#include <bits/stdc++.h>

#ifdef _MSC_VER
#  include <intrin.h>
#else
#  include <x86intrin.h>
#endif

#include <limits>
#include <type_traits>

namespace suisen {
// ! utility
template <typename ...Types>
using constraints_t = std::enable_if_t<std::conjunction_v<Types...>, std::nullptr_t>;
template <bool cond_v, typename Then, typename OrElse>
constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) {
    if constexpr (cond_v) {
        return std::forward<Then>(then);
    } else {
        return std::forward<OrElse>(or_else);
    }
}

// ! function
template <typename ReturnType, typename Callable, typename ...Args>
using is_same_as_invoke_result = std::is_same<std::invoke_result_t<Callable, Args...>, ReturnType>;
template <typename F, typename T>
using is_uni_op = is_same_as_invoke_result<T, F, T>;
template <typename F, typename T>
using is_bin_op = is_same_as_invoke_result<T, F, T, T>;

template <typename Comparator, typename T>
using is_comparator = std::is_same<std::invoke_result_t<Comparator, T, T>, bool>;

// ! integral
template <typename T, typename = constraints_t<std::is_integral<T>>>
constexpr int bit_num = std::numeric_limits<std::make_unsigned_t<T>>::digits;
template <typename T, unsigned int n>
struct is_nbit { static constexpr bool value = bit_num<T> == n; };
template <typename T, unsigned int n>
static constexpr bool is_nbit_v = is_nbit<T, n>::value;

// ?
template <typename T>
struct safely_multipliable {};
template <>
struct safely_multipliable<int> { using type = long long; };
template <>
struct safely_multipliable<long long> { using type = __int128_t; };
template <>
struct safely_multipliable<unsigned int> { using type = unsigned long long; };
template <>
struct safely_multipliable<unsigned long int> { using type = __uint128_t; };
template <>
struct safely_multipliable<unsigned long long> { using type = __uint128_t; };
template <>
struct safely_multipliable<float> { using type = float; };
template <>
struct safely_multipliable<double> { using type = double; };
template <>
struct safely_multipliable<long double> { using type = long double; };
template <typename T>
using safely_multipliable_t = typename safely_multipliable<T>::type;

template <typename T, typename = void>
struct rec_value_type {
    using type = T;
};
template <typename T>
struct rec_value_type<T, std::void_t<typename T::value_type>> {
    using type = typename rec_value_type<typename T::value_type>::type;
};
template <typename T>
using rec_value_type_t = typename rec_value_type<T>::type;

} // namespace suisen

// ! type aliases
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using pq_greater = std::priority_queue<T, std::vector<T>, std::greater<T>>;

// ! macros (internal)
#define DETAIL_OVERLOAD2(_1,_2,name,...) name
#define DETAIL_OVERLOAD3(_1,_2,_3,name,...) name
#define DETAIL_OVERLOAD4(_1,_2,_3,_4,name,...) name

#define DETAIL_REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define DETAIL_REP3(i,l,r)    DETAIL_REP4(i,l,r,1)
#define DETAIL_REP2(i,n)      DETAIL_REP3(i,0,n)
#define DETAIL_REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define DETAIL_REPINF2(i,l)   DETAIL_REPINF3(i,l,1)
#define DETAIL_REPINF1(i)     DETAIL_REPINF2(i,0)
#define DETAIL_RREP4(i,l,r,s) for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l)+fld((r)-(l)-1,s)*(s);i>=(l);i-=(s))
#define DETAIL_RREP3(i,l,r)   DETAIL_RREP4(i,l,r,1)
#define DETAIL_RREP2(i,n)     DETAIL_RREP3(i,0,n)

#define DETAIL_CAT_I(a, b) a##b
#define DETAIL_CAT(a, b) DETAIL_CAT_I(a, b)
#define DETAIL_UNIQVAR(tag) DETAIL_CAT(tag, __LINE__)

// ! macros
#define REP(...)    DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_REP4   , DETAIL_REP3   , DETAIL_REP2   )(__VA_ARGS__)
#define RREP(...)   DETAIL_OVERLOAD4(__VA_ARGS__, DETAIL_RREP4  , DETAIL_RREP3  , DETAIL_RREP2  )(__VA_ARGS__)
#define REPINF(...) DETAIL_OVERLOAD3(__VA_ARGS__, DETAIL_REPINF3, DETAIL_REPINF2, DETAIL_REPINF1)(__VA_ARGS__)

#define LOOP(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> DETAIL_UNIQVAR(loop_variable) = n; DETAIL_UNIQVAR(loop_variable) --> 0;)

#define ALL(iterable) std::begin(iterable), std::end(iterable)
#define INPUT(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

// ! debug

#ifdef LOCAL
#  define debug(...) debug_internal(#__VA_ARGS__, __VA_ARGS__)

template <class T, class... Args>
void debug_internal(const char* s, T&& first, Args&&... args) {
    constexpr const char* prefix = "[\033[32mDEBUG\033[m] ";
    constexpr const char* open_brakets = sizeof...(args) == 0 ? "" : "(";
    constexpr const char* close_brakets = sizeof...(args) == 0 ? "" : ")";
    std::cerr << prefix << open_brakets << s << close_brakets << ": " << open_brakets << std::forward<T>(first);
    ((std::cerr << ", " << std::forward<Args>(args)), ...);
    std::cerr << close_brakets << "\n";
}

#else
#  define debug(...) void(0)
#endif

// ! I/O utilities

// __int128_t
std::ostream& operator<<(std::ostream& dest, __int128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        __uint128_t tmp = value < 0 ? -value : value;
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[tmp % 10];
            tmp /= 10;
        } while (tmp != 0);
        if (value < 0) {
            --d;
            *d = '-';
        }
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}
// __uint128_t
std::ostream& operator<<(std::ostream& dest, __uint128_t value) {
    std::ostream::sentry s(dest);
    if (s) {
        char buffer[128];
        char* d = std::end(buffer);
        do {
            --d;
            *d = "0123456789"[value % 10];
            value /= 10;
        } while (value != 0);
        int len = std::end(buffer) - d;
        if (dest.rdbuf()->sputn(d, len) != len) {
            dest.setstate(std::ios_base::badbit);
        }
    }
    return dest;
}

// pair
template <typename T, typename U>
std::ostream& operator<<(std::ostream& out, const std::pair<T, U>& a) {
    return out << a.first << ' ' << a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::ostream& operator<<(std::ostream& out, const std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return out;
    else {
        out << std::get<N>(a);
        if constexpr (N + 1 < std::tuple_size_v<std::tuple<Args...>>) out << ' ';
        return operator<<<N + 1>(out, a);
    }
}
// vector
template <typename T>
std::ostream& operator<<(std::ostream& out, const std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
// array
template <typename T, size_t N>
std::ostream& operator<<(std::ostream& out, const std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end();) {
        out << *it;
        if (++it != a.end()) out << ' ';
    }
    return out;
}
inline void print() { std::cout << '\n'; }
template <typename Head, typename... Tail>
inline void print(const Head& head, const Tail &...tails) {
    std::cout << head;
    if (sizeof...(tails)) std::cout << ' ';
    print(tails...);
}
template <typename Iterable>
auto print_all(const Iterable& v, std::string sep = " ", std::string end = "\n") -> decltype(std::cout << *v.begin(), void()) {
    for (auto it = v.begin(); it != v.end();) {
        std::cout << *it;
        if (++it != v.end()) std::cout << sep;
    }
    std::cout << end;
}

__int128_t stoi128(const std::string& s) {
    __int128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    if (s[0] == '-') ret = -ret;
    return ret;
}
__uint128_t stou128(const std::string& s) {
    __uint128_t ret = 0;
    for (int i = 0; i < int(s.size()); i++) if ('0' <= s[i] and s[i] <= '9') ret = 10 * ret + s[i] - '0';
    return ret;
}
// __int128_t
std::istream& operator>>(std::istream& in, __int128_t& v) {
    std::string s;
    in >> s;
    v = stoi128(s);
    return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
    std::string s;
    in >> s;
    v = stou128(s);
    return in;
}
// pair
template <typename T, typename U>
std::istream& operator>>(std::istream& in, std::pair<T, U>& a) {
    return in >> a.first >> a.second;
}
// tuple
template <unsigned int N = 0, typename ...Args>
std::istream& operator>>(std::istream& in, std::tuple<Args...>& a) {
    if constexpr (N >= std::tuple_size_v<std::tuple<Args...>>) return in;
    else return operator>><N + 1>(in >> std::get<N>(a), a);
}
// vector
template <typename T>
std::istream& operator>>(std::istream& in, std::vector<T>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
// array
template <typename T, size_t N>
std::istream& operator>>(std::istream& in, std::array<T, N>& a) {
    for (auto it = a.begin(); it != a.end(); ++it) in >> *it;
    return in;
}
template <typename ...Args>
void read(Args &...args) {
    (std::cin >> ... >> args);
}

// ! integral utilities

// Returns pow(-1, n)
template <typename T> constexpr inline int pow_m1(T n) {
    return -(n & 1) | 1;
}
// Returns pow(-1, n)
template <> constexpr inline int pow_m1<bool>(bool n) {
    return -int(n) | 1;
}

// Returns floor(x / y)
template <typename T> constexpr inline T fld(const T x, const T y) {
    return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y;
}
template <typename T> constexpr inline T cld(const T x, const T y) {
    return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y;
}

template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<std::negation_v<suisen::is_nbit<T, 64>>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, std::enable_if_t<suisen::is_nbit_v<T, 64>, std::nullptr_t> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num<T>; }
template <typename T> constexpr inline int floor_log2(const T x) { return suisen::bit_num<T> - 1 - count_lz(x); }
template <typename T> constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); }
template <typename T> constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; }
template <typename T> constexpr inline int parity(const T x) { return popcount(x) & 1; }

// ! container

template <typename T, typename Comparator>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Container>
void sort_unique_erase(Container& a) {
    std::sort(a.begin(), a.end());
    a.erase(std::unique(a.begin(), a.end()), a.end());
}

template <typename InputIterator, typename BiConsumer>
auto foreach_adjacent_values(InputIterator first, InputIterator last, BiConsumer f) -> decltype(f(*first++, *last), void()) {
    if (first != last) for (auto itr = first, itl = itr++; itr != last; itl = itr++) f(*itl, *itr);
}
template <typename Container, typename BiConsumer>
auto foreach_adjacent_values(Container &&c, BiConsumer f) -> decltype(c.begin(), c.end(), void()) {
    foreach_adjacent_values(c.begin(), c.end(), f);
}

// ! other utilities

// x <- min(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmin(T& x, const T& y) {
    return y >= x ? false : (x = y, true);
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T& x, const T& y) {
    return y <= x ? false : (x = y, true);
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::string bin(T val, int bit_num = -1) {
    std::string res;
    if (bit_num != -1) {
        for (int bit = bit_num; bit-- > 0;) res += '0' + ((val >> bit) & 1);
    } else {
        for (; val; val >>= 1) res += '0' + (val & 1);
        std::reverse(res.begin(), res.end());
    }
    return res;
}

template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_low_to_high(T val, T base = 10) {
    std::vector<T> res;
    for (; val; val /= base) res.push_back(val % base);
    if (res.empty()) res.push_back(T{ 0 });
    return res;
}
template <typename T, std::enable_if_t<std::is_integral_v<T>, std::nullptr_t> = nullptr>
std::vector<T> digits_high_to_low(T val, T base = 10) {
    auto res = digits_low_to_high(val, base);
    std::reverse(res.begin(), res.end());
    return res;
}

template <typename T>
std::string join(const std::vector<T>& v, const std::string& sep, const std::string& end) {
    std::ostringstream ss;
    for (auto it = v.begin(); it != v.end();) {
        ss << *it;
        if (++it != v.end()) ss << sep;
    }
    ss << end;
    return ss.str();
}

template <typename Func, typename Seq>
auto transform_to_vector(const Func &f, const Seq &s) {
    std::vector<std::invoke_result_t<Func, typename Seq::value_type>> v;
    v.reserve(std::size(s)), std::transform(std::begin(s), std::end(s), std::back_inserter(v), f);
    return v;
}
template <typename T, typename Seq>
auto copy_to_vector(const Seq &s) {
    std::vector<T> v;
    v.reserve(std::size(s)), std::copy(std::begin(s), std::end(s), std::back_inserter(v));
    return v;
}
template <typename Seq>
Seq concat(Seq s, const Seq &t) {
    s.reserve(std::size(s) + std::size(t));
    std::copy(std::begin(t), std::end(t), std::back_inserter(s));
    return s;
}
template <typename Seq>
std::vector<Seq> split(const Seq s, typename Seq::value_type delim) {
    std::vector<Seq> res;
    for (auto itl = std::begin(s), itr = itl;; itl = ++itr) {
        while (itr != std::end(s) and *itr != delim) ++itr;
        res.emplace_back(itl, itr);
        if (itr == std::end(s)) return res;
    }
}

int digit_to_int(char c) { return c - '0'; }
int lowercase_to_int(char c) { return c - 'a'; }
int uppercase_to_int(char c) { return c - 'A'; }

std::vector<int> digit_str_to_ints(const std::string &s) {
    return transform_to_vector(digit_to_int, s);
}
std::vector<int> lowercase_str_to_ints(const std::string &s) {
    return transform_to_vector(lowercase_to_int, s);
}
std::vector<int> uppercase_str_to_ints(const std::string &s) {
    return transform_to_vector(uppercase_to_int, s);
}

const std::string Yes = "Yes", No = "No", YES = "YES", NO = "NO";

namespace suisen {}
using namespace suisen;
using namespace std;

struct io_setup {
    io_setup(int precision = 20) {
        std::ios::sync_with_stdio(false);
        std::cin.tie(nullptr);
        std::cout << std::fixed << std::setprecision(precision);
    }
} io_setup_ {};

// ! code from here

#include <atcoder/modint>

using mint = atcoder::modint998244353;

namespace atcoder {
    std::istream& operator>>(std::istream& in, mint& a) {
        long long e; in >> e; a = e;
        return in;
    }

    std::ostream& operator<<(std::ostream& out, const mint& a) {
        out << a.val();
        return out;
    }
} // namespace atcoder

#include <algorithm>
#include <cassert>
#include <optional>
#include <vector>

namespace suisen {
    template <typename T>
    struct Matrix {
        std::vector<std::vector<T>> dat;

        Matrix() {}
        Matrix(int n) : Matrix(n, n) {}
        Matrix(int n, int m, T fill_value = T(0)) : dat(n, std::vector<T>(m, fill_value)) {}
        Matrix(const std::vector<std::vector<T>>& dat) : dat(dat) {}

        const std::vector<T>& operator[](int i) const { return dat[i]; }
        std::vector<T>& operator[](int i) { return dat[i]; }

        operator std::vector<std::vector<T>>() const { return dat; }

        friend bool operator==(const Matrix<T>& A, const Matrix<T>& B) { return A.dat == B.dat; }
        friend bool operator!=(const Matrix<T>& A, const Matrix<T>& B) { return A.dat != B.dat; }

        std::pair<int, int> shape() const { return dat.empty() ? std::make_pair<int, int>(0, 0) : std::make_pair<int, int>(dat.size(), dat[0].size()); }
        int row_size() const { return dat.size(); }
        int col_size() const { return dat.empty() ? 0 : dat[0].size(); }

        friend Matrix<T>& operator+=(Matrix<T>& A, const Matrix<T>& B) {
            assert(A.shape() == B.shape());
            auto [n, m] = A.shape();
            for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) A.dat[i][j] += B.dat[i][j];
            return A;
        }
        friend Matrix<T>& operator-=(Matrix<T>& A, const Matrix<T>& B) {
            assert(A.shape() == B.shape());
            auto [n, m] = A.shape();
            for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) A.dat[i][j] -= B.dat[i][j];
            return A;
        }
        friend Matrix<T>& operator*=(Matrix<T>& A, const Matrix<T>& B) { return A = A * B; }
        friend Matrix<T>& operator*=(Matrix<T>& A, const T& val) {
            for (auto& row : A.dat) for (auto& elm : row) elm *= val;
            return A;
        }
        friend Matrix<T>& operator/=(Matrix<T>& A, const T& val) { return A *= T(1) / val; }
        friend Matrix<T>& operator/=(Matrix<T>& A, const Matrix<T>& B) { return A *= B.inv(); }

        friend Matrix<T> operator+(Matrix<T> A, const Matrix<T>& B) { A += B; return A; }
        friend Matrix<T> operator-(Matrix<T> A, const Matrix<T>& B) { A -= B; return A; }
        friend Matrix<T> operator*(const Matrix<T>& A, const Matrix<T>& B) {
            assert(A.col_size() == B.row_size());
            const int n = A.row_size(), m = A.col_size(), l = B.col_size();

            if (std::min({ n, m, l }) <= 70) {
                // naive
                Matrix<T> C(n, l);
                for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) for (int k = 0; k < l; ++k) {
                    C.dat[i][k] += A.dat[i][j] * B.dat[j][k];
                }
                return C;
            }

            // strassen
            const int nl = 0, nm = n >> 1, nr = nm + nm;
            const int ml = 0, mm = m >> 1, mr = mm + mm;
            const int ll = 0, lm = l >> 1, lr = lm + lm;

            auto A00 = A.submatrix(nl, nm, ml, mm), A01 = A.submatrix(nl, nm, mm, mr);
            auto A10 = A.submatrix(nm, nr, ml, mm), A11 = A.submatrix(nm, nr, mm, mr);

            auto B00 = B.submatrix(ml, mm, ll, lm), B01 = B.submatrix(ml, mm, lm, lr);
            auto B10 = B.submatrix(mm, mr, ll, lm), B11 = B.submatrix(mm, mr, lm, lr);

            auto P0 = (A00 + A11) * (B00 + B11);
            auto P1 = (A10 + A11) * B00;
            auto P2 = A00 * (B01 - B11);
            auto P3 = A11 * (B10 - B00);
            auto P4 = (A00 + A01) * B11;
            auto P5 = (A10 - A00) * (B00 + B01);
            auto P6 = (A01 - A11) * (B10 + B11);

            Matrix<T> C(n, l);

            C.assign_submatrix(nl, ll, P0 + P3 - P4 + P6), C.assign_submatrix(nl, lm, P2 + P4);
            C.assign_submatrix(nm, ll, P1 + P3), C.assign_submatrix(nm, lm, P0 + P2 - P1 + P5);

            // fractions
            if (l != lr) {
                for (int i = 0; i < nr; ++i) for (int j = 0; j < mr; ++j) C.dat[i][lr] += A.dat[i][j] * B.dat[j][lr];
            }
            if (m != mr) {
                for (int i = 0; i < nr; ++i) for (int k = 0; k < l; ++k) C.dat[i][k] += A.dat[i][mr] * B.dat[mr][k];
            }
            if (n != nr) {
                for (int j = 0; j < m; ++j) for (int k = 0; k < l; ++k) C.dat[nr][k] += A.dat[nr][j] * B.dat[j][k];
            }

            return C;
        }
        friend Matrix<T> operator*(const T& val, Matrix<T> A) { A *= val; return A; }
        friend Matrix<T> operator*(Matrix<T> A, const T& val) { A *= val; return A; }
        friend Matrix<T> operator/(const Matrix<T>& A, const Matrix<T>& B) { return A * B.inv(); }
        friend Matrix<T> operator/(Matrix<T> A, const T& val) { A /= val; return A; }
        friend Matrix<T> operator/(const T& val, const Matrix<T>& A) { return val * A.inv(); }

        friend std::vector<T> operator*(const Matrix<T>& A, const std::vector<T>& x) {
            const auto [n, m] = A.shape();
            assert(m == int(x.size()));
            std::vector<T> b(n, T(0));
            for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) b[i] += A.dat[i][j] * x[j];
            return b;
        }

        static Matrix<T> e0(int n) { return Matrix<T>(n, Identity::ADD); }
        static Matrix<T> e1(int n) { return Matrix<T>(n, Identity::MUL); }

        Matrix<T> pow(long long b) const {
            assert_square();
            assert(b >= 0);
            Matrix<T> res = e1(row_size()), p = *this;
            for (; b; b >>= 1) {
                if (b & 1) res *= p;
                p *= p;
            }
            return res;
        }
        Matrix<T> inv() const { return *safe_inv(); }

        std::optional<Matrix<T>> safe_inv() const {
            assert_square();
            Matrix<T> A = *this;
            const int n = A.row_size();
            for (int i = 0; i < n; ++i) {
                A[i].resize(2 * n, T{ 0 });
                A[i][n + i] = T{ 1 };
            }
            for (int i = 0; i < n; ++i) {
                for (int k = i; k < n; ++k) if (A[k][i] != T{ 0 }) {
                    std::swap(A[i], A[k]);
                    T c = T{ 1 } / A[i][i];
                    for (int j = i; j < 2 * n; ++j) A[i][j] *= c;
                    break;
                }
                if (A[i][i] == T{ 0 }) return std::nullopt;
                for (int k = 0; k < n; ++k) if (k != i and A[k][i] != T{ 0 }) {
                    T c = A[k][i];
                    for (int j = i; j < 2 * n; ++j) A[k][j] -= c * A[i][j];
                }
            }
            for (auto& row : A.dat) row.erase(row.begin(), row.begin() + n);
            return A;
        }

        T det() const {
            assert_square();
            Matrix<T> A = *this;
            bool sgn = false;
            const int n = A.row_size();
            for (int j = 0; j < n; ++j) for (int i = j + 1; i < n; ++i) if (A[i][j] != T{ 0 }) {
                std::swap(A[j], A[i]);
                T q = A[i][j] / A[j][j];
                for (int k = j; k < n; ++k) A[i][k] -= A[j][k] * q;
                sgn = not sgn;
            }
            T res = sgn ? T{ -1 } : T{ +1 };
            for (int i = 0; i < n; ++i) res *= A[i][i];
            return res;
        }
        T det_arbitrary_mod() const {
            assert_square();
            Matrix<T> A = *this;
            bool sgn = false;
            const int n = A.row_size();
            for (int j = 0; j < n; ++j) for (int i = j + 1; i < n; ++i) {
                for (; A[i][j].val(); sgn = not sgn) {
                    std::swap(A[j], A[i]);
                    T q = A[i][j].val() / A[j][j].val();
                    for (int k = j; k < n; ++k) A[i][k] -= A[j][k] * q;
                }
            }
            T res = sgn ? -1 : +1;
            for (int i = 0; i < n; ++i) res *= A[i][i];
            return res;
        }
        void assert_square() const { assert(row_size() == col_size()); }

        Matrix<T> submatrix(int row_begin, int row_end, int col_begin, int col_end) const {
            Matrix<T> A(row_end - row_begin, col_end - col_begin);
            for (int i = row_begin; i < row_end; ++i) for (int j = col_begin; j < col_end; ++j) {
                A[i - row_begin][j - col_begin] = dat[i][j];
            }
            return A;
        }
        void assign_submatrix(int row_begin, int col_begin, const Matrix<T>& A) {
            const int n = A.row_size(), m = A.col_size();
            assert(row_begin + n <= row_size() and col_begin + m <= col_size());
            for (int i = 0; i < n; ++i) for (int j = 0; j < m; ++j) {
                dat[row_begin + i][col_begin + j] = A[i][j];
            }
        }
    private:
        enum class Identity {
            ADD, MUL
        };
        Matrix(int n, Identity ident) : Matrix<T>::Matrix(n) {
            if (ident == Identity::MUL) for (int i = 0; i < n; ++i) dat[i][i] = 1;
        }
    };
} // namespace suisen

namespace suisen {
template <typename T>
class CoordinateCompressorBuilder {
    public:
        struct Compressor {
            public:
                static constexpr int absent = -1;

                // default constructor
                Compressor() : _xs(std::vector<T>{}) {}
                // Construct from strictly sorted vector
                Compressor(const std::vector<T> &xs) : _xs(xs) {
                    assert(is_strictly_sorted(xs));
                }

                // Return the number of distinct keys.
                int size() const {
                    return _xs.size();
                }
                // Check if the element is registered.
                bool has_key(const T &e) const {
                    return std::binary_search(_xs.begin(), _xs.end(), e);
                }
                // Compress the element. if not registered, returns `default_value`. (default: Compressor::absent)
                int comp(const T &e, int default_value = absent) const {
                    const int res = min_geq_index(e);
                    return res != size() and _xs[res] == e ? res : default_value;
                }
                // Restore the element from the index.
                T decomp(const int compressed_index) const {
                    return _xs[compressed_index];
                }
                // Compress the element. Equivalent to call `comp(e)`
                int operator[](const T &e) const {
                    return comp(e);
                }
                // Return the minimum registered value greater than `e`. if not exists, return `default_value`.
                T min_gt(const T &e, const T &default_value) const {
                    auto it = std::upper_bound(_xs.begin(), _xs.end(), e);
                    return it == _xs.end() ? default_value : *it;
                }
                // Return the minimum registered value greater than or equal to `e`. if not exists, return `default_value`.
                T min_geq(const T &e, const T &default_value) const {
                    auto it = std::lower_bound(_xs.begin(), _xs.end(), e);
                    return it == _xs.end() ? default_value : *it;
                }
                // Return the maximum registered value less than `e`. if not exists, return `default_value`
                T max_lt(const T &e, const T &default_value) const {
                    auto it = std::upper_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>());
                    return it == _xs.rend() ? default_value : *it;
                }
                // Return the maximum registered value less than or equal to `e`. if not exists, return `default_value`
                T max_leq(const T &e, const T &default_value) const {
                    auto it = std::lower_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>());
                    return it == _xs.rend() ? default_value : *it;
                }
                // Return the compressed index of the minimum registered value greater than `e`. if not exists, return `compressor.size()`.
                int min_gt_index(const T &e) const {
                    return std::upper_bound(_xs.begin(), _xs.end(), e) - _xs.begin();
                }
                // Return the compressed index of the minimum registered value greater than or equal to `e`. if not exists, return `compressor.size()`.
                int min_geq_index(const T &e) const {
                    return std::lower_bound(_xs.begin(), _xs.end(), e) - _xs.begin();
                }
                // Return the compressed index of the maximum registered value less than `e`. if not exists, return -1.
                int max_lt_index(const T &e) const {
                    return int(_xs.rend() - std::upper_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>())) - 1;
                }
                // Return the compressed index of the maximum registered value less than or equal to `e`. if not exists, return -1.
                int max_leq_index(const T &e) const {
                    return int(_xs.rend() - std::lower_bound(_xs.rbegin(), _xs.rend(), e, std::greater<T>())) - 1;
                }
            private:
                std::vector<T> _xs;
                static bool is_strictly_sorted(const std::vector<T> &v) {
                    return std::adjacent_find(v.begin(), v.end(), std::greater_equal<T>()) == v.end();
                }
        };
        CoordinateCompressorBuilder() : _xs(std::vector<T>{}) {}
        explicit CoordinateCompressorBuilder(const std::vector<T> &xs) : _xs(xs) {}
        explicit CoordinateCompressorBuilder(std::vector<T> &&xs) : _xs(std::move(xs)) {}
        template <typename Gen, constraints_t<is_same_as_invoke_result<T, Gen, int>> = nullptr>
        CoordinateCompressorBuilder(const int n, Gen generator) {
            reserve(n);
            for (int i = 0; i < n; ++i) push(generator(i));
        }
        // Attempt to preallocate enough memory for specified number of elements.
        void reserve(int n) {
            _xs.reserve(n);
        }
        // Add data.
        void push(const T &first) {
            _xs.push_back(first);
        }
        // Add data.
        void push(T &&first) {
            _xs.push_back(std::move(first));
        }
        // Add data in the range of [first, last). 
        template <typename Iterator>
        auto push(const Iterator &first, const Iterator &last) -> decltype(std::vector<T>{}.push_back(*first), void()) {
            for (auto it = first; it != last; ++it) _xs.push_back(*it);
        }
        // Add all data in the container. Equivalent to `push(iterable.begin(), iterable.end())`.
        template <typename Iterable>
        auto push(const Iterable &iterable) -> decltype(std::vector<T>{}.push_back(*iterable.begin()), void()) {
            push(iterable.begin(), iterable.end());
        }
        // Add data.
        template <typename ...Args>
        void emplace(Args &&...args) {
            _xs.emplace_back(std::forward<Args>(args)...);
        }
        // Build compressor.
        auto build() {
            std::sort(_xs.begin(), _xs.end()), _xs.erase(std::unique(_xs.begin(), _xs.end()), _xs.end());
            return Compressor {_xs};
        }
        // Build compressor from vector.
        static auto build(const std::vector<T> &xs) {
            return CoordinateCompressorBuilder(xs).build();
        }
        // Build compressor from vector.
        static auto build(std::vector<T> &&xs) {
            return CoordinateCompressorBuilder(std::move(xs)).build();
        }
        // Build compressor from generator.
        template <typename Gen, constraints_t<is_same_as_invoke_result<T, Gen, int>> = nullptr>
        static auto build(const int n, Gen generator) {
            return CoordinateCompressorBuilder<T>(n, generator).build();
        }
    private:
        std::vector<T> _xs;
};

} // namespace suisen

int main() {
    int n;
    read(n);

    ++n;

    Matrix<mint> A(n, n);
    REP(i, n) {
        REP(j, n) {
            mint x;
            read(x);
            A[i][j] = -x;
        }
        A[i][i] = 1;
    }
    A = A.inv();

    REP(i, n) {
        debug(A[i]);
    }

    int q;
    read(q);
    LOOP(q) {
        int k;
        read(k);

        CoordinateCompressorBuilder<int> builder;
        builder.push(0);
        builder.push(n - 1);

        vector<tuple<int, int, mint>> ts(k);
        for (auto& [u, v, c] : ts) {
            read(u, v, c);
            builder.push(u);
            builder.push(v);
        }
        auto comp = builder.build();

        const int m = comp.size();

        vector<vector<pair<int, mint>>> h(m);

        for (auto& [u, v, c] : ts) {
            u = comp[u];
            v = comp[v];
            h[u].emplace_back(v, c);
        }

        array<vector<mint>, 2> g{ vector<mint>(m), vector<mint>(m) };
        g[0][0] = 1;
        REP(i, m) {
            REP(j, i + 1, m) {
                g[1][j] += g[0][i] * A[comp.decomp(i)][comp.decomp(j)];
            }
            for (auto [j, c] : h[i]) {
                g[0][j] += (g[0][i] + g[1][i]) * c;
            }
        }
        print(g[0].back() + g[1].back());
    }
    return 0;
}