結果

問題 No.2019 Digits Filling for All Substrings
ユーザー suisen
提出日時 2022-07-22 22:36:30
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
CE  
(最新)
AC  
(最初)
実行時間 -
コード長 28,712 bytes
コンパイル時間 3,397 ms
コンパイル使用メモリ 302,992 KB
最終ジャッジ日時 2025-01-30 12:44:28
ジャッジサーバーID
(参考情報)
judge3 / judge1
このコードへのチャレンジ
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コンパイルエラー時のメッセージ・ソースコードは、提出者また管理者しか表示できないようにしております。(リジャッジ後のコンパイルエラーは公開されます)
ただし、clay言語の場合は開発者のデバッグのため、公開されます。

コンパイルメッセージ
main.cpp: In instantiation of ‘void print(const Head&, const Tail& ...) [with Head = atcoder::static_modint<998244353>; Tail = {}]’:
main.cpp:773:10:   required from here
main.cpp:215:15: error: no match for ‘operator<<’ (operand types are ‘std::ostream’ {aka ‘std::basic_ostream<char>’} and ‘const atcoder::static_modint<998244353>’)
  215 |     std::cout << head;
      |     ~~~~~~~~~~^~~~~~~
In file included from /usr/include/c++/13/istream:41,
                 from /usr/include/c++/13/sstream:40,
                 from /usr/include/c++/13/complex:45,
                 from /usr/include/c++/13/ccomplex:39,
                 from /usr/include/x86_64-linux-gnu/c++/13/bits/stdc++.h:127,
                 from main.cpp:1:
/usr/include/c++/13/ostream:110:7: note: candidate: ‘std::basic_ostream<_CharT, _Traits>::__ostream_type& std::basic_ostream<_CharT, _Traits>::operator<<(__ostream_type& (*)(__ostream_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __ostream_type = std::basic_ostream<char>]’
  110 |       operator<<(__ostream_type& (*__pf)(__ostream_type&))
      |       ^~~~~~~~
/usr/include/c++/13/ostream:110:36: note:   no known conversion for argument 1 from ‘const atcoder::static_modint<998244353>’ to ‘std::basic_ostream<char>::__ostream_type& (*)(std::basic_ostream<char>::__ostream_type&)’ {aka ‘std::basic_ostream<char>& (*)(std::basic_ostream<char>&)’}
  110 |       operator<<(__ostream_type& (*__pf)(__ostream_type&))
      |                  ~~~~~~~~~~~~~~~~~~^~~~~~~~~~~~~~~~~~~~~~
/usr/include/c++/13/ostream:119:7: note: candidate: ‘std::basic_ostream<_CharT, _Traits>::__ostream_type& std::basic_ostream<_CharT, _Traits>::operator<<(__ios_type& (*)(__ios_type&)) [with _CharT = char; _Traits = std::char_traits<char>; __ostream_type = std::basic_ostream<char>; __ios_type = std::basic_ios<char>]’
  119 |       operator<<(__ios_type& (*__pf)(__ios_type&))
      |       ^~~~~~~~
/usr/include/c++/13/ostream:119:32: 

ソースコード

diff #
プレゼンテーションモードにする

#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;
}
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0