#include #ifdef _MSC_VER # include #else # include #endif #include #include namespace suisen { // ! utility template using constraints_t = std::enable_if_t, std::nullptr_t>; template constexpr decltype(auto) constexpr_if(Then&& then, OrElse&& or_else) { if constexpr (cond_v) { return std::forward(then); } else { return std::forward(or_else); } } // ! function template using is_same_as_invoke_result = std::is_same, ReturnType>; template using is_uni_op = is_same_as_invoke_result; template using is_bin_op = is_same_as_invoke_result; template using is_comparator = std::is_same, bool>; // ! integral template >> constexpr int bit_num = std::numeric_limits>::digits; template struct is_nbit { static constexpr bool value = bit_num == n; }; template static constexpr bool is_nbit_v = is_nbit::value; // ? template struct safely_multipliable {}; template <> struct safely_multipliable { using type = long long; }; template <> struct safely_multipliable { using type = __int128_t; }; template <> struct safely_multipliable { using type = unsigned long long; }; template <> struct safely_multipliable { using type = __uint128_t; }; template <> struct safely_multipliable { using type = __uint128_t; }; template <> struct safely_multipliable { using type = float; }; template <> struct safely_multipliable { using type = double; }; template <> struct safely_multipliable { using type = long double; }; template using safely_multipliable_t = typename safely_multipliable::type; template struct rec_value_type { using type = T; }; template struct rec_value_type> { using type = typename rec_value_type::type; }; template using rec_value_type_t = typename rec_value_type::type; } // namespace suisen // ! type aliases using i128 = __int128_t; using u128 = __uint128_t; template using pq_greater = std::priority_queue, std::greater>; // ! 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>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>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>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> 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 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(first); ((std::cerr << ", " << std::forward(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 std::ostream& operator<<(std::ostream& out, const std::pair& a) { return out << a.first << ' ' << a.second; } // tuple template std::ostream& operator<<(std::ostream& out, const std::tuple& a) { if constexpr (N >= std::tuple_size_v>) return out; else { out << std::get(a); if constexpr (N + 1 < std::tuple_size_v>) out << ' '; return operator<<(out, a); } } // vector template std::ostream& operator<<(std::ostream& out, const std::vector& a) { for (auto it = a.begin(); it != a.end();) { out << *it; if (++it != a.end()) out << ' '; } return out; } // array template std::ostream& operator<<(std::ostream& out, const std::array& 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 inline void print(const Head& head, const Tail &...tails) { std::cout << head; if (sizeof...(tails)) std::cout << ' '; print(tails...); } template 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 std::istream& operator>>(std::istream& in, std::pair& a) { return in >> a.first >> a.second; } // tuple template std::istream& operator>>(std::istream& in, std::tuple& a) { if constexpr (N >= std::tuple_size_v>) return in; else return operator>>(in >> std::get(a), a); } // vector template std::istream& operator>>(std::istream& in, std::vector& a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } // array template std::istream& operator>>(std::istream& in, std::array& a) { for (auto it = a.begin(); it != a.end(); ++it) in >> *it; return in; } template void read(Args &...args) { (std::cin >> ... >> args); } // ! integral utilities // Returns pow(-1, n) template constexpr inline int pow_m1(T n) { return -(n & 1) | 1; } // Returns pow(-1, n) template <> constexpr inline int pow_m1(bool n) { return -int(n) | 1; } // Returns floor(x / y) template constexpr inline T fld(const T x, const T y) { return (x ^ y) >= 0 ? x / y : (x - (y + pow_m1(y >= 0))) / y; } template constexpr inline T cld(const T x, const T y) { return (x ^ y) <= 0 ? x / y : (x + (y + pow_m1(y >= 0))) / y; } template >, std::nullptr_t> = nullptr> __attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u32(x); } template , std::nullptr_t> = nullptr> __attribute__((target("popcnt"))) constexpr inline int popcount(const T x) { return _mm_popcnt_u64(x); } template >, std::nullptr_t> = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clz(x) : suisen::bit_num; } template , std::nullptr_t> = nullptr> constexpr inline int count_lz(const T x) { return x ? __builtin_clzll(x) : suisen::bit_num; } template >, std::nullptr_t> = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctz(x) : suisen::bit_num; } template , std::nullptr_t> = nullptr> constexpr inline int count_tz(const T x) { return x ? __builtin_ctzll(x) : suisen::bit_num; } template constexpr inline int floor_log2(const T x) { return suisen::bit_num - 1 - count_lz(x); } template constexpr inline int ceil_log2(const T x) { return floor_log2(x) + ((x & -x) != x); } template constexpr inline int kth_bit(const T x, const unsigned int k) { return (x >> k) & 1; } template constexpr inline int parity(const T x) { return popcount(x) & 1; } // ! container template auto priqueue_comp(const Comparator comparator) { return std::priority_queue, Comparator>(comparator); } template void sort_unique_erase(Container& a) { std::sort(a.begin(), a.end()); a.erase(std::unique(a.begin(), a.end()), a.end()); } template 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 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 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 inline bool chmax(T& x, const T& y) { return y <= x ? false : (x = y, true); } template , 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 , std::nullptr_t> = nullptr> std::vector digits_low_to_high(T val, T base = 10) { std::vector res; for (; val; val /= base) res.push_back(val % base); if (res.empty()) res.push_back(T{ 0 }); return res; } template , std::nullptr_t> = nullptr> std::vector 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 std::string join(const std::vector& 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 auto transform_to_vector(const Func &f, const Seq &s) { std::vector> v; v.reserve(std::size(s)), std::transform(std::begin(s), std::end(s), std::back_inserter(v), f); return v; } template auto copy_to_vector(const Seq &s) { std::vector v; v.reserve(std::size(s)), std::copy(std::begin(s), std::end(s), std::back_inserter(v)); return v; } template 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 std::vector split(const Seq s, typename Seq::value_type delim) { std::vector 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 digit_str_to_ints(const std::string &s) { return transform_to_vector(digit_to_int, s); } std::vector lowercase_str_to_ints(const std::string &s) { return transform_to_vector(lowercase_to_int, s); } std::vector 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 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 namespace suisen { template struct static_pow_mods { static_pow_mods() {} static_pow_mods(int n) { ensure(n); } const mint& operator[](int i) const { ensure(i); return pows[i]; } static void ensure(int n) { int sz = pows.size(); if (sz > n) return; pows.resize(n + 1); for (int i = sz; i <= n; ++i) pows[i] = base * pows[i - 1]; } private: static inline std::vector pows { 1 }; static inline mint base = base_as_int; static constexpr int mod = mint::mod(); }; template struct pow_mods { pow_mods() {} pow_mods(mint base, int n) : base(base) { ensure(n); } const mint& operator[](int i) const { ensure(i); return pows[i]; } void ensure(int n) const { int sz = pows.size(); if (sz > n) return; pows.resize(n + 1); for (int i = sz; i <= n; ++i) pows[i] = base * pows[i - 1]; } private: mutable std::vector pows { 1 }; mint base; static constexpr int mod = mint::mod(); }; } int main() { int n; string s_; int q; read(n, s_, q); const int m = 1 << n; vector s(m); REP(i, m) { s[i] = s_[i] - '0'; } const mint inv11 = mint(11).inv(); pow_mods pow_2(2, m); pow_mods pow_inv11(inv11, m); pow_mods pow_11(11, m); pow_mods pow_2_inv11(2 * inv11, m); auto merge = [&](pair l, pair r) -> pair { auto [ll, sl] = l; auto [lr, sr] = r; return { ll + lr, sl * pow_11[lr] + sr * pow_2[ll] }; }; vector> seg(2 * m); REP(i, m) { seg[m + i] = { { 0, s[i] } }; } auto set = [&](int i, mint v) { s[i] = v; i += m; seg[i].clear(); while (i >>= 1) { seg[i].clear(); } }; auto query = [&](auto rec, int k, int ql, int qr, int tl, int tr, int x, int bit) -> pair { if (ql >= tr or qr <= tl) return { 0, 0 }; if (ql <= tl and tr <= qr) { if (auto it = seg[k].find(x); it != seg[k].end()) { return { tr - tl, it->second }; } if (tr - tl == 1) { return { 1, s[k - m] }; } } pair ans; int tm = (tl + tr) >> 1; if (kth_bit(x, bit - 1) == 0) { auto l = rec(rec, 2 * k + 0, ql, qr, tl, tm, x, bit - 1); auto r = rec(rec, 2 * k + 1, ql, qr, tm, tr, x, bit - 1); ans = merge(l, r); } else { x ^= 1 << (bit - 1); auto l = rec(rec, 2 * k + 1, ql, qr, tl, tm, x, bit - 1); auto r = rec(rec, 2 * k + 0, ql, qr, tm, tr, x, bit - 1); ans = merge(l, r); } if (ql <= tl and tr <= qr) { seg[k][x] = ans.second; } return ans; }; LOOP(q) { int qt; read(qt); if (qt == 1) { int x, y; read(x, y); set(x, y); } else { int l, r, x; read(l, r, x); ++r; mint ans = query(query, 1, l, r, 0, m, x, n).second; print(ans); } } return 0; }