; }
template<typename T>
void dbg(const T &t) { cerr << t << '\n'; }
template<typename Head, typename... Tail>
void dbg(const Head &head, const Tail &... tail) {
    cerr << head << ' ';
    dbg(tail...);
}
#else
template<typename... Args>
void dbg(const Args &... args) {}
#endif

template<typename T>
Vector<Vector<T>> split(typename vector<T>::const_iterator begin, typename vector<T>::const_iterator end, T val) {
    Vector<Vector<T>> res;
    Vector<T> cur;
    for(auto it = begin; it != end; it++) {
        if(*it == val) {
            res.push_back(cur);
            cur.clear();
        } else cur.push_back(*it);
    }
    res.push_back(cur);
    return res;
}

Vector<string> split(typename string::const_iterator begin, typename string::const_iterator end, char val) {
    Vector<string> res;
    string cur = "";
    for(auto it = begin; it != end; it++) {
        if(*it == val) {
            res.push_back(cur);
            cur.clear();
        } else cur.push_back(*it);
    }
    res.push_back(cur);
    return res;
}

template< typename T1, typename T2 >
inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }

template< typename T1, typename T2 >
inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }

template <typename T>
pair<VI, Vector<T>> compress(const vector<T> &a) {
    int n = a.size();
    Vector<T> x;
    REP(i, n) x.push_back(a[i]);
    sort(ALL(x)); x.erase(unique(ALL(x)), x.end());
    VI res(n);
    REP(i, n) res[i] = lower_bound(ALL(x), a[i]) - x.begin();
    return make_pair(res, x);
}

template <typename It>
auto rle(It begin, It end) {
    Vector<pair<typename It::value_type, int>> res;
    if(begin == end) return res;
    auto pre = *begin;
    int num = 1;
    for(auto it = begin + 1; it != end; it++) {
        if(pre != *it) {
            res.emplace_back(pre, num);
            pre = *it;
            num = 1;
        } else num++;
    }
    res.emplace_back(pre, num);
    return res;
}

template <typename It>
Vector<pair<typename It::value_type, int>> rle_sort(It begin, It end) {
    Vector<typename It::value_type> cloned(begin, end);
    sort(ALL(cloned));
    auto e = rle(ALL(cloned));
    sort(ALL(e), [](const auto& l, const auto& r) { return l.second < r.second; });
    return e;
}

template <typename T>
Pair<Vector<T>, Vector<T>> factorial(int n) {
    Vector<T> res(n+1), rev(n+1);
    res[0] = 1;
    REP(i, n) res[i+1] = res[i] * (i+1);
    rev[n] = 1 / res[n];
    for(int i = n; i > 0; i--) {
        rev[i-1] = rev[i] * i;
    }
    return make_pair(res, rev);
}
#line 3 "library/KowerKoint/operator.hpp"

template <typename T>
T add_op(T a, T b) { return a + b; }
template <typename T>
T sub_op(T a, T b) { return a - b; }
template <typename T>
T zero_e() { return T(0); }
template <typename T>
T div_op(T a, T b) { return a / b; }
template <typename T>
T mult_op(T a, T b) { return a * b; }
template <typename T>
T one_e() { return T(1); }
template <typename T>
T xor_op(T a, T b) { return a ^ b; }
template <typename T>
T and_op(T a, T b) { return a & b; }
template <typename T>
T or_op(T a, T b) { return a | b; }
ll mod3() { return 998244353LL; }
ll mod7() { return 1000000007LL; }
ll mod9() { return 1000000009LL; }
template <typename T>
T max_op(T a, T b) { return max(a, b); }
template <typename T>
T min_op(T a, T b) { return min(a, b); }

template <typename T>
T max_e() { return numeric_limits<T>::max(); }
template <typename T>
T min_e() { return numeric_limits<T>::min(); }
#line 3 "library/KowerKoint/integer/extgcd.hpp"

ll extgcd(ll a, ll b, ll& x, ll& y) {
    x = 1, y = 0;
    ll nx = 0, ny = 1;
    while(b) {
        ll q = a / b;
        tie(a, b) = LP(b, a % b);
        tie(x, nx) = LP(nx, x - nx*q);
        tie(y, ny) = LP(ny, y - ny*q);
    }
    return a;
}
#line 2 "library/KowerKoint/integer/pow-mod.hpp"

ll inv_mod(ll n, ll m) {
    n %= m;
    if (n < 0) n += m;
    ll x, y;
    assert(extgcd(n, m, x, y) == 1);
    x %= m;
    if(x < 0) x += m;
    return x;
}

ll pow_mod(ll a, ll n, ll m) {
    if(n == 0) return 1LL;
    if(n < 0) return inv_mod(pow_mod(a, -n, m), m);
    a %= m;
    if (a < 0) n += m;
    ll res = 1;
    while(n) {
        if(n & 1) {
            res *= a;
            res %= m;
        }
        n >>= 1;
        a *= a;
        a %= m;
    }
    return res;
}
#line 4 "library/KowerKoint/integer/modint.hpp"

template <ll (*mod)()>
struct Modint {
    ll val;
    
    Modint(): val(0) {}

    Modint(ll x): val(x) {
        val %= mod();
        if(val < 0) val += mod();
    }

    Modint& operator+=(const Modint& r) {
        val += r.val;
        if(val >= mod()) val -= mod();
        return *this;
    }
    friend Modint operator+(const Modint& l, const Modint& r) {
        return Modint(l) += r;
    }

    Modint& operator-=(const Modint& r) {
        val -= r.val;
        if(val < 0) val += mod();
        return *this;
    }
    friend Modint operator-(const Modint& l, const Modint& r) {
        return Modint(l) -= r;
    }

    Modint& operator*=(const Modint& r) {
        val *= r.val;
        val %= mod();
        return *this;
    }
    Modint operator*(const Modint& r) {
        return (Modint(*this) *= r);
    }
    friend Modint operator*(const Modint& l, const Modint& r) {
        return Modint(l) *= r;
    }

    Modint pow(ll n) const {
        return Modint(pow_mod(val, n, mod()));
    }

    Modint inv() const {
        return Modint(inv_mod(val, mod()));
    }

    Modint& operator/=(const Modint& r) {
        return (*this *= r.inv());
    }
    friend Modint operator/(const Modint& l, const Modint& r) {
        return Modint(l) /= r;
    }

    Modint& operator^=(const ll n) {
        val = pow_mod(val, n, mod());
        return *this;
    }
    Modint operator^(const ll n) {
        return this->pow(n);
    }

    Modint operator+() const { return *this; }
    Modint operator-() const { return Modint() - *this; }

    Modint& operator++() {
        val++;
        if(val == mod()) val = 0LL;
        return *this;
    }
    Modint& operator++(int) {
        Modint res(*this);
        ++*this;
        return res;
    }

    Modint& operator--() {
        if(val == 0LL) val = mod();
        val--;
        return *this;
    }
    Modint& operator--(int) {
        Modint res(*this);
        --*this;
        return res;
    }

    friend bool operator==(const Modint& l, const Modint& r) {
        return l.val == r.val;
    }
    friend bool operator!=(const Modint& l, const Modint& r) {
        return l.val != r.val;
    }

    static Pair<Vector<Modint>, Vector<Modint>> factorial(int n) {
        Vector<Modint> fact(n+1), rfact(n+1);
        fact[0] = 1;
        REP(i, n) fact[i+1] = fact[i] * (i+1);
        rfact[n] = 1 / fact[n];
        for(int i = n-1; i >= 0; i--) rfact[i] = rfact[i+1] * (i+1);
        return {fact, rfact};
    }

    friend istream& operator>>(istream& is, Modint& mi) {
        is >> mi.val;
        return is;
    }

    friend ostream& operator<<(ostream& os, const Modint& mi) {
        os << mi.val;
        return os;
    }
};

namespace std {
    template<ll (*mod)()>
    struct hash<Modint<mod>> {
        size_t operator()(const Modint<mod> &p) const {
            return hash<ll>()(p.val);
        }
    };
}

using MI3 = Modint<mod3>;
using V3 = Vector<MI3>;
using VV3 = Vector<V3>;
using VVV3 = Vector<VV3>;
using MI7 = Modint<mod7>;
using V7 = Vector<MI7>;
using VV7 = Vector<V7>;
using VVV7 = Vector<VV7>;
using MI9 = Modint<mod9>;
using V9 = Vector<MI9>;
using VV9 = Vector<V9>;
using VVV9 = Vector<VV9>;
#line 3 "library/KowerKoint/counting/counting.hpp"

template <typename T>
struct Counting {
    Vector<T> fact, ifact;

    Counting() {}
    Counting(ll n) {
        assert(n >= 0);
        expand(n);
    }

    void expand(ll n) {
        assert(n >= 0);
        ll sz = (ll)fact.size();
        if(sz > n) return;
        fact.resize(n+1);
        ifact.resize(n+1);
        fact[0] = 1;
        FOR(i, max(1LL, sz), n+1) fact[i] = fact[i-1] * i;
        ifact[n] = 1 / fact[n];
        for(ll i = n-1; i >= sz; i--) ifact[i] = ifact[i+1] * (i+1);
    }

    T p(ll n, ll r) {
        if(n < r) return 0;
        assert(r >= 0);
        expand(n);
        return fact[n] * ifact[n-r];
    }

    T c(ll n, ll r) {
        if(n < r) return 0;
        assert(r >= 0);
        expand(n);
        return fact[n] * ifact[r] * ifact[n-r];
    }

    T h(ll n, ll r) {
        assert(n >= 0);
        assert(r >= 0);
        return c(n+r-1, r);
    }

    T stirling(ll n, ll k) {
        if(n < k) return 0;
        assert(k >= 0);
        if(n == 0) return 1;
        T res = 0;
        int sign = k%2? -1 : 1;
        expand(k);
        REP(i, k+1) {
            res += sign * ifact[i] * ifact[k-i] * T(i).pow(n);
            sign *= -1;
        }
        return res;
    }

    Vector<Vector<T>> stirling_table(ll n, ll k) {
        assert(n >= 0 && k >= 0);
        Vector<Vector<T>> res(n+1, Vector<T>(k+1));
        res[0][0] = 1;
        FOR(i, 1, n+1) FOR(j, 1, k+1) {
            res[i][j] = res[i-1][j-1] + j * res[i-1][j];
        }
        return res;
    }

    T bell(ll n, ll k) {
        assert(n >= 0 && k >= 0);
        expand(k);
        Vector<T> tmp(k+1);
        int sign = 1;
        tmp[0] = 1;
        FOR(i, 1, k+1) {
            sign *= -1;
            tmp[i] = tmp[i-1] + sign * ifact[i];
        }
        T res = 0;
        REP(i, k+1) {
            res += T(i).pow(n) * ifact[i] * tmp[k-i];
        }
        return res;
    }

    Vector<Vector<T>> partition_table(ll n, ll k) {
        assert(n >= 0 && k >= 0);
        Vector<Vector<T>> res(n+1, Vector<T>(k+1));
        REP(i, k+1) res[0][i] = 1;
        FOR(i, 1, n+1) FOR(j, 1, k+1) {
            res[i][j] = res[i][j-1] + (i<j? 0 : res[i-j][j]);
        }
        return res;
    }
};
#line 4 "library/KowerKoint/matrix/matrix.hpp"

template <
    typename T,
    T (*add)(const T, const T)=add_op,
    T (*zero)()=zero_e,
    T (*mult)(const T, const T)=mult_op,
    T (*one)()=one_e,
    T (*sub)(const T, const T)=sub_op,
    T (*div)(const T, const T)=div_op
>
struct Matrix {
    int n, m;
    Vector<Vector<T>> A;

    Matrix() : n(0), m(0), A(Vector<Vector<T>>(0)) {}
    Matrix(size_t _n, size_t _m) : n(_n), m(_m), A(_n, Vector<T>(_m, zero())) {}
    Matrix(const vector<vector<T>>& _A) : n(_A.size()), m(_A[0].size()), A(_A) {}

    Vector<T> &operator[](int i) {
        assert(0 <= i && i < n);
        return A.at(i);
    }
    const Vector<T> &operator[](int i) const {
        assert(0 <= i && i < n);
        return A.at(i);
    }

    static Matrix I(size_t n) {
        assert(n >= 0);
        Matrix ret(n, n);
        REP(i, n) ret[i][i] = one();
        return ret;
    }

    Matrix &operator+=(const Matrix &B) {
        assert(n == B.n && m == B.m);
        REP(i, n) REP(j, m) A[i][j] = add(A[i][j], B[i][j]);
        return *this;
    }
    Matrix operator+(const Matrix &B) const {
        assert(n == B.n && m == B.m);
        return (Matrix(*this) += B);
    }

    Matrix &operator-=(const Matrix &B) {
        assert(n == B.n && m == B.m);
        REP(i, n) REP(j, m) A[i][j] = sub(A[i][j], B[i][j]);
        return *this;
    }
    Matrix operator-(const Matrix &B) const {
        assert(n == B.n && m == B.m);
        return (Matrix(*this) -= B);
    }

    Matrix &operator*=(const Matrix &B) {
        assert(m == B.n);
        Vector<Vector<T>> res(n, Vector<T>(B.m, zero()));
        REP(i, n) REP(j, m) REP(k, B.m) res[i][k] = add(res[i][k], mult(A[i][j], B[j][k]));
        A.swap(res);
        m = B.m;
        return (*this);
    }
    Matrix operator*(const Matrix &B) const {
        assert(m == B.n);
        return (Matrix(*this) *= B);
    }

    Matrix &operator|=(const Matrix &B) {
        assert(B.n == n);
        REP(i, n) {
            A[i].resize(m+B.m);
            REP(j, B.m) A[i][m+j] = B[i][j];
        }
        m += B.m;
        return (*this);
    }
    Matrix operator|(const Matrix &B) const {
        assert(B.n == n);
        return (Matrix(*this) |= B);
    }

    Matrix &operator|=(const vector<T> &B) {
        assert(B.size() == n);
        REP(i, n) {
            A[i].push_back(B[i]);
        }
        m++;
        return (*this);
    }
    Matrix operator|(const vector<T> &B) const {
        assert(B.size() == n);
        return (Matrix(*this) |= B);
    }

    Matrix &operator&=(const Matrix &B) {
        assert(B.m == m);
        A.resize(n+B.n);
        REP(i, B.n) {
            A[n+i] = B[i];
        }
        n += B.n;
        return (*this);
    }
    Matrix operator&(const Matrix &B) const {
        assert(B.m == m);
        return (Matrix(*this) &= B);
    }

    Matrix &operator&=(const vector<T> &B) {
        assert(B.size() == m);
        A.push_back(B);
        n++;
        return (*this);
    }
    Matrix operator&(const vector<T> &B) const {
        assert(B.size() == m);
        return (Matrix(*this) &= B);
    }

    friend istream &operator>>(istream &is, Matrix &mat) {
        REP(i, mat.n) REP(j, mat.m) is >> mat[i][j];
        return is;
    }

    friend ostream &operator<<(ostream &os, const Matrix &mat) {
        REP(i, mat.n) {
            REP(j, mat.m) os << mat[i][j] << (j==mat.m-1? '\n' : ' ');
        }
        return os;
    }

    Pair<Matrix, T> gaussian_elimination() const {
        Matrix mat(*this);
        T det = one();
        VI columns;
        int i = 0;
        int j = 0;
        while(i < n && j < m) {
            int idx = -1;
            FOR(k, i, n) if(mat[k][j] != zero()) idx = k;
            if(idx == -1) {
                det = zero();
                j++;
                continue;
            }
            if(i != idx) {
                det *= sub(zero(), one());
                swap(mat[i], mat[idx]);
            }
            det *= mat[i][j];
            T scale = mat[i][j];
            REP(l, m) mat[i][l] = div(mat[i][l], scale);
            FOR(k, i+1, n) {
                T scale = mat[k][j];
                REP(l, m) mat[k][l] = sub(mat[k][l], mult(mat[i][l], scale));
            }
            columns.push_back(j);
            i++;
            j++;
        }
        REP(i, columns.size()) {
            int j = columns[i];
            REP(k, i) {
                T scale = mat[k][j];
                FOR(l, j, m) {
                    mat[k][l] = sub(mat[k][l], mult(mat[i][l], scale));
                }
            }
        }
        return {mat, det};
    }

    void make_basis() {
        *this = gaussian_elimination().first;
        while(n && get_bra(n-1) == Vector<T>(m, zero())) pop_bra();
    }

    Matrix inv() const {
        Matrix and_i = (*this) | I(n);
        auto [i_and, det] = and_i.gaussian_elimination();
        assert(det != zero());
        Matrix res(n, n);
        REP(i, n) REP(j, n) res[i][j] = i_and[i][n+j];
        return res;
    }

    Vector<T> get_bra(int i) const {
        assert(0 <= i && i < n);
        return A[i];
    }

    Vector<T> get_ket(int i) const {
        assert(0 <= i && i < m);
        Vector<T> res(n);
        REP(i, n) res[i] = A[i][i];
        return res;
    }

    void pop_bra() {
        assert(n > 0);
        A.pop_back();
        n--;
    }

    void pop_ket() {
        assert(m > 0);
        REP(i, n) A[i].pop_back();
        m--;
    }

    Matrix transpose() const {
        Matrix res(m, n);
        REP(i, n) REP(j, m) res[j][i] = A[i][j];
        return res;
    }

    Matrix operator^=(ll k) {
        if(k < 0) {
            *this = this->inv();
            k = -k;
        }
        Matrix res = Matrix::I(n);
        while(k) {
            if(k & 1) res *= *this;
            *this *= *this;
            k >>= 1LL;
        }
        A.swap(res.A);
        return (*this);
    }
    Matrix operator^(const ll k) const {
        return (Matrix(*this) ^= k);
    }
};

using XorMatrix = Matrix<
    int,
    xor_op<int>,
    zero_e<int>,
    and_op<int>,
    one_e<int>,
    xor_op<int>,
    and_op<int>
>;
#line 3 "Contests/main.cpp"

/* #include <atcoder/all> */
/* using namespace atcoder; */
/* #include "KowerKoint/expansion/ac-library/all.hpp" */

void solve(){
    ll n; cin >> n;
    Matrix<MI3> m(2, 2);
    m[0][0] = m[0][1] = m[1][0] = 1;
    m ^= n-1;
    print(m[0][0] + m[0][1] - 1);
}

// generated by oj-template v4.7.2 (https://github.com/online-judge-tools/template-generator)
int main() {
    // Fasterize input/output script
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(100);
    // scanf/printf user should delete this fasterize input/output script

    int t = 1;
    //cin >> t; // comment out if solving multi testcase
    for(int testCase = 1;testCase <= t;++testCase){
        solve();
    }
    return 0;
}