結果

問題 No.2330 Eat Slime
ユーザー shiomusubi496shiomusubi496
提出日時 2023-05-28 14:21:58
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 60,964 bytes
コンパイル時間 4,624 ms
コンパイル使用メモリ 263,976 KB
実行使用メモリ 22,488 KB
最終ジャッジ日時 2024-06-08 05:14:25
合計ジャッジ時間 15,262 ms
ジャッジサーバーID
(参考情報)
judge1 / judge4
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
5,248 KB
testcase_01 AC 2 ms
5,248 KB
testcase_02 AC 2 ms
5,376 KB
testcase_03 AC 2 ms
5,376 KB
testcase_04 AC 2 ms
5,376 KB
testcase_05 WA -
testcase_06 WA -
testcase_07 AC 421 ms
18,108 KB
testcase_08 WA -
testcase_09 WA -
testcase_10 WA -
testcase_11 AC 33 ms
6,532 KB
testcase_12 AC 432 ms
17,608 KB
testcase_13 AC 424 ms
17,108 KB
testcase_14 AC 65 ms
9,116 KB
testcase_15 AC 221 ms
15,384 KB
testcase_16 AC 415 ms
16,000 KB
testcase_17 WA -
testcase_18 AC 445 ms
22,304 KB
testcase_19 WA -
testcase_20 AC 441 ms
22,364 KB
testcase_21 WA -
testcase_22 AC 444 ms
22,360 KB
testcase_23 AC 442 ms
22,236 KB
testcase_24 AC 443 ms
22,444 KB
testcase_25 AC 441 ms
22,356 KB
testcase_26 AC 444 ms
22,364 KB
testcase_27 AC 443 ms
22,360 KB
testcase_28 AC 445 ms
22,360 KB
testcase_29 AC 443 ms
22,364 KB
testcase_30 AC 444 ms
22,364 KB
testcase_31 AC 450 ms
22,360 KB
権限があれば一括ダウンロードができます

ソースコード

diff #

#line 2 "library/other/template.hpp"

#include <bits/stdc++.h>
#line 2 "library/template/macros.hpp"

#line 4 "library/template/macros.hpp"

#ifndef __COUNTER__
#define __COUNTER__ __LINE__
#endif

#define REP_SELECTER(a, b, c, d, e, ...) e
#define REP1_0(b, c) REP1_1(b, c)
#define REP1_1(b, c)                                                           \
    for (ll REP_COUNTER_##c = 0; REP_COUNTER_##c < (ll)(b); ++REP_COUNTER_##c)
#define REP1(b) REP1_0(b, __COUNTER__)
#define REP2(i, b) for (ll i = 0; i < (ll)(b); ++i)
#define REP3(i, a, b) for (ll i = (ll)(a); i < (ll)(b); ++i)
#define REP4(i, a, b, c) for (ll i = (ll)(a); i < (ll)(b); i += (ll)(c))
#define rep(...) REP_SELECTER(__VA_ARGS__, REP4, REP3, REP2, REP1)(__VA_ARGS__)
#define RREP2(i, a) for (ll i = (ll)(a)-1; i >= 0; --i)
#define RREP3(i, a, b) for (ll i = (ll)(a)-1; i >= (ll)(b); --i)
#define RREP4(i, a, b, c) for (ll i = (ll)(a)-1; i >= (ll)(b); i -= (ll)(c))
#define rrep(...) REP_SELECTER(__VA_ARGS__, RREP4, RREP3, RREP2)(__VA_ARGS__)
#define REPS2(i, b) for (ll i = 1; i <= (ll)(b); ++i)
#define REPS3(i, a, b) for (ll i = (ll)(a) + 1; i <= (ll)(b); ++i)
#define REPS4(i, a, b, c) for (ll i = (ll)(a) + 1; i <= (ll)(b); i += (ll)(c))
#define reps(...) REP_SELECTER(__VA_ARGS__, REPS4, REPS3, REPS2)(__VA_ARGS__)
#define RREPS2(i, a) for (ll i = (ll)(a); i > 0; --i)
#define RREPS3(i, a, b) for (ll i = (ll)(a); i > (ll)(b); --i)
#define RREPS4(i, a, b, c) for (ll i = (ll)(a); i > (ll)(b); i -= (ll)(c))
#define rreps(...)                                                             \
    REP_SELECTER(__VA_ARGS__, RREPS4, RREPS3, RREPS2)(__VA_ARGS__)

#define each_for(...) for (auto&& __VA_ARGS__)
#define each_const(...) for (const auto& __VA_ARGS__)

#define all(v) std::begin(v), std::end(v)
#if __cplusplus >= 201402L
#define rall(v) std::rbegin(v), std::rend(v)
#else
#define rall(v) v.rbegin(), v.rend()
#endif

#if __cpp_constexpr >= 201304L
#define CONSTEXPR constexpr
#else
#define CONSTEXPR
#endif

#if __cpp_if_constexpr >= 201606L
#define IF_CONSTEXPR constexpr
#else
#define IF_CONSTEXPR
#endif

#define IO_BUFFER_SIZE 2048
#line 2 "library/template/alias.hpp"

#line 4 "library/template/alias.hpp"

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PLL = std::pair<ll, ll>;
template<class T>
using prique = std::priority_queue<T, std::vector<T>, std::greater<T>>;

template<class T> class infinity {
public:
    static constexpr T value = std::numeric_limits<T>::max() / 2;
    static constexpr T mvalue = std::numeric_limits<T>::min() / 2;
    static constexpr T max = std::numeric_limits<T>::max();
    static constexpr T min = std::numeric_limits<T>::min();
};

#if __cplusplus <= 201402L
template<class T> constexpr T infinity<T>::value;
template<class T> constexpr T infinity<T>::mvalue;
template<class T> constexpr T infinity<T>::max;
template<class T> constexpr T infinity<T>::min;
#endif

#if __cpp_variable_templates >= 201304L
template<class T> constexpr T INF = infinity<T>::value;
#endif

constexpr ll inf = infinity<ll>::value;
constexpr ld EPS = 1e-8;
constexpr ld PI = 3.1415926535897932384626;
#line 2 "library/template/type_traits.hpp"

#line 5 "library/template/type_traits.hpp"

template<class T, class... Args> struct function_traits_impl {
    using result_type = T;
    template<std::size_t idx>
    using argument_type =
        typename std::tuple_element<idx, std::tuple<Args...>>::type;
    using argument_tuple = std::tuple<Args...>;
    static constexpr std::size_t arg_size() { return sizeof...(Args); }
};

template<class> struct function_traits_helper;

template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)&> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const&> {
    using type = function_traits_impl<Res, Args...>;
};

#if __cpp_noexcept_function_type >= 201510L
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...)& noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
template<class Res, class Tp, class... Args>
struct function_traits_helper<Res (Tp::*)(Args...) const& noexcept> {
    using type = function_traits_impl<Res, Args...>;
};
#endif

template<class F>
using function_traits =
    typename function_traits_helper<decltype(&F::operator())>::type;


template<class T>
using is_signed_int =
    std::disjunction<std::conjunction<std::is_integral<T>, std::is_signed<T>>,
                     std::is_same<T, __int128_t>>;
template<class T>
using is_unsigned_int =
    std::disjunction<std::conjunction<std::is_integral<T>, std::is_unsigned<T>>,
                     std::is_same<T, __uint128_t>>;
template<class T>
using is_int = std::disjunction<is_signed_int<T>, is_unsigned_int<T>>;
template<class T>
using make_signed_int = typename std::conditional<
    std::is_same<T, __int128_t>::value || std::is_same<T, __uint128_t>::value,
    std::common_type<__int128_t>, std::make_signed<T>>::type;
template<class T>
using make_unsigned_int = typename std::conditional<
    std::is_same<T, __int128_t>::value || std::is_same<T, __uint128_t>::value,
    std::common_type<__uint128_t>, std::make_unsigned<T>>::type;


template<class T, class = void> struct is_range : std::false_type {};
template<class T>
struct is_range<
    T,
    decltype(all(std::declval<typename std::add_lvalue_reference<T>::type>()),
             (void)0)> : std::true_type {};

template<class T, bool = is_range<T>::value>
struct range_rank : std::integral_constant<std::size_t, 0> {};
template<class T>
struct range_rank<T, true>
    : std::integral_constant<std::size_t,
                             range_rank<typename T::value_type>::value + 1> {};

template<std::size_t size> struct int_least {
    static_assert(size <= 128, "size must be less than or equal to 128");

    using type = typename std::conditional<
        size <= 8, std::int_least8_t,
        typename std::conditional<
            size <= 16, std::int_least16_t,
            typename std::conditional<
                size <= 32, std::int_least32_t,
                typename std::conditional<size <= 64, std::int_least64_t,
                                          __int128_t>::type>::type>::type>::
        type;
};

template<std::size_t size> using int_least_t = typename int_least<size>::type;

template<std::size_t size> struct uint_least {
    static_assert(size <= 128, "size must be less than or equal to 128");

    using type = typename std::conditional<
        size <= 8, std::uint_least8_t,
        typename std::conditional<
            size <= 16, std::uint_least16_t,
            typename std::conditional<
                size <= 32, std::uint_least32_t,
                typename std::conditional<size <= 64, std::uint_least64_t,
                                          __uint128_t>::type>::type>::type>::
        type;
};

template<std::size_t size> using uint_least_t = typename uint_least<size>::type;

template<class T>
using double_size_int = int_least<std::numeric_limits<T>::digits * 2 + 1>;
template<class T> using double_size_int_t = typename double_size_int<T>::type;
template<class T>
using double_size_uint = uint_least<std::numeric_limits<T>::digits * 2>;
template<class T> using double_size_uint_t = typename double_size_uint<T>::type;

template<class T>
using double_size =
    typename std::conditional<is_signed_int<T>::value, double_size_int<T>,
                              double_size_uint<T>>::type;
template<class T> using double_size_t = typename double_size<T>::type;
#line 2 "library/template/in.hpp"

#line 4 "library/template/in.hpp"
#include <unistd.h>
#line 8 "library/template/in.hpp"

template<std::size_t buf_size = IO_BUFFER_SIZE> class Reader {
private:
    int fd, idx, sz;
    bool state;
    std::array<char, buf_size> buffer;
    inline void read_buf() {
        sz = read(fd, buffer.begin(), buf_size);
        idx = 0;
        if (sz < 0) throw std::runtime_error("input failed");
    }

public:
    static constexpr int get_buf_size() { return buf_size; }
    Reader() noexcept : fd(0), idx(0), sz(0), state(true) {}
    Reader(int fd) noexcept : fd(fd), idx(0), sz(0), state(true) {}
    Reader(FILE* fp) noexcept : fd(fileno(fp)), idx(0), sz(0), state(true) {}

    class iterator {
    private:
        Reader* reader;

    public:
        using difference_type = void;
        using value_type = void;
        using pointer = void;
        using reference = void;
        using iterator_category = std::input_iterator_tag;

        iterator() : reader(nullptr) {}
        explicit iterator(Reader& reader) : reader(&reader) {}
        explicit iterator(Reader* reader) : reader(reader) {}

        iterator& operator++() {
            if (reader->idx == reader->sz) reader->read_buf();
            ++reader->idx;
            return *this;
        }
        iterator operator++(int) {
            iterator res = *this;
            ++(*this);
            return res;
        }
        char operator*() const {
            if (reader->idx == reader->sz) reader->read_buf();
            if (reader->idx < reader->sz) return reader->buffer[reader->idx];
            reader->state = false;
            return '\0';
        }
        bool rdstate() const { return reader->state; }
    };

    iterator begin() noexcept { return iterator(this); }
};

Reader<> reader(0);

template<class Iterator, std::size_t decimal_precision = 16> class Scanner {
public:
    using iterator_type = Iterator;

private:
    template<class, class = void> struct has_scan : std::false_type {};
    template<class T>
    struct has_scan<
        T, decltype(std::declval<T>().scan(std::declval<Scanner&>()), (void)0)>
        : std::true_type {};
    Iterator itr;

public:
    Scanner() = default;
    Scanner(const Iterator& itr) : itr(itr) {}

    char scan_char() {
        char c = *itr;
        ++itr;
        return c;
    }

    Scanner ignore(int n = 1) {
        rep (n) ++itr;
        return *this;
    }

    inline void discard_space() {
        while (('\t' <= *itr && *itr <= '\r') || *itr == ' ') ++itr;
    }
    void scan(char& a) {
        discard_space();
        a = *itr;
        ++itr;
    }
    void scan(bool& a) {
        discard_space();
        a = *itr != '0';
        ++itr;
    }
    void scan(std::string& a) {
        discard_space();
        a.clear();
        while ((*itr < '\t' || '\r' < *itr) && *itr != ' ' && *itr != '\0') {
            a += *itr;
            ++itr;
        }
    }
    template<std::size_t len> void scan(std::bitset<len>& a) {
        discard_space();
        rrep (i, len) {
            a[i] = *itr != '0';
            ++itr;
        }
    }
    template<class T,
             typename std::enable_if<is_signed_int<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        discard_space();
        if (*itr == '-') {
            ++itr;
            a = 0;
            while ('0' <= *itr && *itr <= '9') {
                a = a * 10 - (*itr - '0');
                ++itr;
            }
        }
        else {
            a = 0;
            while ('0' <= *itr && *itr <= '9') {
                a = a * 10 + (*itr - '0');
                ++itr;
            }
        }
    }
    template<class T,
             typename std::enable_if<is_unsigned_int<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        discard_space();
        a = 0;
        while ('0' <= *itr && *itr <= '9') {
            a = a * 10 + *itr - '0';
            ++itr;
        }
    }
    template<class T,
             typename std::enable_if<std::is_floating_point<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        discard_space();
        bool sgn = false;
        if (*itr == '-') {
            sgn = true;
            ++itr;
        }
        a = 0;
        while ('0' <= *itr && *itr <= '9') {
            a = a * 10 + *itr - '0';
            ++itr;
        }
        if (*itr == '.') {
            ++itr;
            T n = 0, d = 1;
            for (int i = 0;
                 '0' <= *itr && *itr <= '9' && i < (int)decimal_precision;
                 ++i) {
                n = n * 10 + *itr - '0';
                d *= 10;
                ++itr;
            }
            while ('0' <= *itr && *itr <= '9') ++itr;
            a += n / d;
        }
        if (sgn) a = -a;
    }

private:
    template<std::size_t i, class... Args> void scan(std::tuple<Args...>& a) {
        if IF_CONSTEXPR (i < sizeof...(Args)) {
            scan(std::get<i>(a));
            scan<i + 1, Args...>(a);
        }
    }

public:
    template<class... Args> void scan(std::tuple<Args...>& a) {
        scan<0, Args...>(a);
    }
    template<class T, class U> void scan(std::pair<T, U>& a) {
        scan(a.first);
        scan(a.second);
    }
    template<class T,
             typename std::enable_if<is_range<T>::value &&
                                     !has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        each_for (i : a) scan(i);
    }
    template<class T,
             typename std::enable_if<has_scan<T>::value>::type* = nullptr>
    void scan(T& a) {
        a.scan(*this);
    }

    void operator()() {}
    template<class Head, class... Args>
    void operator()(Head& head, Args&... args) {
        scan(head);
        operator()(args...);
    }

    template<class T> Scanner& operator>>(T& a) {
        scan(a);
        return *this;
    }

    explicit operator bool() const { return itr.rdstate(); }
};

Scanner<Reader<>::iterator> scan(reader.begin());

template<class Iterator, std::size_t decimal_precision>
Scanner<Iterator, decimal_precision>&
getline(Scanner<Iterator, decimal_precision>& scan, std::string& a) {
    a.clear();
    char c;
    while ((c = scan.scan_char()) != '\n') {
        a += c;
    }
    return scan;
}
#line 2 "library/template/out.hpp"

#line 8 "library/template/out.hpp"

template<std::size_t buf_size = IO_BUFFER_SIZE> class Writer {
private:
    int fd, idx;
    std::array<char, buf_size> buffer;
    inline void write_buf() {
        int num = write(fd, buffer.begin(), idx);
        idx = 0;
        if (num < 0) throw std::runtime_error("output failed");
    }

public:
    Writer() noexcept : fd(1), idx(0) {}
    Writer(int fd) noexcept : fd(fd), idx(0) {}
    Writer(FILE* fp) noexcept : fd(fileno(fp)), idx(0) {}

    ~Writer() { write_buf(); }

    class iterator {
    private:
        Writer* writer;

    public:
        using difference_type = void;
        using value_type = void;
        using pointer = void;
        using reference = void;
        using iterator_category = std::output_iterator_tag;

        iterator() noexcept : writer(nullptr) {}
        explicit iterator(Writer& writer) noexcept : writer(&writer) {}
        explicit iterator(Writer* writer) noexcept : writer(writer) {}

        iterator& operator++() {
            ++writer->idx;
            if (writer->idx == buf_size) writer->write_buf();
            return *this;
        }
        iterator operator++(int) {
            iterator res = *this;
            ++(*this);
            return res;
        }
        char& operator*() const { return writer->buffer[writer->idx]; }
        void flush() const { writer->write_buf(); }
    };

    iterator begin() noexcept { return iterator(this); }
};

Writer<> writer(1), ewriter(2);

template<class Iterator, bool debug = false> class Printer {
public:
    using iterator_type = Iterator;

private:
    template<class, bool = debug, class = void>
    struct has_print : std::false_type {};
    template<class T>
    struct has_print<T, false,
                     decltype(std::declval<T>().print(std::declval<Printer&>()),
                              (void)0)> : std::true_type {};
    template<class T>
    struct has_print<T, true,
                     decltype(std::declval<T>().debug(std::declval<Printer&>()),
                              (void)0)> : std::true_type {};
    Iterator itr;
    std::size_t decimal_precision;

public:
    void print_char(char c) {
        *itr = c;
        ++itr;
    }

    void flush() { itr.flush(); }

    Printer() noexcept = default;
    explicit Printer(const Iterator& itr) noexcept
        : itr(itr), decimal_precision(16) {}

    void set_decimal_precision(std::size_t decimal_precision) {
        this->decimal_precision = decimal_precision;
    }

    void print(char c) {
        if IF_CONSTEXPR (debug) print_char('\'');
        print_char(c);
        if IF_CONSTEXPR (debug) print_char('\'');
    }
    void print(bool b) { print_char((char)(b + '0')); }
    void print(const char* a) {
        if IF_CONSTEXPR (debug) print_char('"');
        for (; *a != '\0'; ++a) print_char(*a);
        if IF_CONSTEXPR (debug) print_char('"');
    }
    template<std::size_t len> void print(const char (&a)[len]) {
        if IF_CONSTEXPR (debug) print_char('"');
        for (auto i : a) print_char(i);
        if IF_CONSTEXPR (debug) print_char('"');
    }
    void print(const std::string& a) {
        if IF_CONSTEXPR (debug) print_char('"');
        for (auto i : a) print_char(i);
        if IF_CONSTEXPR (debug) print_char('"');
    }
    template<std::size_t len> void print(const std::bitset<len>& a) {
        rrep (i, len) print_char((char)(a[i] + '0'));
    }
    template<class T,
             typename std::enable_if<is_int<T>::value &&
                                     !has_print<T>::value>::type* = nullptr>
    void print(T a) {
        if (!a) {
            print_char('0');
            return;
        }
        if IF_CONSTEXPR (is_signed_int<T>::value) {
            if (a < 0) {
                print_char('-');
                using U = typename make_unsigned_int<T>::type;
                print(static_cast<U>(-static_cast<U>(a)));
                return;
            }
        }
        std::string s;
        while (a) {
            s += (char)(a % 10 + '0');
            a /= 10;
        }
        for (auto i = s.rbegin(); i != s.rend(); ++i) print_char(*i);
    }
    template<class T,
             typename std::enable_if<std::is_floating_point<T>::value &&
                                     !has_print<T>::value>::type* = nullptr>
    void print(T a) {
        if (a == std::numeric_limits<T>::infinity()) {
            print("inf");
            return;
        }
        if (a == -std::numeric_limits<T>::infinity()) {
            print("-inf");
            return;
        }
        if (std::isnan(a)) {
            print("nan");
            return;
        }
        if (a < 0) {
            print_char('-');
            a = -a;
        }
        T b = a;
        if (b < 1) {
            print_char('0');
        }
        else {
            std::string s;
            while (b >= 1) {
                s += (char)('0' + (int)std::fmod(b, 10.0));
                b /= 10;
            }
            for (auto i = s.rbegin(); i != s.rend(); ++i) print_char(*i);
        }
        print_char('.');
        rep (decimal_precision) {
            a *= 10;
            print_char((char)('0' + (int)std::fmod(a, 10.0)));
        }
    }

private:
    template<std::size_t i, class... Args>
    void print(const std::tuple<Args...>& a) {
        if IF_CONSTEXPR (i < sizeof...(Args)) {
            if IF_CONSTEXPR (debug) print_char(',');
            print_char(' ');
            print(std::get<i>(a));
            print<i + 1, Args...>(a);
        }
    }

public:
    template<class... Args> void print(const std::tuple<Args...>& a) {
        if IF_CONSTEXPR (debug) print_char('(');
        if IF_CONSTEXPR (sizeof...(Args) != 0) print(std::get<0>(a));
        print<1, Args...>(a);
        if IF_CONSTEXPR (debug) print_char(')');
    }
    template<class T, class U> void print(const std::pair<T, U>& a) {
        if IF_CONSTEXPR (debug) print_char('(');
        print(a.first);
        if IF_CONSTEXPR (debug) print_char(',');
        print_char(' ');
        print(a.second);
        if IF_CONSTEXPR (debug) print_char(')');
    }
    template<class T,
             typename std::enable_if<is_range<T>::value &&
                                     !has_print<T>::value>::type* = nullptr>
    void print(const T& a) {
        if IF_CONSTEXPR (debug) print_char('{');
        for (auto i = std::begin(a); i != std::end(a); ++i) {
            if (i != std::begin(a)) {
                if IF_CONSTEXPR (debug) print_char(',');
                print_char(' ');
            }
            print(*i);
        }
        if IF_CONSTEXPR (debug) print_char('}');
    }
    template<class T, typename std::enable_if<has_print<T>::value &&
                                              !debug>::type* = nullptr>
    void print(const T& a) {
        a.print(*this);
    }
    template<class T, typename std::enable_if<has_print<T>::value &&
                                              debug>::type* = nullptr>
    void print(const T& a) {
        a.debug(*this);
    }

    void operator()() {}
    template<class Head, class... Args>
    void operator()(const Head& head, const Args&... args) {
        print(head);
        operator()(args...);
    }

    template<class T> Printer& operator<<(const T& a) {
        print(a);
        return *this;
    }

    Printer& operator<<(Printer& (*pf)(Printer&)) { return pf(*this); }
};

template<class Iterator, bool debug>
Printer<Iterator, debug>& endl(Printer<Iterator, debug>& pr) {
    pr.print_char('\n');
    pr.flush();
    return pr;
}
template<class Iterator, bool debug>
Printer<Iterator, debug>& flush(Printer<Iterator, debug>& pr) {
    pr.flush();
    return pr;
}

struct SetPrec {
    int n;
    template<class Pr> void print(Pr& pr) const { pr.set_decimal_precision(n); }
    template<class Pr> void debug(Pr& pr) const { pr.set_decimal_precision(n); }
};
SetPrec setprec(int n) { return SetPrec{n}; };

Printer<Writer<>::iterator> print(writer.begin()), eprint(ewriter.begin());

template<class T> auto prints(const T& v) -> decltype(print << v, (void)0) {
    print << v;
    print.print_char('\n');
}

template<class Head, class... Tail>
auto prints(const Head& head, const Tail&... tail)
    -> decltype(print << head, (void)0) {
    print << head;
    print.print_char(' ');
    prints(tail...);
}

#ifdef SHIO_LOCAL
Printer<Writer<>::iterator, true> debug(writer.begin()),
    edebug(ewriter.begin());
#else
char debug_iterator_character;
class DebugIterator {
public:
    DebugIterator() noexcept = default;
    DebugIterator& operator++() { return *this; }
    DebugIterator& operator++(int) { return *this; }
    char& operator*() const { return debug_iterator_character; }
    void flush() const {}
};
Printer<DebugIterator> debug, edebug;
#endif

template<class T> auto debugs(const T& v) -> decltype(debug << v, (void)0) {
    debug << v;
    debug.print_char('\n');
}

template<class Head, class... Tail>
auto debugs(const Head& head, const Tail&... tail)
    -> decltype(debug << head, (void)0) {
    debug << head;
    debug.print_char(' ');
    debugs(tail...);
}
#line 2 "library/template/bitop.hpp"

#line 6 "library/template/bitop.hpp"

namespace bitop {

#define KTH_BIT(b, k) (((b) >> (k)) & 1)
#define POW2(k) (1ull << (k))

inline ull next_combination(int n, ull x) {
    if (n == 0) return 1;
    ull a = x & -x;
    ull b = x + a;
    return (x & ~b) / a >> 1 | b;
}

#define rep_comb(i, n, k)                                                      \
    for (ull i = (1ull << (k)) - 1; i < (1ull << (n));                         \
         i = bitop::next_combination((n), i))

inline CONSTEXPR int msb(ull x) {
    int res = x ? 0 : -1;
    if (x & 0xFFFFFFFF00000000) x &= 0xFFFFFFFF00000000, res += 32;
    if (x & 0xFFFF0000FFFF0000) x &= 0xFFFF0000FFFF0000, res += 16;
    if (x & 0xFF00FF00FF00FF00) x &= 0xFF00FF00FF00FF00, res += 8;
    if (x & 0xF0F0F0F0F0F0F0F0) x &= 0xF0F0F0F0F0F0F0F0, res += 4;
    if (x & 0xCCCCCCCCCCCCCCCC) x &= 0xCCCCCCCCCCCCCCCC, res += 2;
    return res + ((x & 0xAAAAAAAAAAAAAAAA) ? 1 : 0);
}

inline CONSTEXPR int ceil_log2(ull x) { return x ? msb(x - 1) + 1 : 0; }

inline CONSTEXPR ull reverse(ull x) {
    x = ((x & 0xAAAAAAAAAAAAAAAA) >> 1) | ((x & 0x5555555555555555) << 1);
    x = ((x & 0xCCCCCCCCCCCCCCCC) >> 2) | ((x & 0x3333333333333333) << 2);
    x = ((x & 0xF0F0F0F0F0F0F0F0) >> 4) | ((x & 0x0F0F0F0F0F0F0F0F) << 4);
    x = ((x & 0xFF00FF00FF00FF00) >> 8) | ((x & 0x00FF00FF00FF00FF) << 8);
    x = ((x & 0xFFFF0000FFFF0000) >> 16) | ((x & 0x0000FFFF0000FFFF) << 16);
    return (x >> 32) | (x << 32);
}

inline CONSTEXPR ull reverse(ull x, int n) { return reverse(x) >> (64 - n); }

} // namespace bitop

inline CONSTEXPR int popcnt(ull x) noexcept {
#if __cplusplus >= 202002L
    return std::popcount(x);
#endif
    x = (x & 0x5555555555555555) + ((x >> 1) & 0x5555555555555555);
    x = (x & 0x3333333333333333) + ((x >> 2) & 0x3333333333333333);
    x = (x & 0x0f0f0f0f0f0f0f0f) + ((x >> 4) & 0x0f0f0f0f0f0f0f0f);
    x = (x & 0x00ff00ff00ff00ff) + ((x >> 8) & 0x00ff00ff00ff00ff);
    x = (x & 0x0000ffff0000ffff) + ((x >> 16) & 0x0000ffff0000ffff);
    return (x & 0x00000000ffffffff) + ((x >> 32) & 0x00000000ffffffff);
}
#line 2 "library/template/func.hpp"

#line 6 "library/template/func.hpp"

template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmin(T& a, const U& b,
                            Comp cmp = Comp()) noexcept(noexcept(cmp(b, a))) {
    return cmp(b, a) ? a = b, true : false;
}
template<class T, class U, class Comp = std::less<>>
inline constexpr bool chmax(T& a, const U& b,
                            Comp cmp = Comp()) noexcept(noexcept(cmp(a, b))) {
    return cmp(a, b) ? a = b, true : false;
}

inline CONSTEXPR ll gcd(ll a, ll b) noexcept {
    if (a < 0) a = -a;
    if (b < 0) b = -b;
    while (b) {
        const ll c = a;
        a = b;
        b = c % b;
    }
    return a;
}
inline CONSTEXPR ll lcm(ll a, ll b) noexcept { return a / gcd(a, b) * b; }

inline CONSTEXPR bool is_prime(ll N) noexcept {
    if (N <= 1) return false;
    for (ll i = 2; i * i <= N; ++i) {
        if (N % i == 0) return false;
    }
    return true;
}
inline std::vector<ll> prime_factor(ll N) {
    std::vector<ll> res;
    for (ll i = 2; i * i <= N; ++i) {
        while (N % i == 0) {
            res.push_back(i);
            N /= i;
        }
    }
    if (N != 1) res.push_back(N);
    return res;
}

inline CONSTEXPR ll my_pow(ll a, ll b) noexcept {
    ll res = 1;
    while (b) {
        if (b & 1) res *= a;
        b >>= 1;
        a *= a;
    }
    return res;
}
inline CONSTEXPR ll mod_pow(ll a, ll b, ll mod) {
    assert(mod > 0);
    if (mod == 1) return 0;
    a %= mod;
    ll res = 1;
    while (b) {
        if (b & 1) (res *= a) %= mod;
        b >>= 1;
        (a *= a) %= mod;
    }
    return res;
}

inline PLL extGCD(ll a, ll b) {
    const ll n = a, m = b;
    ll x = 1, y = 0, u = 0, v = 1;
    ll t;
    while (b) {
        t = a / b;
        std::swap(a -= t * b, b);
        std::swap(x -= t * u, u);
        std::swap(y -= t * v, v);
    }
    if (x < 0) {
        x += m;
        y -= n;
    }
    return {x, y};
}
inline ll mod_inv(ll a, ll mod) {
    ll b = mod;
    ll x = 1, u = 0;
    ll t;
    while (b) {
        t = a / b;
        std::swap(a -= t * b, b);
        std::swap(x -= t * u, u);
    }
    if (x < 0) x += mod;
    assert(a == 1);
    return x;
}
#line 2 "library/template/util.hpp"

#line 6 "library/template/util.hpp"

template<class F> class RecLambda {
private:
    F f;

public:
    explicit constexpr RecLambda(F&& f_) : f(std::forward<F>(f_)) {}
    template<class... Args>
    constexpr auto operator()(Args&&... args)
        -> decltype(f(*this, std::forward<Args>(args)...)) {
        return f(*this, std::forward<Args>(args)...);
    }
};

template<class F> inline constexpr RecLambda<F> rec_lambda(F&& f) {
    return RecLambda<F>(std::forward<F>(f));
}

template<class Head, class... Tail> struct multi_dim_vector {
    using type = std::vector<typename multi_dim_vector<Tail...>::type>;
};
template<class T> struct multi_dim_vector<T> { using type = T; };

template<class T, class Arg>
constexpr std::vector<T> make_vec(int n, Arg&& arg) {
    return std::vector<T>(n, std::forward<Arg>(arg));
}
template<class T, class... Args>
constexpr typename multi_dim_vector<Args..., T>::type make_vec(int n,
                                                               Args&&... args) {
    return typename multi_dim_vector<Args..., T>::type(
        n, make_vec<T>(std::forward<Args>(args)...));
}

template<class T, class Comp = std::less<T>> class presser {
private:
    std::vector<T> dat;
    Comp cmp;
    bool sorted = false;

public:
    presser() : presser(Comp()) {}
    presser(const Comp& cmp) : cmp(cmp) {}
    presser(const std::vector<T>& vec, const Comp& cmp = Comp())
        : dat(vec), cmp(cmp) {}
    presser(std::vector<T>&& vec, const Comp& cmp = Comp())
        : dat(std::move(vec)), cmp(cmp) {}
    presser(std::initializer_list<T> il, const Comp& cmp = Comp())
        : dat(all(il)), cmp(cmp) {}
    void reserve(int n) {
        assert(!sorted);
        dat.reserve(n);
    }
    void push_back(const T& v) {
        assert(!sorted);
        dat.push_back(v);
    }
    void push_back(T&& v) {
        assert(!sorted);
        dat.push_back(std::move(v));
    }
    template<class... Args> void emplace_back(Args&&... args) {
        assert(!sorted);
        dat.emplace_back(std::forward<Args>(args)...);
    }
    void push(const std::vector<T>& vec) {
        assert(!sorted);
        const int n = dat.size();
        dat.resize(n + vec.size());
        rep (i, vec.size()) dat[n + i] = vec[i];
    }
    int build() {
        assert(!sorted);
        sorted = true;
        std::sort(all(dat), cmp);
        dat.erase(std::unique(all(dat),
                              [&](const T& a, const T& b) -> bool {
                                  return !cmp(a, b) && !cmp(b, a);
                              }),
                  dat.end());
        return dat.size();
    }
    const T& operator[](int k) const& {
        assert(sorted);
        assert(0 <= k && k < (int)dat.size());
        return dat[k];
    }
    T operator[](int k) && {
        assert(sorted);
        assert(0 <= k && k < (int)dat.size());
        return std::move(dat[k]);
    }
    int get(const T& val) const {
        assert(sorted);
        auto itr = std::lower_bound(all(dat), val, cmp);
        assert(itr != dat.end() && !cmp(val, *itr));
        return itr - dat.begin();
    }
    int lower_bound(const T& val) const {
        assert(sorted);
        auto itr = std::lower_bound(all(dat), val, cmp);
        return itr - dat.begin();
    }
    int upper_bound(const T& val) const {
        assert(sorted);
        auto itr = std::upper_bound(all(dat), val, cmp);
        return itr - dat.begin();
    }
    bool contains(const T& val) const {
        assert(sorted);
        return std::binary_search(all(dat), val, cmp);
    }
    std::vector<int> pressed(const std::vector<T>& vec) const {
        assert(sorted);
        std::vector<int> res(vec.size());
        rep (i, vec.size()) res[i] = get(vec[i]);
        return res;
    }
    void press(std::vector<T>& vec) const {
        static_assert(std::is_convertible<T, int>::value,
                      "template argument must be convertible from int type");
        assert(sorted);
        each_for (i : vec) i = get(i);
    }
    int size() const {
        assert(sorted);
        return dat.size();
    }
    const std::vector<T>& data() const& { return dat; }
    std::vector<T> data() && { return std::move(dat); }
};
#line 2 "library/math/convolution/Convolution.hpp"

#line 2 "library/math/ModInt.hpp"

#line 4 "library/math/ModInt.hpp"

template<class T, T mod> class StaticModInt {
    static_assert(std::is_integral<T>::value, "T must be integral");
    static_assert(std::is_unsigned<T>::value, "T must be unsigned");
    static_assert(mod > 0, "mod must be positive");
    static_assert(mod <= std::numeric_limits<T>::max() / 2,
                  "mod * 2 must be less than or equal to T::max()");

private:
    using large_t = typename double_size_uint<T>::type;
    using signed_t = typename std::make_signed<T>::type;
    T val;
    static constexpr unsigned int inv1000000007[] = {
        0,         1,         500000004, 333333336, 250000002, 400000003,
        166666668, 142857144, 125000001, 111111112, 700000005};
    static constexpr unsigned int inv998244353[] = {
        0,         1,         499122177, 332748118, 748683265, 598946612,
        166374059, 855638017, 873463809, 443664157, 299473306};

public:
    constexpr StaticModInt() : val(0) {}
    template<class U,
             typename std::enable_if<std::is_integral<U>::value &&
                                     std::is_signed<U>::value>::type* = nullptr>
    constexpr StaticModInt(U v) : val{} {
        v %= static_cast<signed_t>(mod);
        if (v < 0) v += static_cast<signed_t>(mod);
        val = static_cast<T>(v);
    }
    template<class U, typename std::enable_if<
                          std::is_integral<U>::value &&
                          std::is_unsigned<U>::value>::type* = nullptr>
    constexpr StaticModInt(U v) : val(v % mod) {}
    T get() const { return val; }
    static constexpr T get_mod() { return mod; }
    static StaticModInt raw(T v) {
        StaticModInt res;
        res.val = v;
        return res;
    }
    StaticModInt inv() const {
        if IF_CONSTEXPR (mod == 1000000007) {
            if (val <= 10) return inv1000000007[val];
        }
        else if IF_CONSTEXPR (mod == 998244353) {
            if (val <= 10) return inv998244353[val];
        }
        return mod_inv(val, mod);
    }
    StaticModInt& operator++() {
        ++val;
        if (val == mod) val = 0;
        return *this;
    }
    StaticModInt operator++(int) {
        StaticModInt res = *this;
        ++*this;
        return res;
    }
    StaticModInt& operator--() {
        if (val == 0) val = mod;
        --val;
        return *this;
    }
    StaticModInt operator--(int) {
        StaticModInt res = *this;
        --*this;
        return res;
    }
    StaticModInt& operator+=(const StaticModInt& other) {
        val += other.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    StaticModInt& operator-=(const StaticModInt& other) {
        if (val < other.val) val += mod;
        val -= other.val;
        return *this;
    }
    StaticModInt& operator*=(const StaticModInt& other) {
        large_t a = val;
        a *= other.val;
        a %= mod;
        val = a;
        return *this;
    }
    StaticModInt& operator/=(const StaticModInt& other) {
        *this *= other.inv();
        return *this;
    }
    friend StaticModInt operator+(const StaticModInt& lhs,
                                  const StaticModInt& rhs) {
        return StaticModInt(lhs) += rhs;
    }
    friend StaticModInt operator-(const StaticModInt& lhs,
                                  const StaticModInt& rhs) {
        return StaticModInt(lhs) -= rhs;
    }
    friend StaticModInt operator*(const StaticModInt& lhs,
                                  const StaticModInt& rhs) {
        return StaticModInt(lhs) *= rhs;
    }
    friend StaticModInt operator/(const StaticModInt& lhs,
                                  const StaticModInt& rhs) {
        return StaticModInt(lhs) /= rhs;
    }
    StaticModInt operator+() const { return StaticModInt(*this); }
    StaticModInt operator-() const { return StaticModInt() - *this; }
    friend bool operator==(const StaticModInt& lhs, const StaticModInt& rhs) {
        return lhs.val == rhs.val;
    }
    friend bool operator!=(const StaticModInt& lhs, const StaticModInt& rhs) {
        return lhs.val != rhs.val;
    }
    StaticModInt pow(ll a) const {
        StaticModInt v = *this, res = 1;
        while (a) {
            if (a & 1) res *= v;
            a >>= 1;
            v *= v;
        }
        return res;
    }
    template<class Pr> void print(Pr& a) const { a.print(val); }
    template<class Pr> void debug(Pr& a) const { a.print(val); }
    template<class Sc> void scan(Sc& a) {
        ll v;
        a.scan(v);
        *this = v;
    }
};

#if __cplusplus < 201703L
template<class T, T mod>
constexpr unsigned int StaticModInt<T, mod>::inv1000000007[];
template<class T, T mod>
constexpr unsigned int StaticModInt<T, mod>::inv998244353[];
#endif

template<unsigned int p> using static_modint = StaticModInt<unsigned int, p>;
using modint1000000007 = static_modint<1000000007>;
using modint998244353 = static_modint<998244353>;

template<class T, int id> class DynamicModInt {
    static_assert(std::is_integral<T>::value, "T must be integral");
    static_assert(std::is_unsigned<T>::value, "T must be unsigned");

private:
    using large_t = typename double_size_uint<T>::type;
    using signed_t = typename std::make_signed<T>::type;
    T val;
    static T mod;

public:
    constexpr DynamicModInt() : val(0) {}
    template<class U,
             typename std::enable_if<std::is_integral<U>::value &&
                                     std::is_signed<U>::value>::type* = nullptr>
    constexpr DynamicModInt(U v) : val{} {
        v %= static_cast<signed_t>(mod);
        if (v < 0) v += static_cast<signed_t>(mod);
        val = static_cast<T>(v);
    }
    template<class U, typename std::enable_if<
                          std::is_integral<U>::value &&
                          std::is_unsigned<U>::value>::type* = nullptr>
    constexpr DynamicModInt(U v) : val(v % mod) {}
    T get() const { return val; }
    static T get_mod() { return mod; }
    static void set_mod(T v) {
        assert(v > 0);
        assert(v <= std::numeric_limits<T>::max() / 2);
        mod = v;
    }
    static DynamicModInt raw(T v) {
        DynamicModInt res;
        res.val = v;
        return res;
    }
    DynamicModInt inv() const { return mod_inv(val, mod); }
    DynamicModInt& operator++() {
        ++val;
        if (val == mod) val = 0;
        return *this;
    }
    DynamicModInt operator++(int) {
        DynamicModInt res = *this;
        ++*this;
        return res;
    }
    DynamicModInt& operator--() {
        if (val == 0) val = mod;
        --val;
        return *this;
    }
    DynamicModInt operator--(int) {
        DynamicModInt res = *this;
        --*this;
        return res;
    }
    DynamicModInt& operator+=(const DynamicModInt& other) {
        val += other.val;
        if (val >= mod) val -= mod;
        return *this;
    }
    DynamicModInt& operator-=(const DynamicModInt& other) {
        if (val < other.val) val += mod;
        val -= other.val;
        return *this;
    }
    DynamicModInt& operator*=(const DynamicModInt& other) {
        large_t a = val;
        a *= other.val;
        a %= mod;
        val = a;
        return *this;
    }
    DynamicModInt& operator/=(const DynamicModInt& other) {
        *this *= other.inv();
        return *this;
    }
    friend DynamicModInt operator+(const DynamicModInt& lhs,
                                   const DynamicModInt& rhs) {
        return DynamicModInt(lhs) += rhs;
    }
    friend DynamicModInt operator-(const DynamicModInt& lhs,
                                   const DynamicModInt& rhs) {
        return DynamicModInt(lhs) -= rhs;
    }
    friend DynamicModInt operator*(const DynamicModInt& lhs,
                                   const DynamicModInt& rhs) {
        return DynamicModInt(lhs) *= rhs;
    }
    friend DynamicModInt operator/(const DynamicModInt& lhs,
                                   const DynamicModInt& rhs) {
        return DynamicModInt(lhs) /= rhs;
    }
    DynamicModInt operator+() const { return DynamicModInt(*this); }
    DynamicModInt operator-() const { return DynamicModInt() - *this; }
    friend bool operator==(const DynamicModInt& lhs, const DynamicModInt& rhs) {
        return lhs.val == rhs.val;
    }
    friend bool operator!=(const DynamicModInt& lhs, const DynamicModInt& rhs) {
        return lhs.val != rhs.val;
    }
    DynamicModInt pow(ll a) const {
        DynamicModInt v = *this, res = 1;
        while (a) {
            if (a & 1) res *= v;
            a >>= 1;
            v *= v;
        }
        return res;
    }
    template<class Pr> void print(Pr& a) const { a.print(val); }
    template<class Pr> void debug(Pr& a) const { a.print(val); }
    template<class Sc> void scan(Sc& a) {
        ll v;
        a.scan(v);
        *this = v;
    }
};

template<class T, int id> T DynamicModInt<T, id>::mod = 998244353;

template<int id> using dynamic_modint = DynamicModInt<unsigned int, id>;
using modint = dynamic_modint<-1>;

/**
 * @brief ModInt
 * @docs docs/math/ModInt.md
 */
#line 2 "library/math/PrimitiveRoot.hpp"

#line 2 "library/random/Random.hpp"

#line 4 "library/random/Random.hpp"

template<class Engine> class Random {
private:
    Engine rnd;

public:
    using result_type = typename Engine::result_type;
    Random() : Random(std::random_device{}()) {}
    Random(result_type seed) : rnd(seed) {}
    result_type operator()() { return rnd(); }
    template<class IntType = ll> IntType uniform(IntType l, IntType r) {
        static_assert(std::is_integral<IntType>::value,
                      "template argument must be an integral type");
        assert(l <= r);
        return std::uniform_int_distribution<IntType>{l, r}(rnd);
    }
    template<class RealType = double>
    RealType uniform_real(RealType l, RealType r) {
        static_assert(std::is_floating_point<RealType>::value,
                      "template argument must be an floating point type");
        assert(l <= r);
        return std::uniform_real_distribution<RealType>{l, r}(rnd);
    }
    bool uniform_bool() { return uniform<int>(0, 1) == 1; }
    template<class T = ll> std::pair<T, T> uniform_pair(T l, T r) {
        assert(l < r);
        T a, b;
        do {
            a = uniform<T>(l, r);
            b = uniform<T>(l, r);
        } while (a == b);
        if (a > b) swap(a, b);
        return {a, b};
    }
    template<class T = ll> std::vector<T> choice(int n, T l, T r) {
        assert(l <= r);
        assert(T(n) <= (r - l + 1));
        std::set<T> res;
        while ((int)res.size() < n) res.insert(uniform<T>(l, r));
        return {res.begin(), res.end()};
    }
    template<class Iter> void shuffle(const Iter& first, const Iter& last) {
        std::shuffle(first, last, rnd);
    }
    template<class T> std::vector<T> permutation(T n) {
        std::vector<T> res(n);
        rep (i, n) res[i] = i;
        shuffle(all(res));
        return res;
    }
    template<class T = ll>
    std::vector<T> choice_shuffle(int n, T l, T r, bool sorted = true) {
        assert(l <= r);
        assert(T(n) <= (r - l + 1));
        std::vector<T> res(r - l + 1);
        rep (i, l, r + 1) res[i - l] = i;
        shuffle(all(res));
        res.erase(res.begin() + n, res.end());
        if (sorted) sort(all(res));
        return res;
    }
};

using Random32 = Random<std::mt19937>;
Random32 rand32;
using Random64 = Random<std::mt19937_64>;
Random64 rand64;

/**
 * @brief Random
 * @docs docs/random/Random.md
 */
#line 2 "library/math/MontgomeryModInt.hpp"

#line 4 "library/math/MontgomeryModInt.hpp"

template<class T> class MontgomeryReduction {
    static_assert(std::is_integral<T>::value, "T must be integral");
    static_assert(std::is_unsigned<T>::value, "T must be unsigned");

private:
    using large_t = typename double_size_uint<T>::type;
    static constexpr int lg = std::numeric_limits<T>::digits;
    T mod;
    T r;
    T r2; // r^2 mod m
    T calc_minv() {
        T t = 0, res = 0;
        rep (i, lg) {
            if (~t & 1) {
                t += mod;
                res += static_cast<T>(1) << i;
            }
            t >>= 1;
        }
        return res;
    }
    T minv;

public:
    MontgomeryReduction(T v) { set_mod(v); }
    static constexpr int get_lg() { return lg; }
    void set_mod(T v) {
        assert(v > 0);
        assert(v & 1);
        assert(v <= std::numeric_limits<T>::max() / 2);
        mod = v;
        r = (-static_cast<T>(mod)) % mod;
        r2 = (-static_cast<large_t>(mod)) % mod;
        minv = calc_minv();
    }
    inline T get_mod() const { return mod; }
    inline T get_r() const { return r; }
    T reduce(large_t x) const {
        large_t tmp =
            (x + static_cast<large_t>(static_cast<T>(x) * minv) * mod) >> lg;
        return tmp >= mod ? tmp - mod : tmp;
    }
    T transform(large_t x) const { return reduce(x * r2); }
};

template<class T, int id> class MontgomeryModInt {
private:
    using large_t = typename double_size_uint<T>::type;
    using signed_t = typename std::make_signed<T>::type;
    T val;

    static MontgomeryReduction<T> mont;

public:
    MontgomeryModInt() : val(0) {}
    template<class U, typename std::enable_if<
                          std::is_integral<U>::value &&
                          std::is_unsigned<U>::value>::type* = nullptr>
    MontgomeryModInt(U x)
        : val(mont.transform(
              x < (static_cast<large_t>(mont.get_mod()) << mont.get_lg())
                  ? x
                  : x % mont.get_mod())) {}
    template<class U,
             typename std::enable_if<std::is_integral<U>::value &&
                                     std::is_signed<U>::value>::type* = nullptr>
    MontgomeryModInt(U x)
        : MontgomeryModInt(static_cast<typename std::make_unsigned<U>::type>(
              x < 0 ? -x : x)) {
        if (x < 0 && val) val = mont.get_mod() - val;
    }

    T get() const { return mont.reduce(val); }
    static T get_mod() { return mont.get_mod(); }

    static void set_mod(T v) { mont.set_mod(v); }

    MontgomeryModInt operator+() const { return *this; }
    MontgomeryModInt operator-() const {
        MontgomeryModInt res;
        if (val) res.val = mont.get_mod() - val;
        return res;
    }
    MontgomeryModInt& operator++() {
        val += mont.get_r();
        if (val >= mont.get_mod()) val -= mont.get_mod();
        return *this;
    }
    MontgomeryModInt& operator--() {
        if (val < mont.get_r()) val += mont.get_mod();
        val -= mont.get_r();
        return *this;
    }
    MontgomeryModInt operator++(int) {
        MontgomeryModInt res = *this;
        ++*this;
        return res;
    }
    MontgomeryModInt operator--(int) {
        MontgomeryModInt res = *this;
        --*this;
        return res;
    }

    MontgomeryModInt& operator+=(const MontgomeryModInt& rhs) {
        val += rhs.val;
        if (val >= mont.get_mod()) val -= mont.get_mod();
        return *this;
    }
    MontgomeryModInt& operator-=(const MontgomeryModInt& rhs) {
        if (val < rhs.val) val += mont.get_mod();
        val -= rhs.val;
        return *this;
    }
    MontgomeryModInt& operator*=(const MontgomeryModInt& rhs) {
        val = mont.reduce(static_cast<large_t>(val) * rhs.val);
        return *this;
    }

    MontgomeryModInt pow(ull n) const {
        MontgomeryModInt res = 1, x = *this;
        while (n) {
            if (n & 1) res *= x;
            x *= x;
            n >>= 1;
        }
        return res;
    }
    MontgomeryModInt inv() const { return pow(mont.get_mod() - 2); }

    MontgomeryModInt& operator/=(const MontgomeryModInt& rhs) {
        return *this *= rhs.inv();
    }

    friend MontgomeryModInt operator+(const MontgomeryModInt& lhs,
                                      const MontgomeryModInt& rhs) {
        return MontgomeryModInt(lhs) += rhs;
    }
    friend MontgomeryModInt operator-(const MontgomeryModInt& lhs,
                                      const MontgomeryModInt& rhs) {
        return MontgomeryModInt(lhs) -= rhs;
    }
    friend MontgomeryModInt operator*(const MontgomeryModInt& lhs,
                                      const MontgomeryModInt& rhs) {
        return MontgomeryModInt(lhs) *= rhs;
    }
    friend MontgomeryModInt operator/(const MontgomeryModInt& lhs,
                                      const MontgomeryModInt& rhs) {
        return MontgomeryModInt(lhs) /= rhs;
    }

    friend bool operator==(const MontgomeryModInt& lhs,
                           const MontgomeryModInt& rhs) {
        return lhs.val == rhs.val;
    }
    friend bool operator!=(const MontgomeryModInt& lhs,
                           const MontgomeryModInt& rhs) {
        return lhs.val != rhs.val;
    }

    template<class Pr> void print(Pr& a) const { a.print(mont.reduce(val)); }
    template<class Pr> void debug(Pr& a) const { a.print(mont.reduce(val)); }
    template<class Sc> void scan(Sc& a) {
        ll v;
        a.scan(v);
        *this = v;
    }
};

template<class T, int id>
MontgomeryReduction<T>
    MontgomeryModInt<T, id>::mont = MontgomeryReduction<T>(998244353);

using mmodint = MontgomeryModInt<unsigned int, -1>;

/**
 * @brief MontgomeryModInt(モンゴメリ乗算)
 * @docs docs/math/MontgomeryModInt.md
 */
#line 2 "library/math/MillerRabin.hpp"

#line 5 "library/math/MillerRabin.hpp"

constexpr ull base_miller_rabin_int[3] = {2, 7, 61};
constexpr ull base_miller_rabin_ll[7] = {2,      325,     9375,      28178,
                                         450775, 9780504, 1795265022};

template<class T> CONSTEXPR bool miller_rabin(ull n, const ull base[], int s) {
    if (T::get_mod() != n) T::set_mod(n);
    ull d = n - 1;
    while (~d & 1) d >>= 1;
    T e{1}, re{n - 1};
    rep (i, s) {
        ull a = base[i];
        if (a >= n) return true;
        ull t = d;
        T y = T(a).pow(t);
        while (t != n - 1 && y != e && y != re) {
            y *= y;
            t <<= 1;
        }
        if (y != re && !(t & 1)) return false;
    }
    return true;
}

CONSTEXPR bool is_prime_mr(ll n) {
    if (n == 2) return true;
    if (n < 2 || n % 2 == 0) return false;
    if (n < (1u << 31))
        return miller_rabin<MontgomeryModInt<unsigned int, -2>>(
            n, base_miller_rabin_int, 3);
    return miller_rabin<MontgomeryModInt<ull, -2>>(n, base_miller_rabin_ll, 7);
}

#if __cpp_variable_templates >= 201304L && __cpp_constexpr >= 201304L
template<ull n> constexpr bool is_prime_v = is_prime_mr(n);
#endif

/**
 * @brief MillerRabin(ミラーラビン素数判定)
 * @docs docs/math/MillerRabin.md
 */
#line 2 "library/math/PollardRho.hpp"

#line 2 "library/string/RunLength.hpp"

#line 4 "library/string/RunLength.hpp"

template<class Cont, class Comp>
std::vector<std::pair<typename Cont::value_type, int>>
RunLength(const Cont& str, const Comp& cmp) {
    std::vector<std::pair<typename Cont::value_type, int>> res;
    if (str.size() == 0) return res;
    res.emplace_back(str[0], 1);
    rep (i, 1, str.size()) {
        if (cmp(res.back().first, str[i])) ++res.back().second;
        else res.emplace_back(str[i], 1);
    }
    return res;
}

template<class Cont>
std::vector<std::pair<typename Cont::value_type, int>>
RunLength(const Cont& str) {
    return RunLength(str, std::equal_to<typename Cont::value_type>());
}

/**
 * @brief RunLength(ランレングス圧縮)
 * @docs docs/string/RunLength.md
 */
#line 8 "library/math/PollardRho.hpp"

template<class T, class Rnd> ull pollard_rho(ull n, Rnd& rnd) {
    if (~n & 1) return 2;
    if (T::get_mod() != n) T::set_mod(n);
    T c, one = 1;
    auto f = [&](T x) -> T { return x * x + c; };
    constexpr int M = 128;
    while (1) {
        c = rnd.uniform(1ull, n - 1);
        T x = rnd.uniform(2ull, n - 1), y = x;
        ull g = 1;
        while (g == 1) {
            T p = one, tx = x, ty = y;
            rep (M) {
                x = f(x);
                y = f(f(y));
                p *= x - y;
            }
            g = gcd(p.get(), n);
            if (g == 1) continue;
            rep (M) {
                tx = f(tx);
                ty = f(f(ty));
                g = gcd((tx - ty).get(), n);
                if (g != 1) {
                    if (g != n) return g;
                    break;
                }
            }
        }
    }
    return -1;
}

template<class T = MontgomeryModInt<ull, -3>, class Rnd = Random64>
std::vector<ull> factorize(ull n, Rnd& rnd = rand64) {
    if (n == 1) return {};
    std::vector<ull> res;
    std::vector<ull> st = {n};
    while (!st.empty()) {
        ull t = st.back();
        st.pop_back();
        if (t == 1) continue;
        if (is_prime_mr(t)) {
            res.push_back(t);
            continue;
        }
        ull f = pollard_rho<T>(t, rnd);
        st.push_back(f);
        st.push_back(t / f);
    }
    std::sort(all(res));
    return res;
}

template<class T = MontgomeryModInt<ull, -3>, class Rnd = Random64>
std::vector<std::pair<ull, int>> expfactorize(ull n, Rnd& rnd = rand64) {
    auto f = factorize<T, Rnd>(n, rnd);
    return RunLength(f);
}

std::vector<ll> divisors_pr(ll n) {
    std::vector<ll> res;
    auto r = expfactorize(n);
    int m = r.size();
    rec_lambda([&](auto&& self, int k, ll d) -> void {
        if (k == m) {
            res.push_back(d);
            return;
        }
        ll t = d;
        rep (r[k].second) {
            self(k + 1, d);
            d *= r[k].first;
        }
        self(k + 1, d);
        d = t;
    })(0, 1);
    std::sort(all(res));
    return res;
}

/**
 * @brief PollardRho(素因数分解)
 * @docs docs/math/PollardRho.md
 */
#line 9 "library/math/PrimitiveRoot.hpp"

template<class T = MontgomeryModInt<ull, -4>> ull primitive_root(ull p) {
    assert(is_prime_mr(p));
    if (p == 2) return 1;
    if (T::get_mod() != p) T::set_mod(p);
    auto pf = factorize(p - 1);
    pf.erase(std::unique(all(pf)), pf.end());
    each_for (x : pf) x = (p - 1) / x;
    T one = 1;
    while (1) {
        ull g = rand64.uniform(2ull, p - 1);
        bool ok = true;
        each_const (x : pf) {
            if (T(g).pow(x) == one) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}

CONSTEXPR ull primitive_root_for_convolution(ull p) {
    if (p == 2) return 1;
    if (p == 998244353) return 3;
    if (p == 469762049) return 3;
    if (p == 1811939329) return 11;
    if (p == 2013265921) return 11;
    rep (g, 2, p) {
        if (mod_pow(g, (p - 1) >> 1, p) != 1) return g;
    }
    return -1;
}

/**
 * @brief PrimitiveRoot(原始根)
 * @docs docs/math/PrimitiveRoot.md
 */
#line 6 "library/math/convolution/Convolution.hpp"

namespace internal {

template<unsigned int p> class NthRoot {
private:
    static constexpr unsigned int lg = bitop::msb((p - 1) & (1 - p));
    unsigned int root[lg + 1];
    unsigned int inv_root[lg + 1];

public:
    constexpr NthRoot() : root{}, inv_root{} {
        root[lg] = mod_pow(primitive_root_for_convolution(p), (p - 1) >> lg, p);
        inv_root[lg] = mod_pow(root[lg], p - 2, p);
        rrep (i, lg) {
            root[i] = (ull)root[i + 1] * root[i + 1] % p;
            inv_root[i] = (ull)inv_root[i + 1] * inv_root[i + 1] % p;
        }
    }
    static constexpr unsigned int get_lg() { return lg; }
    constexpr unsigned int get(int n) const { return root[n]; }
    constexpr unsigned int inv(int n) const { return inv_root[n]; }
};

template<unsigned int p> constexpr NthRoot<p> nth_root;

template<class T>
std::vector<T> convolution(std::vector<T> a, std::vector<T> b) {
    int n = a.size() + b.size() - 1;
    int lg = bitop::msb(n - 1) + 1;
    int m = 1 << lg;
    a.resize(m);
    b.resize(m);
    rep (i, m) {
        int j = bitop::reverse(i, lg);
        if (i < j) {
            std::swap(a[i], a[j]);
            std::swap(b[i], b[j]);
        }
    }
    rep (i, lg) {
        const T w = nth_root<T::get_mod()>.get(i + 1);
        rep (j, 0, m, 1 << (i + 1)) {
            T z = 1;
            rep (k, 1 << i) {
                T x = a[j + k];
                T y = a[j + k + (1 << i)] * z;
                a[j + k] = x + y;
                a[j + k + (1 << i)] = x - y;
                x = b[j + k];
                y = b[j + k + (1 << i)] * z;
                b[j + k] = x + y;
                b[j + k + (1 << i)] = x - y;
                z *= w;
            }
        }
    }
    rep (i, m) a[i] *= b[i];
    rep (i, m) {
        int j = bitop::reverse(i, lg);
        if (i < j) std::swap(a[i], a[j]);
    }
    rep (i, lg) {
        const T w = nth_root<T::get_mod()>.inv(i + 1);
        rep (j, 0, m, 1 << (i + 1)) {
            T z = 1;
            rep (k, 1 << i) {
                T x = a[j + k];
                T y = a[j + k + (1 << i)] * z;
                a[j + k] = x + y;
                a[j + k + (1 << i)] = x - y;
                z *= w;
            }
        }
    }
    a.resize(n);
    T inv_m = T(1) / m;
    each_for (x : a) x *= inv_m;
    return a;
}


template<class T>
std::vector<T> convolution_naive(const std::vector<T>& a,
                                 const std::vector<T>& b) {
    int n = a.size(), m = b.size();
    std::vector<T> c(n + m - 1);
    rep (i, n)
        rep (j, m) c[i + j] += a[i] * b[j];
    return c;
}

} // namespace internal

template<unsigned int p>
std::vector<static_modint<p>>
convolution_for_any_mod(const std::vector<static_modint<p>>& a,
                        const std::vector<static_modint<p>>& b);

template<unsigned int p>
std::vector<static_modint<p>>
convolution(const std::vector<static_modint<p>>& a,
            const std::vector<static_modint<p>>& b) {
    unsigned int n = a.size(), m = b.size();
    if (n == 0 || m == 0) return {};
    if (n <= 60 || m <= 60) return internal::convolution_naive(a, b);
    if (n + m - 1 > ((1 - p) & (p - 1))) return convolution_for_any_mod(a, b);
    return internal::convolution(a, b);
}

template<unsigned int p>
std::vector<ll> convolution(const std::vector<ll>& a,
                            const std::vector<ll>& b) {
    int n = a.size(), m = b.size();
    std::vector<static_modint<p>> a2(n), b2(m);
    rep (i, n) a2[i] = a[i];
    rep (i, m) b2[i] = b[i];
    auto c2 = convolution(a2, b2);
    std::vector<ll> c(n + m - 1);
    rep (i, n + m - 1) c[i] = c2[i].get();
    return c;
}

template<unsigned int p>
std::vector<static_modint<p>>
convolution_for_any_mod(const std::vector<static_modint<p>>& a,
                        const std::vector<static_modint<p>>& b) {
    int n = a.size(), m = b.size();
    assert(n + m - 1 <= (1 << 26));
    std::vector<ll> a2(n), b2(m);
    rep (i, n) a2[i] = a[i].get();
    rep (i, m) b2[i] = b[i].get();
    static constexpr ull MOD1 = 469762049;
    static constexpr ull MOD2 = 1811939329;
    static constexpr ull MOD3 = 2013265921;
    static constexpr ull INV1_2 = mod_pow(MOD1, MOD2 - 2, MOD2);
    static constexpr ull INV1_3 = mod_pow(MOD1, MOD3 - 2, MOD3);
    static constexpr ull INV2_3 = mod_pow(MOD2, MOD3 - 2, MOD3);
    auto c1 = convolution<MOD1>(a2, b2);
    auto c2 = convolution<MOD2>(a2, b2);
    auto c3 = convolution<MOD3>(a2, b2);
    std::vector<static_modint<p>> res(n + m - 1);
    rep (i, n + m - 1) {
        ull t1 = c1[i];
        ull t2 = (c2[i] - t1 + MOD2) * INV1_2 % MOD2;
        if (t2 < 0) t2 += MOD2;
        ull t3 =
            ((c3[i] - t1 + MOD3) * INV1_3 % MOD3 - t2 + MOD3) * INV2_3 % MOD3;
        if (t3 < 0) t3 += MOD3;
        assert(0 <= t1 && t1 < MOD1);
        assert(0 <= t2 && t2 < MOD2);
        assert(0 <= t3 && t3 < MOD3);
        res[i] = static_modint<p>(t1 + (t2 + t3 * MOD2) % p * MOD1);
    }
    return res;
}

/**
 * @brief Convolution(畳み込み)
 * @docs docs/math/convolution.md
 */
#line 3 "main.cpp"

using namespace std;

int main() {
    ll N, M, X; scan >> N >> M >> X;
    vector<ll> C(N); scan >> C;
    vector<array<ll, 3>> A(M); scan >> A;
    rep (i, N) --C[i];
    rep (i, M) {
        --A[i][0];
        --A[i][1];
    }
    vector<ll> ans(N);
    rep (i, 5) {
        vector<ll> X(N);
        rep (j, N) {
            if (C[j] == i) X[j] = 1;
        }
        vector<ll> Y(N);
        rep (j, M) {
            if (A[j][1] == i) Y[N - 1 - A[j][0]] += A[j][2];
        }
        auto Z = convolution<998244353>(X, Y);
        rep (i, N) ans[i] += Z[N - 1 + i];
    }
    ll mx = 0;
    rep (i, N) chmax(mx, ans[i] + i * X);
    prints(mx);
}
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