#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_; #define ALL(x) (x).begin(), (x).end() #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}}; int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } #ifdef HITONANODE_LOCAL const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m"; #define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl #define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr) #else #define dbg(x) ((void)0) #define dbgif(cond, x) ((void)0) #endif template struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set fac; int v = md - 1; for (lint i = 2; i * i <= v; i++) while (v % i == 0) fac.insert(i), v /= i; if (v > 1) fac.insert(v); for (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val_; int val() const noexcept { return val_; } MDCONST ModInt() : val_(0) {} MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } MDCONST ModInt(lint v) { _setval(v % md + md); } MDCONST explicit operator bool() const { return val_ != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val_ + x.val_); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val_ - x.val_ + md); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } MDCONST ModInt operator-() const { return ModInt()._setval(md - val_); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % md + x.val_); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val_ + md); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val_ % md); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.inv().val() % md); } MDCONST bool operator==(const ModInt &x) const { return val_ == x.val_; } MDCONST bool operator!=(const ModInt &x) const { return val_ != x.val_; } MDCONST bool operator<(const ModInt &x) const { return val_ < x.val_; } // To use std::map friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val_; } MDCONST ModInt pow(lint n) const { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static std::vector facs, facinvs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } MDCONST ModInt inv() const { if (this->val_ < std::min(md >> 1, 1 << 21)) { if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0}; while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } MDCONST ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } MDCONST ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[this->val_]; } MDCONST ModInt doublefac() const { lint k = (this->val_ + 1) / 2; return (this->val_ & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv() * r.facinv(); } MDCONST ModInt nPr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val_, md - x.val_)); } }; template std::vector> ModInt::facs = {1}; template std::vector> ModInt::facinvs = {1}; template std::vector> ModInt::invs = {0}; using mint = ModInt<998244353>; struct S { mint v00, v10, v11; static S id() { return S{1, 0, 1}; } // static S mono(char c) { return S{2, c - '0', 11}; } }; S op(S l, S r) { return S{l.v00 * r.v00, r.v10 * l.v00 + r.v11 * l.v10, l.v11 * r.v11}; } // S e() { return S::id(); } // using S = mint; // Enumerate nodes of nonrecursive segtree which cover [l, r) std::vector segtree_range_covering_nodes(int N, int l, int r) { std::vector ret, ret_rev; l += N, r += N; while (l < r) { if (l & 1) ret.push_back(l++); if (r & 1) ret_rev.push_back(--r); l >>= 1, r >>= 1; } ret.insert(ret.end(), ret_rev.rbegin(), ret_rev.rend()); return ret; } int main() { int D; string str; cin >> D >> str; const int N = 1 << D; vector last_update(N * 2, -1); vector ds(N * 2, D); FOR(i, 2, ds.size()) ds.at(i) = ds.at(i / 2) - 1; vector heads{0}; for (int d : ds) { int n = heads.back() + (1 << d); heads.push_back(n); } // vector>> segtree(N * 2); vector> segtree(heads.back(), make_pair(-100, mint())); vector pow2s(20, 2), pow11s(20, 11); FOR(i, 1, pow2s.size()) pow2s.at(i) = pow2s.at(i - 1).pow(2); FOR(i, 1, pow11s.size()) pow11s.at(i) = pow11s.at(i - 1).pow(2); int Q; cin >> Q; REP(q, Q) { auto getter = [&](auto &&self, const int node, const int xor_, const int d) -> mint { if (d <= 0) return str.at((node - N) ^ xor_) - '0'; const int lenmax = 1 << d; if (segtree.at(heads.at(node) + xor_).first < last_update.at(node)) { segtree.at(heads.at(node) + xor_).first = q; mint lhs, rhs; if (xor_ >= lenmax / 2) { lhs = self(self, node * 2 + 1, xor_ - lenmax / 2, d - 1); rhs = self(self, node * 2, xor_ - lenmax / 2, d - 1); } else { lhs = self(self, node * 2, xor_, d - 1); rhs = self(self, node * 2 + 1, xor_, d - 1); } segtree.at(heads.at(node) + xor_).second = rhs * pow2s.at(d - 1) + lhs * pow11s.at(d - 1); } return segtree.at(heads.at(node) + xor_).second; }; int tp; cin >> tp; if (tp == 1) { int x; char y; cin >> x >> y; str.at(x) = y; int now = x + N; while (now) last_update.at(now) = q, now /= 2; } else { int l, r, x; cin >> l >> r >> x; ++r; S ret = S::id(); dbg(make_tuple(l, r)); for (auto p_ : segtree_range_covering_nodes(N, l, r)) { int ptgt = p_ ^ (x >> ds.at(p_)); const int d = ds.at(ptgt); ret = op(ret, S{pow2s.at(d), getter(getter, ptgt, x & ((1 << ds.at(p_)) - 1), d), pow11s.at(d)}); } cout << ret.v10 << '\n'; } } }