#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>>;
template <typename T, typename U>
using umap = std::unordered_map<T, U>;

// ! macros (capital: internal macro)
#define OVERLOAD2(_1,_2,name,...) name
#define OVERLOAD3(_1,_2,_3,name,...) name
#define OVERLOAD4(_1,_2,_3,_4,name,...) name

#define REP4(i,l,r,s)  for(std::remove_reference_t<std::remove_const_t<decltype(r)>>i=(l);i<(r);i+=(s))
#define REP3(i,l,r)    REP4(i,l,r,1)
#define REP2(i,n)      REP3(i,0,n)
#define REPINF3(i,l,s) for(std::remove_reference_t<std::remove_const_t<decltype(l)>>i=(l);;i+=(s))
#define REPINF2(i,l)   REPINF3(i,l,1)
#define REPINF1(i)     REPINF2(i,0)
#define 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 RREP3(i,l,r)   RREP4(i,l,r,1)
#define RREP2(i,n)     RREP3(i,0,n)

#define rep(...)    OVERLOAD4(__VA_ARGS__, REP4   , REP3   , REP2   )(__VA_ARGS__)
#define rrep(...)   OVERLOAD4(__VA_ARGS__, RREP4  , RREP3  , RREP2  )(__VA_ARGS__)
#define repinf(...) OVERLOAD3(__VA_ARGS__, REPINF3, REPINF2, REPINF1)(__VA_ARGS__)

#define CAT_I(a, b) a##b
#define CAT(a, b) CAT_I(a, b)
#define UNIQVAR(tag) CAT(tag, __LINE__)
#define loop(n) for (std::remove_reference_t<std::remove_const_t<decltype(n)>> UNIQVAR(loop_variable) = n; UNIQVAR(loop_variable) --> 0;)

#define all(iterable) std::begin(iterable), std::end(iterable)
#define input(type, ...) type __VA_ARGS__; read(__VA_ARGS__)

#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 parse_i128(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 parse_u128(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 = parse_i128(s);
    return in;
}
// __uint128_t
std::istream& operator>>(std::istream& in, __uint128_t& v) {
    std::string s;
    in >> s;
    v = parse_u128(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, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
__attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = nullptr>
constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 16>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 32>> = nullptr>
constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num<T>; }
template <typename T, suisen::constraints_t<suisen::is_nbit<T, 64>> = 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, suisen::constraints_t<suisen::is_comparator<Comparator, T>> = nullptr>
auto priqueue_comp(const Comparator comparator) {
    return std::priority_queue<T, std::vector<T>, Comparator>(comparator);
}

template <typename Iterable>
auto isize(const Iterable& iterable) -> decltype(int(iterable.size())) {
    return iterable.size();
}

template <typename T, typename Gen, suisen::constraints_t<suisen::is_same_as_invoke_result<T, Gen, int>> = nullptr>
auto generate_vector(int n, Gen generator) {
    std::vector<T> v(n);
    for (int i = 0; i < n; ++i) v[i] = generator(i);
    return v;
}
template <typename T>
auto generate_range_vector(T l, T r) {
    return generate_vector(r - l, [l](int i) { return l + i; });
}
template <typename T>
auto generate_range_vector(T n) {
    return generate_range_vector(0, n);
}

template <typename T>
void sort_unique_erase(std::vector<T>& 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) {
    if (y >= x) return false;
    x = y;
    return true;
}
// x <- max(x, y). returns true iff `x` has chenged.
template <typename T>
inline bool chmax(T& x, const T& y) {
    if (y <= x) return false;
    x = y;
    return 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 >= 0) {
        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();
}

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;

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;
}

#include <array>
#include <cassert>
#include <optional>

namespace suisen {
    namespace default_operator {
        template <typename T>
        auto zero() -> decltype(T { 0 }) { return T { 0 }; }
        template <typename T>
        auto one()  -> decltype(T { 1 }) { return T { 1 }; }
        template <typename T>
        auto add(const T &x, const T &y) -> decltype(x + y) { return x + y; }
        template <typename T>
        auto sub(const T &x, const T &y) -> decltype(x - y) { return x - y; }
        template <typename T>
        auto mul(const T &x, const T &y) -> decltype(x * y) { return x * y; }
        template <typename T>
        auto div(const T &x, const T &y) -> decltype(x / y) { return x / y; }
        template <typename T>
        auto mod(const T &x, const T &y) -> decltype(x % y) { return x % y; }
        template <typename T>
        auto neg(const T &x) -> decltype(-x) { return -x; }
        template <typename T>
        auto inv(const T &x) -> decltype(one<T>() / x)  { return one<T>() / x; }
    } // default_operator
    namespace default_operator_noref {
        template <typename T>
        auto zero() -> decltype(T { 0 }) { return T { 0 }; }
        template <typename T>
        auto one()  -> decltype(T { 1 }) { return T { 1 }; }
        template <typename T>
        auto add(T x, T y) -> decltype(x + y) { return x + y; }
        template <typename T>
        auto sub(T x, T y) -> decltype(x - y) { return x - y; }
        template <typename T>
        auto mul(T x, T y) -> decltype(x * y) { return x * y; }
        template <typename T>
        auto div(T x, T y) -> decltype(x / y) { return x / y; }
        template <typename T>
        auto mod(T x, T y) -> decltype(x % y) { return x % y; }
        template <typename T>
        auto neg(T x) -> decltype(-x) { return -x; }
        template <typename T>
        auto inv(T x) -> decltype(one<T>() / x)  { return one<T>() / x; }
    } // default_operator
} // namespace suisen

namespace suisen {
    template <
        typename T,
        size_t N,
        size_t M,
        T(*_add)(T, T) = default_operator_noref::add<T>,
        T(*_neg)(T) = default_operator_noref::neg<T>,
        T(*_zero)() = default_operator_noref::zero<T>,
        T(*_mul)(T, T) = default_operator_noref::mul<T>,
        T(*_inv)(T) = default_operator_noref::inv<T>,
        T(*_one)()  = default_operator_noref::one<T>
    >
    struct ArrayMatrix : public std::array<std::array<T, M>, N> {
#define MatrixType(N, M) ArrayMatrix<T, N, M, _add, _neg, _zero, _mul, _inv, _one>
        using base_type = std::array<std::array<T, M>, N>;
        using container_type = base_type;
        using row_type = std::array<T, M>;

        using base_type::base_type;
        constexpr ArrayMatrix() : ArrayMatrix(_zero()) {}
        constexpr ArrayMatrix(T fill_value) {
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) (*this)[i][j] = fill_value;
        }
        constexpr ArrayMatrix(const container_type &c) {
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) (*this)[i][j] = c[i][j];
        }

        constexpr std::pair<int, int> shape() const {
            return { N, M };
        }
        constexpr int row_size() const {
            return N;
        }
        constexpr int col_size() const {
            return M;
        }

        constexpr MatrixType(N, M) operator+() {
            return *this;
        }
        constexpr MatrixType(N, M) operator-() {
            ArrayMatrix res;
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) res[i][j] = _add(res[i][j], _neg((*this)[i][j]));
            return res;
        }
        constexpr MatrixType(N, M)& operator+=(const MatrixType(N, M)& other) {
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) (*this)[i][j] = _add((*this)[i][j], other[i][j]);
            return *this;
        }
        constexpr MatrixType(N, M)& operator-=(const MatrixType(N, M)& other) {
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) (*this)[i][j] = _add((*this)[i][j], _neg(other[i][j]));
            return *this;
        }
        template <size_t K>
        constexpr MatrixType(N, M)& operator*=(const MatrixType(M, K)& other) {
            return *this = *this * other;
        }
        constexpr MatrixType(N, M)& operator*=(const T& val) {
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) (*this)[i][j] = _mul((*this)[i][j], val);
            return *this;
        }
        constexpr MatrixType(N, M)& operator/=(const T& val) {
            return *this *= _inv(val);
        }
        constexpr friend MatrixType(N, M) operator+(const MatrixType(N, M)& lhs, const MatrixType(N, M)& rhs) {
            return MatrixType(N, M)(lhs) += rhs;
        }
        constexpr friend MatrixType(N, M) operator-(const MatrixType(N, M)& lhs, const MatrixType(N, M)& rhs) {
            return MatrixType(N, M)(lhs) -= rhs;
        }
        template <size_t K>
        constexpr friend MatrixType(N, K) operator*(const MatrixType(N, M)& lhs, const MatrixType(M, K)& rhs) {
            MatrixType(N, K) res;
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) for (size_t k = 0; k < K; ++k) {
                res[i][k] = _add(res[i][k], _mul(lhs[i][j], rhs[j][k]));
            }
            return res;
        }
        constexpr friend MatrixType(N, M) operator*(const MatrixType(N, M)& A, const T& val) {
            MatrixType(N, M) res;
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) res[i][j] = _mul(A[i][j], val);
            return res;
        }
        constexpr friend MatrixType(N, M) operator*(const T& val, const MatrixType(N, M)& A) {
            MatrixType(N, M) res;
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) res[i][j] = _mul(val, A[i][j]);
            return res;
        }
        constexpr friend MatrixType(N, M) operator/(const MatrixType(N, M)& A, const T& val) {
            return MatrixType(N, M)(A) /= val;
        }

        constexpr std::array<T, N> operator*(const std::array<T, M>& x) const {
            std::array<T, N> b;
            b.fill(_zero());
            for (size_t i = 0; i < N; ++i) for (size_t j = 0; j < M; ++j) b[i] = _add(b[i], _mul((*this)[i][j], x[j]));
            return b;
        }
#undef MatrixType
    };

    template <
        typename T,
        size_t N,
        T(*_add)(T, T) = default_operator_noref::add<T>,
        T(*_neg)(T) = default_operator_noref::neg<T>,
        T(*_zero)() = default_operator_noref::zero<T>,
        T(*_mul)(T, T) = default_operator_noref::mul<T>,
        T(*_inv)(T) = default_operator_noref::inv<T>,
        T(*_one)()  = default_operator_noref::one<T>
    >
    class SquareArrayMatrix : public ArrayMatrix<T, N, N, _add, _neg, _zero, _mul, _inv, _one> {
    private:
        enum Operator { Add, Mul };
    public:
#define MatrixType(N) SquareArrayMatrix<T, N, _add, _neg, _zero, _mul, _inv, _one>
        using base_type = ArrayMatrix<T, N, N, _add, _neg, _zero, _mul, _inv, _one>;
        using container_type = typename base_type::container_type;
        using row_type = typename base_type::row_type;

        using base_type::base_type;

        static SquareArrayMatrix e0() { return SquareArrayMatrix(Operator::Add); }
        static SquareArrayMatrix e1() { return SquareArrayMatrix(Operator::Mul); }

        static constexpr std::optional<SquareArrayMatrix> inv(const SquareArrayMatrix& A) {
            std::array<std::array<T, 2 * N>, N> data;
            for (size_t i = 0; i < N; ++i) {
                for (size_t j = 0; j < N; ++j) {
                    data[i][j] = A[i][j];
                    data[i][N + j] = i == j ? _one() : _zero();
                }
            }
            for (size_t i = 0; i < N; ++i) {
                int pivot = -1;
                for (size_t k = i; k < N; ++k) if (data[k][i] != _zero()) {
                    pivot = k;
                    break;
                }
                if (pivot < 0) return std::nullopt;
                data[i].swap(data[pivot]);
                T coef = _inv(data[i][i]);
                for (size_t j = i; j < 2 * N; ++j) data[i][j] = _mul(data[i][j], coef);
                for (size_t k = 0; k < N; ++k) if (k != i and data[k][i] != _zero()) {
                    T c = data[k][i];
                    for (size_t j = i; j < 2 * N; ++j) data[k][j] = _add(data[k][j], _neg(_mul(c, data[i][j])));
                }
            }
            SquareArrayMatrix res;
            for (size_t i = 0; i < N; ++i) std::copy(data[i].begin(), data[i].begin() + N, res[i].begin());
            return res;
        }
        static constexpr T det(SquareArrayMatrix&& A) {
            T det_inv = _one();
            for (size_t i = 0; i < N; ++i) {
                int pivot = -1;
                for (size_t k = i; k < N; ++k) if (A[k][i] != _zero()) {
                    pivot = k;
                    break;
                }
                if (pivot < 0) return _zero();
                A[i].swap(A[pivot]);
                if (pivot != i) det_inv = _mul(det_inv, _neg(_one()));
                T coef = _inv(A[i][i]);
                for (size_t j = i; j < N; ++j) A[i][j] = _mul(A[i][j], coef);
                det_inv = _mul(det_inv, coef);
                for (size_t k = i + 1; k < N; ++k) if (A[k][i] != _zero()) {
                    T c = A[k][i];
                    for (size_t j = i; j < N; ++j) A[k][j] = _add(A[k][j], _neg(_mul(c, A[i][j])));
                }
            }
            return _inv(det_inv);
        }
        static constexpr T det(const SquareArrayMatrix& A) {
            return det(SquareArrayMatrix(A));
        }
        constexpr SquareArrayMatrix inv() const {
            return *inv(*this);
        }
        constexpr T det() const {
            return det(*this);
        }

        constexpr friend SquareArrayMatrix operator+(const SquareArrayMatrix& A, const SquareArrayMatrix& B) {
            auto res = *static_cast<base_type const*>(&A) + *static_cast<base_type const*>(&B);
            return *static_cast<SquareArrayMatrix*>(&res);
        }
        constexpr SquareArrayMatrix& operator+=(const SquareArrayMatrix& B) {
            return *static_cast<SquareArrayMatrix*>(&(*static_cast<base_type*>(this) += *static_cast<base_type const*>(&B)));
        }
        constexpr friend SquareArrayMatrix operator-(const SquareArrayMatrix& A, const SquareArrayMatrix& B) {
            auto res = *static_cast<base_type const*>(&A) - *static_cast<base_type const*>(&B);
            return *static_cast<SquareArrayMatrix*>(&res);
        }
        constexpr SquareArrayMatrix& operator-=(const SquareArrayMatrix& B) {
            return *static_cast<SquareArrayMatrix*>(&(*static_cast<base_type*>(this) -= *static_cast<base_type const*>(&B)));
        }
        constexpr friend SquareArrayMatrix operator*(const SquareArrayMatrix& A, const SquareArrayMatrix& B) {
            auto res = *static_cast<base_type const*>(&A) * *static_cast<base_type const*>(&B);
            return *static_cast<SquareArrayMatrix*>(&res);
        }
        constexpr SquareArrayMatrix& operator*=(const SquareArrayMatrix& B) {
            return *static_cast<SquareArrayMatrix*>(&(*static_cast<base_type*>(this) *= *static_cast<base_type const*>(&B)));
        }
        constexpr friend SquareArrayMatrix operator*(const SquareArrayMatrix& A, const T& x) {
            auto res = *static_cast<base_type const*>(&A) * x;
            return *static_cast<SquareArrayMatrix*>(&res);
        }
        constexpr friend SquareArrayMatrix operator*(const T& x, const SquareArrayMatrix& A) {
            auto res = x * *static_cast<base_type const*>(&A);
            return *static_cast<SquareArrayMatrix*>(&res);
        }
        constexpr SquareArrayMatrix& operator*=(const T& x) {
            return *static_cast<SquareArrayMatrix*>(&(*static_cast<base_type*>(this) *= x));
        }
        constexpr SquareArrayMatrix& operator/=(const SquareArrayMatrix& other) { return *this *= other.inv(); }
        constexpr SquareArrayMatrix  operator/ (const SquareArrayMatrix& other) const { return SquareArrayMatrix(*this) *= other.inv(); }

        constexpr SquareArrayMatrix pow(long long b) const {
            assert(b >= 0);
            SquareArrayMatrix res(e1()), p(*this);
            for (; b; b >>= 1) {
                if (b & 1) res *= p;
                p *= p;
            }
            return res;
        }
    private:
        SquareArrayMatrix(Operator op) : base_type() {
            if (op == Operator::Mul) for (size_t i = 0; i < N; ++i) (*this)[i][i] = _one();
        }
#undef MatrixType
    };
} // namespace suisen

using Matrix = SquareArrayMatrix<mint, 3>;

array<Matrix, 3> T {
    Matrix {{
        1, 0, 0,
        0, 1, 0,
        0, 0, 1
    }},
    Matrix {{
        0, 0, 1,
        1, 0, 0,
        0, 1, 0
    }},
    Matrix {{
        0, 1, 0,
        0, 0, 1,
        1, 0, 0
    }},
};
Matrix Q {{
    4, 3, 3,
    3, 4, 3,
    3, 3, 4
}};

int main() {
    input(int, n);
    input(string, s);

    vector<Matrix> S(n + 1);
    rrep(i, n) {
        S[i] = (s[i] == '?' ? Q : T[(s[i] - '0') % 3]) * (S[i + 1] + Matrix::e1());
    }
    print(accumulate(all(S), Matrix::e0())[0][0]);

    return 0;
}