/** * date : 2022-12-18 21:45:24 */ #define NDEBUG using namespace std; // intrinstic #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 #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include // utility namespace Nyaan { using ll = long long; using i64 = long long; using u64 = unsigned long long; using i128 = __int128_t; using u128 = __uint128_t; template using V = vector; template using VV = vector>; using vi = vector; using vl = vector; using vd = V; using vs = V; using vvi = vector>; using vvl = vector>; template struct P : pair { template P(Args... args) : pair(args...) {} using pair::first; using pair::second; P &operator+=(const P &r) { first += r.first; second += r.second; return *this; } P &operator-=(const P &r) { first -= r.first; second -= r.second; return *this; } P &operator*=(const P &r) { first *= r.first; second *= r.second; return *this; } template P &operator*=(const S &r) { first *= r, second *= r; return *this; } P operator+(const P &r) const { return P(*this) += r; } P operator-(const P &r) const { return P(*this) -= r; } P operator*(const P &r) const { return P(*this) *= r; } template P operator*(const S &r) const { return P(*this) *= r; } P operator-() const { return P{-first, -second}; } }; using pl = P; using pi = P; using vp = V; constexpr int inf = 1001001001; constexpr long long infLL = 4004004004004004004LL; template int sz(const T &t) { return t.size(); } template inline bool amin(T &x, U y) { return (y < x) ? (x = y, true) : false; } template inline bool amax(T &x, U y) { return (x < y) ? (x = y, true) : false; } template inline T Max(const vector &v) { return *max_element(begin(v), end(v)); } template inline T Min(const vector &v) { return *min_element(begin(v), end(v)); } template inline long long Sum(const vector &v) { return accumulate(begin(v), end(v), 0LL); } template int lb(const vector &v, const T &a) { return lower_bound(begin(v), end(v), a) - begin(v); } template int ub(const vector &v, const T &a) { return upper_bound(begin(v), end(v), a) - begin(v); } constexpr long long TEN(int n) { long long ret = 1, x = 10; for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1); return ret; } template pair mkp(const T &t, const U &u) { return make_pair(t, u); } template vector mkrui(const vector &v, bool rev = false) { vector ret(v.size() + 1); if (rev) { for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1]; } else { for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i]; } return ret; }; template vector mkuni(const vector &v) { vector ret(v); sort(ret.begin(), ret.end()); ret.erase(unique(ret.begin(), ret.end()), ret.end()); return ret; } template vector mkord(int N,F f) { vector ord(N); iota(begin(ord), end(ord), 0); sort(begin(ord), end(ord), f); return ord; } template vector mkinv(vector &v) { int max_val = *max_element(begin(v), end(v)); vector inv(max_val + 1, -1); for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i; return inv; } vector mkiota(int n) { vector ret(n); iota(begin(ret), end(ret), 0); return ret; } template T mkrev(const T &v) { T w{v}; reverse(begin(w), end(w)); return w; } template bool nxp(vector &v) { return next_permutation(begin(v), end(v)); } template using minpq = priority_queue, greater>; } // namespace Nyaan // bit operation namespace Nyaan { __attribute__((target("popcnt"))) inline int popcnt(const u64 &a) { return _mm_popcnt_u64(a); } inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; } inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; } template inline int gbit(const T &a, int i) { return (a >> i) & 1; } template inline void sbit(T &a, int i, bool b) { if (gbit(a, i) != b) a ^= T(1) << i; } constexpr long long PW(int n) { return 1LL << n; } constexpr long long MSK(int n) { return (1LL << n) - 1; } } // namespace Nyaan // inout namespace Nyaan { template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const vector &v) { int s = (int)v.size(); for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i]; return os; } template istream &operator>>(istream &is, vector &v) { for (auto &x : v) is >> x; return is; } istream &operator>>(istream &is, __int128_t &x) { string S; is >> S; x = 0; int flag = 0; for (auto &c : S) { if (c == '-') { flag = true; continue; } x *= 10; x += c - '0'; } if (flag) x = -x; return is; } istream &operator>>(istream &is, __uint128_t &x) { string S; is >> S; x = 0; for (auto &c : S) { x *= 10; x += c - '0'; } return is; } ostream &operator<<(ostream &os, __int128_t x) { if (x == 0) return os << 0; if (x < 0) os << '-', x = -x; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } ostream &operator<<(ostream &os, __uint128_t x) { if (x == 0) return os << 0; string S; while (x) S.push_back('0' + x % 10), x /= 10; reverse(begin(S), end(S)); return os << S; } void in() {} template void in(T &t, U &...u) { cin >> t; in(u...); } void out() { cout << "\n"; } template void out(const T &t, const U &...u) { cout << t; if (sizeof...(u)) cout << sep; out(u...); } void outr() {} template void outr(const T &t, const U &...u) { cout << t; outr(u...); } struct IoSetupNya { IoSetupNya() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); cerr << fixed << setprecision(7); } } iosetupnya; } // namespace Nyaan // debug #ifdef NyaanDebug #define trc(...) (void(0)) #else #define trc(...) (void(0)) #endif #ifdef NyaanLocal #define trc2(...) (void(0)) #else #define trc2(...) (void(0)) #endif // macro #define each(x, v) for (auto&& x : v) #define each2(x, y, v) for (auto&& [x, y] : v) #define all(v) (v).begin(), (v).end() #define rep(i, N) for (long long i = 0; i < (long long)(N); i++) #define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--) #define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++) #define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--) #define reg(i, a, b) for (long long i = (a); i < (b); i++) #define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--) #define fi first #define se second #define ini(...) \ int __VA_ARGS__; \ in(__VA_ARGS__) #define inl(...) \ long long __VA_ARGS__; \ in(__VA_ARGS__) #define ins(...) \ string __VA_ARGS__; \ in(__VA_ARGS__) #define in2(s, t) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i]); \ } #define in3(s, t, u) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i]); \ } #define in4(s, t, u, v) \ for (int i = 0; i < (int)s.size(); i++) { \ in(s[i], t[i], u[i], v[i]); \ } #define die(...) \ do { \ Nyaan::out(__VA_ARGS__); \ return; \ } while (0) namespace Nyaan { void solve(); } int main() { Nyaan::solve(); } // namespace inner { using i64 = long long; using u64 = unsigned long long; using u128 = __uint128_t; template struct Hash : array { using array::operator[]; static constexpr int n = BASE_NUM; Hash() : array() {} static constexpr u64 md = (1ull << 61) - 1; constexpr static Hash set(const i64 &a) { Hash res; fill(begin(res), end(res), cast(a)); return res; } Hash &operator+=(const Hash &r) { for (int i = 0; i < n; i++) if (((*this)[i] += r[i]) >= md) (*this)[i] -= md; return *this; } Hash &operator+=(const i64 &r) { u64 s = cast(r); for (int i = 0; i < n; i++) if (((*this)[i] += s) >= md) (*this)[i] -= md; return *this; } Hash &operator-=(const Hash &r) { for (int i = 0; i < n; i++) if (((*this)[i] += md - r[i]) >= md) (*this)[i] -= md; return *this; } Hash &operator-=(const i64 &r) { u64 s = cast(r); for (int i = 0; i < n; i++) if (((*this)[i] += md - s) >= md) (*this)[i] -= md; return *this; } Hash &operator*=(const Hash &r) { for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], r[i]); return *this; } Hash &operator*=(const i64 &r) { u64 s = cast(r); for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], s); return *this; } Hash operator+(const Hash &r) { return Hash(*this) += r; } Hash operator+(const i64 &r) { return Hash(*this) += r; } Hash operator-(const Hash &r) { return Hash(*this) -= r; } Hash operator-(const i64 &r) { return Hash(*this) -= r; } Hash operator*(const Hash &r) { return Hash(*this) *= r; } Hash operator*(const i64 &r) { return Hash(*this) *= r; } Hash operator-() const { Hash res; for (int i = 0; i < n; i++) res[i] = (*this)[i] == 0 ? 0 : md - (*this)[i]; return res; } friend Hash pfma(const Hash &a, const Hash &b, const Hash &c) { Hash res; for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], c[i]); return res; } friend Hash pfma(const Hash &a, const Hash &b, const i64 &c) { Hash res; u64 s = cast(c); for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], s); return res; } static Hash get_basis() { static auto rand_time = chrono::duration_cast( chrono::high_resolution_clock::now().time_since_epoch()) .count(); static mt19937_64 rng(rand_time); Hash h; for (int i = 0; i < n; i++) { while (isPrimitive(h[i] = rng() % (md - 1) + 1) == false) ; } return h; } private: static u64 modpow(u64 a, u64 b) { u64 r = 1; for (a %= md; b; a = modmul(a, a), b >>= 1) r = modmul(r, a); return r; } static bool isPrimitive(u64 x) { for (auto &d : vector{2, 3, 5, 7, 11, 13, 31, 41, 61, 151, 331, 1321}) if (modpow(x, (md - 1) / d) <= 1) return false; return true; } static inline constexpr u64 cast(const long long &a) { return a < 0 ? a + md : a; } static inline constexpr u64 modmul(const u64 &a, const u64 &b) { u128 ret = u128(a) * b; ret = (ret & md) + (ret >> 61); return ret >= md ? ret - md : ret; } static inline constexpr u64 modfma(const u64 &a, const u64 &b, const u64 &c) { u128 ret = u128(a) * b + c; ret = (ret & md) + (ret >> 61); return ret >= md ? ret - md : ret; } }; } // namespace inner /** * @brief ハッシュ構造体 * @docs docs/inner/inner-hash.md */ template struct RollingHash { using Hash = inner::Hash; Str data; vector hs, pw; int s; static Hash basis; RollingHash(const Str &S = Str()) { build(S); } void build(const Str &S) { data = S; s = S.size(); hs.resize(s + 1); pw.resize(s + 1); pw[0] = Hash::set(1); hs[0] = Hash::set(0); for (int i = 1; i <= s; i++) { pw[i] = pw[i - 1] * basis; hs[i] = pfma(hs[i - 1], basis, S[i - 1]); } } Hash get(int l, int r = -1) const { if (r == -1) r = s; return pfma(hs[l], -pw[r - l], hs[r]); } static Hash get_hash(const Str &T) { Hash ret = Hash::set(0); for (int i = 0; i < (int)T.size(); i++) ret = pfma(ret, basis, T[i]); return ret; } int find(Str &T, int lower = 0) const { auto ths = get_hash(T); for (int i = lower; i <= s - (int)T.size(); i++) if (ths == get(i, i + (int)T.size())) return i; return -1; } friend int LCP(const RollingHash &a, const RollingHash &b, int al, int bl) { int ok = 0, ng = min(a.size() - al, b.size() - bl) + 1; while (ok + 1 < ng) { int med = (ok + ng) / 2; (a.get(al, med + al) == b.get(bl, med + bl) ? ok : ng) = med; } return ok; } friend int strcmp(const RollingHash &a, const RollingHash &b, int al, int bl, int ar = -1, int br = -1) { if (ar == -1) ar = a.size(); if (br == -1) br = b.size(); int n = min({LCP(a, b, al, bl), ar - al, br - bl}); return al + n == ar ? bl + n == br ? 0 : 1 : bl + n == br ? -1 : a.data[al + n] < b.data[bl + n] ? 1 : -1; } int size() const { return s; } }; template typename RollingHash::Hash RollingHash::basis = inner::Hash::get_basis(); using roriha = RollingHash; /** * @brief Rolling Hash * @docs docs/string/rolling-hash.md */ // template struct LazyMontgomeryModInt { using mint = LazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static constexpr u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static constexpr u32 r = get_r(); static constexpr u32 n2 = -u64(mod) % mod; static_assert(r * mod == 1, "invalid, r * mod != 1"); static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30"); static_assert((mod & 1) == 1, "invalid, mod % 2 == 0"); u32 a; constexpr LazyMontgomeryModInt() : a(0) {} constexpr LazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static constexpr u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } constexpr mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } constexpr mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } constexpr mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } constexpr mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } constexpr mint operator+(const mint &b) const { return mint(*this) += b; } constexpr mint operator-(const mint &b) const { return mint(*this) -= b; } constexpr mint operator*(const mint &b) const { return mint(*this) *= b; } constexpr mint operator/(const mint &b) const { return mint(*this) /= b; } constexpr bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } constexpr bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } constexpr mint operator-() const { return mint() - mint(*this); } constexpr mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } constexpr mint inverse() const { return pow(mod - 2); } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = LazyMontgomeryModInt(t); return (is); } constexpr u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static constexpr u32 get_mod() { return mod; } }; template struct Binomial { vector f, g, h; Binomial(int MAX = 0) { assert(T::get_mod() != 0 && "Binomial()"); f.resize(1, T{1}); g.resize(1, T{1}); h.resize(1, T{1}); while (MAX >= (int)f.size()) extend(); } void extend() { int n = f.size(); int m = n * 2; f.resize(m); g.resize(m); h.resize(m); for (int i = n; i < m; i++) f[i] = f[i - 1] * T(i); g[m - 1] = f[m - 1].inverse(); h[m - 1] = g[m - 1] * f[m - 2]; for (int i = m - 2; i >= n; i--) { g[i] = g[i + 1] * T(i + 1); h[i] = g[i] * f[i - 1]; } } T fac(int i) { if (i < 0) return T(0); while (i >= (int)f.size()) extend(); return f[i]; } T finv(int i) { if (i < 0) return T(0); while (i >= (int)g.size()) extend(); return g[i]; } T inv(int i) { if (i < 0) return -inv(-i); while (i >= (int)h.size()) extend(); return h[i]; } T C(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r) * finv(r); } inline T operator()(int n, int r) { return C(n, r); } template T multinomial(const vector& r) { static_assert(is_integral::value == true); int n = 0; for (auto& x : r) { if (x < 0) return T(0); n += x; } T res = fac(n); for (auto& x : r) res *= finv(x); return res; } template T operator()(const vector& r) { return multinomial(r); } T C_naive(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); T ret = T(1); r = min(r, n - r); for (int i = 1; i <= r; ++i) ret *= inv(i) * (n--); return ret; } T P(int n, int r) { if (n < 0 || n < r || r < 0) return T(0); return fac(n) * finv(n - r); } // [x^r] 1 / (1-x)^n T H(int n, int r) { if (n < 0 || r < 0) return T(0); return r == 0 ? 1 : C(n + r - 1, r); } }; // using namespace Nyaan; using mint = LazyMontgomeryModInt<998244353>; void q() { ini(N); ins(T); roriha rt{T}; // |T| - 1 文字以下の prefix/suffix int limit = sz(T) - 1; V pre(N), suf(N); V cnt(N); // auto count1 = [&](string S) -> mint { if (sz(S) < sz(T)) return 0; roriha rs{S}; mint res = 0; rep(i, sz(S) - sz(T) + 1) { if (rs.get(i, i + sz(T)) == rt.get(0)) res += 1; } return res; }; auto count2 = [&](string A, string B) -> mint { if (sz(A) + sz(B) < sz(T)) return 0; roriha rc{A + B}; mint res = 0; rep(i, min(sz(A) + sz(B) - sz(T) + 1, sz(A))) { if (rc.get(i, i + sz(T)) == rt.get(0)) res += 1; } return res; }; rep(i, N) { ins(S); if (S == "~") { ini(j, k); --j, --k; if (sz(pre[j]) < limit) { int len = min(limit - sz(pre[i]), sz(pre[k])); pre[i] = pre[j] + string{begin(pre[k]), begin(pre[k]) + len}; } else { pre[i] = pre[j]; } if (sz(suf[i]) < limit) { int len = min(limit - sz(suf[i]), sz(suf[j])); suf[i] = string{end(suf[j]) - len, end(suf[j])} + suf[k]; } else { suf[i] = suf[k]; } cnt[i] = cnt[j] + cnt[k] + count2(suf[j], pre[k]); } else { pre[i] = {begin(S), begin(S) + min(limit, sz(S))}; suf[i] = {end(S) - min(limit, sz(S)), end(S)}; cnt[i] = count1(S); } } cout << cnt.back() << endl; } void Nyaan::solve() { int t = 1; // in(t); while (t--) q(); }