結果
| 問題 | No.2874 Gunegune Tree |
| ユーザー |
 fuppy_kyopro
|
| 提出日時 | 2024-09-06 21:56:40 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 16 ms / 2,000 ms |
| コード長 | 30,490 bytes |
| コンパイル時間 | 3,586 ms |
| コンパイル使用メモリ | 234,144 KB |
| 最終ジャッジ日時 | 2025-02-24 04:19:11 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 30 |
ソースコード
/*#pragma GCC target("avx2")#pragma GCC optimize("O3")#pragma GCC optimize("unroll-loops")//*/// #include <atcoder/all>// #include <atcoder/segtree>#include <bits/stdc++.h>using namespace std;// using namespace atcoder;// #define _GLIBCXX_DEBUG#define DEBUG(x) cerr << #x << ": " << x << endl;#define DEBUG_VEC(v) \cerr << #v << ":"; \for (int iiiiiiii = 0; iiiiiiii < v.size(); iiiiiiii++) \cerr << " " << v[iiiiiiii]; \cerr << endl;#define DEBUG_MAT(v) \cerr << #v << endl; \for (int iv = 0; iv < v.size(); iv++) { \for (int jv = 0; jv < v[iv].size(); jv++) { \cerr << v[iv][jv] << " "; \} \cerr << endl; \}typedef long long ll;// #define int ll#define vi vector<int>#define vl vector<ll>#define vii vector<vector<int>>#define vll vector<vector<ll>>#define pii pair<int, int>#define pis pair<int, string>#define psi pair<string, int>#define pll pair<ll, ll>template <class S, class T>pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) {return pair<S, T>(s.first + t.first, s.second + t.second);}template <class S, class T>pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }template <class S, class T>ostream &operator<<(ostream &os, pair<S, T> p) {os << "(" << p.first << ", " << p.second << ")";return os;}#define rep(i, n) for (int i = 0; i < (int)(n); i++)#define rep1(i, n) for (int i = 1; i <= (int)(n); i++)#define rrep(i, n) for (int i = (int)(n) - 1; i >= 0; i--)#define rrep1(i, n) for (int i = (int)(n); i > 0; i--)#define REP(i, a, b) for (int i = a; i < b; i++)#define in(x, a, b) (a <= x && x < b)#define all(c) c.begin(), c.end()void YES(bool t = true) {cout << (t ? "YES" : "NO") << endl;}void Yes(bool t = true) { cout << (t ? "Yes" : "No") << endl; }void yes(bool t = true) { cout << (t ? "yes" : "no") << endl; }void NO(bool t = true) { cout << (t ? "NO" : "YES") << endl; }void No(bool t = true) { cout << (t ? "No" : "Yes") << endl; }void no(bool t = true) { cout << (t ? "no" : "yes") << endl; }template <class T>bool chmax(T &a, const T &b) {if (a < b) {a = b;return 1;}return 0;}template <class T>bool chmin(T &a, const T &b) {if (a > b) {a = b;return 1;}return 0;}template <class T, class U>T ceil_div(T a, U b) {return (a + b - 1) / b;}template <class T>T safe_mul(T a, T b) {if (a == 0 || b == 0) return 0;if (numeric_limits<T>::max() / a < b) return numeric_limits<T>::max();return a * b;}#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());const ll inf = 1000000001;const ll INF = (ll)1e18 + 1;const long double pi = 3.1415926535897932384626433832795028841971L;int popcount(ll t) { return __builtin_popcountll(t); }vector<int> gen_perm(int n) {vector<int> ret(n);iota(all(ret), 0);return ret;}// int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1};// int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };vi dx = {0, 0, -1, 1}, dy = {-1, 1, 0, 0};vi dx2 = {1, 1, 0, -1, -1, -1, 0, 1}, dy2 = {0, 1, 1, 1, 0, -1, -1, -1};struct Setup_io {Setup_io() {ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);cout << fixed << setprecision(25);cerr << fixed << setprecision(25);}} setup_io;// constexpr ll MOD = 1000000007;constexpr ll MOD = 998244353;// #define mp make_pairtemplate <uint32_t mod>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(mod < (1 << 30), "invalid, mod >= 2 ^ 30");static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");static_assert(r * mod == 1, "this code has bugs.");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 operator+() const { return 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 {int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;while (y > 0) {t = x / y;x -= t * y, u -= t * v;tmp = x, x = y, y = tmp;tmp = u, u = v, v = tmp;}return mint{u};}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<mod>(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 <typename mint>struct NTT {static constexpr uint32_t get_pr() {uint32_t _mod = mint::get_mod();using u64 = uint64_t;u64 ds[32] = {};int idx = 0;u64 m = _mod - 1;for (u64 i = 2; i * i <= m; ++i) {if (m % i == 0) {ds[idx++] = i;while (m % i == 0)m /= i;}}if (m != 1) ds[idx++] = m;uint32_t _pr = 2;while (1) {int flg = 1;for (int i = 0; i < idx; ++i) {u64 a = _pr, b = (_mod - 1) / ds[i], r = 1;while (b) {if (b & 1) r = r * a % _mod;a = a * a % _mod;b >>= 1;}if (r == 1) {flg = 0;break;}}if (flg == 1) break;++_pr;}return _pr;};static constexpr uint32_t mod = mint::get_mod();static constexpr uint32_t pr = get_pr();static constexpr int level = __builtin_ctzll(mod - 1);mint dw[level], dy[level];void setwy(int k) {mint w[level], y[level];w[k - 1] = mint(pr).pow((mod - 1) / (1 << k));y[k - 1] = w[k - 1].inverse();for (int i = k - 2; i > 0; --i)w[i] = w[i + 1] * w[i + 1], y[i] = y[i + 1] * y[i + 1];dw[1] = w[1], dy[1] = y[1], dw[2] = w[2], dy[2] = y[2];for (int i = 3; i < k; ++i) {dw[i] = dw[i - 1] * y[i - 2] * w[i];dy[i] = dy[i - 1] * w[i - 2] * y[i];}}NTT() { setwy(level); }void fft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}if (k & 1) {int v = 1 << (k - 1);for (int j = 0; j < v; ++j) {mint ajv = a[j + v];a[j + v] = a[j] - ajv;a[j] += ajv;}}int u = 1 << (2 + (k & 1));int v = 1 << (k - 2 - (k & 1));mint one = mint(1);mint imag = dw[1];while (v) {// jh = 0{int j0 = 0;int j1 = v;int j2 = j1 + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j1] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j3] = t0m2 - t1m3;}}// jh >= 1mint ww = one, xx = one * dw[2], wx = one;for (int jh = 4; jh < u;) {ww = xx * xx, wx = ww * xx;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v] * xx, t2 = a[j2] * ww,t3 = a[j2 + v] * wx;mint t0p2 = t0 + t2, t1p3 = t1 + t3;mint t0m2 = t0 - t2, t1m3 = (t1 - t3) * imag;a[j0] = t0p2 + t1p3, a[j0 + v] = t0p2 - t1p3;a[j2] = t0m2 + t1m3, a[j2 + v] = t0m2 - t1m3;}xx *= dw[__builtin_ctzll((jh += 4))];}u <<= 2;v >>= 2;}}void ifft4(vector<mint> &a, int k) {if ((int)a.size() <= 1) return;if (k == 1) {mint a1 = a[1];a[1] = a[0] - a[1];a[0] = a[0] + a1;return;}int u = 1 << (k - 2);int v = 1;mint one = mint(1);mint imag = dy[1];while (u) {// jh = 0{int j0 = 0;int j1 = v;int j2 = v + v;int j3 = j2 + v;for (; j0 < v; ++j0, ++j1, ++j2, ++j3) {mint t0 = a[j0], t1 = a[j1], t2 = a[j2], t3 = a[j3];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = t0 - t1, t2m3 = (t2 - t3) * imag;a[j0] = t0p1 + t2p3, a[j2] = t0p1 - t2p3;a[j1] = t0m1 + t2m3, a[j3] = t0m1 - t2m3;}}// jh >= 1mint ww = one, xx = one * dy[2], yy = one;u <<= 2;for (int jh = 4; jh < u;) {ww = xx * xx, yy = xx * imag;int j0 = jh * v;int je = j0 + v;int j2 = je + v;for (; j0 < je; ++j0, ++j2) {mint t0 = a[j0], t1 = a[j0 + v], t2 = a[j2], t3 = a[j2 + v];mint t0p1 = t0 + t1, t2p3 = t2 + t3;mint t0m1 = (t0 - t1) * xx, t2m3 = (t2 - t3) * yy;a[j0] = t0p1 + t2p3, a[j2] = (t0p1 - t2p3) * ww;a[j0 + v] = t0m1 + t2m3, a[j2 + v] = (t0m1 - t2m3) * ww;}xx *= dy[__builtin_ctzll(jh += 4)];}u >>= 4;v <<= 2;}if (k & 1) {u = 1 << (k - 1);for (int j = 0; j < u; ++j) {mint ajv = a[j] - a[j + u];a[j] += a[j + u];a[j + u] = ajv;}}}void ntt(vector<mint> &a) {if ((int)a.size() <= 1) return;fft4(a, __builtin_ctz(a.size()));}void intt(vector<mint> &a) {if ((int)a.size() <= 1) return;ifft4(a, __builtin_ctz(a.size()));mint iv = mint(a.size()).inverse();for (auto &x : a)x *= iv;}vector<mint> multiply(const vector<mint> &a, const vector<mint> &b) {int l = a.size() + b.size() - 1;if (min<int>(a.size(), b.size()) <= 40) {vector<mint> s(l);for (int i = 0; i < (int)a.size(); ++i)for (int j = 0; j < (int)b.size(); ++j)s[i + j] += a[i] * b[j];return s;}int k = 2, M = 4;while (M < l)M <<= 1, ++k;setwy(k);vector<mint> s(M);for (int i = 0; i < (int)a.size(); ++i)s[i] = a[i];fft4(s, k);if (a.size() == b.size() && a == b) {for (int i = 0; i < M; ++i)s[i] *= s[i];} else {vector<mint> t(M);for (int i = 0; i < (int)b.size(); ++i)t[i] = b[i];fft4(t, k);for (int i = 0; i < M; ++i)s[i] *= t[i];}ifft4(s, k);s.resize(l);mint invm = mint(M).inverse();for (int i = 0; i < l; ++i)s[i] *= invm;return s;}void ntt_doubling(vector<mint> &a) {int M = (int)a.size();auto b = a;intt(b);mint r = 1, zeta = mint(pr).pow((mint::get_mod() - 1) / (M << 1));for (int i = 0; i < M; i++)b[i] *= r, r *= zeta;ntt(b);copy(begin(b), end(b), back_inserter(a));}};template <typename mint>struct FormalPowerSeries : vector<mint> {using vector<mint>::vector;using FPS = FormalPowerSeries;FPS &operator+=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++)(*this)[i] += r[i];return *this;}FPS &operator+=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] += r;return *this;}FPS &operator-=(const FPS &r) {if (r.size() > this->size()) this->resize(r.size());for (int i = 0; i < (int)r.size(); i++)(*this)[i] -= r[i];return *this;}FPS &operator-=(const mint &r) {if (this->empty()) this->resize(1);(*this)[0] -= r;return *this;}FPS &operator*=(const mint &v) {for (int k = 0; k < (int)this->size(); k++)(*this)[k] *= v;return *this;}FPS &operator/=(const FPS &r) {if (this->size() < r.size()) {this->clear();return *this;}int n = this->size() - r.size() + 1;if ((int)r.size() <= 64) {FPS f(*this), g(r);g.shrink();mint coeff = g.back().inverse();for (auto &x : g)x *= coeff;int deg = (int)f.size() - (int)g.size() + 1;int gs = g.size();FPS quo(deg);for (int i = deg - 1; i >= 0; i--) {quo[i] = f[i + gs - 1];for (int j = 0; j < gs; j++)f[i + j] -= quo[i] * g[j];}*this = quo * coeff;this->resize(n, mint(0));return *this;}return *this = ((*this).rev().pre(n) * r.rev().inv(n)).pre(n).rev();}FPS &operator%=(const FPS &r) {*this -= *this / r * r;shrink();return *this;}FPS operator+(const FPS &r) const { return FPS(*this) += r; }FPS operator+(const mint &v) const { return FPS(*this) += v; }FPS operator-(const FPS &r) const { return FPS(*this) -= r; }FPS operator-(const mint &v) const { return FPS(*this) -= v; }FPS operator*(const FPS &r) const { return FPS(*this) *= r; }FPS operator*(const mint &v) const { return FPS(*this) *= v; }FPS operator/(const FPS &r) const { return FPS(*this) /= r; }FPS operator%(const FPS &r) const { return FPS(*this) %= r; }FPS operator-() const {FPS ret(this->size());for (int i = 0; i < (int)this->size(); i++)ret[i] = -(*this)[i];return ret;}void shrink() {while (this->size() && this->back() == mint(0))this->pop_back();}FPS rev() const {FPS ret(*this);reverse(begin(ret), end(ret));return ret;}FPS dot(FPS r) const {FPS ret(min(this->size(), r.size()));for (int i = 0; i < (int)ret.size(); i++)ret[i] = (*this)[i] * r[i];return ret;}// 前 sz 項を取ってくる。sz に足りない項は 0 埋めするFPS pre(int sz) const {FPS ret(begin(*this), begin(*this) + min((int)this->size(), sz));if ((int)ret.size() < sz) ret.resize(sz);return ret;}FPS operator>>(int sz) const {if ((int)this->size() <= sz) return {};FPS ret(*this);ret.erase(ret.begin(), ret.begin() + sz);return ret;}FPS operator<<(int sz) const {FPS ret(*this);ret.insert(ret.begin(), sz, mint(0));return ret;}FPS diff() const {const int n = (int)this->size();FPS ret(max(0, n - 1));mint one(1), coeff(1);for (int i = 1; i < n; i++) {ret[i - 1] = (*this)[i] * coeff;coeff += one;}return ret;}FPS integral() const {const int n = (int)this->size();FPS ret(n + 1);ret[0] = mint(0);if (n > 0) ret[1] = mint(1);auto mod = mint::get_mod();for (int i = 2; i <= n; i++)ret[i] = (-ret[mod % i]) * (mod / i);for (int i = 0; i < n; i++)ret[i + 1] *= (*this)[i];return ret;}mint eval(mint x) const {mint r = 0, w = 1;for (auto &v : *this)r += w * v, w *= x;return r;}FPS log(int deg = -1) const {assert(!(*this).empty() && (*this)[0] == mint(1));if (deg == -1) deg = (int)this->size();return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}FPS pow(int64_t k, int deg = -1) const {const int n = (int)this->size();if (deg == -1) deg = n;if (k == 0) {FPS ret(deg);if (deg) ret[0] = 1;return ret;}for (int i = 0; i < n; i++) {if ((*this)[i] != mint(0)) {mint rev = mint(1) / (*this)[i];FPS ret = (((*this * rev) >> i).log(deg) * k).exp(deg);ret *= (*this)[i].pow(k);ret = (ret << (i * k)).pre(deg);if ((int)ret.size() < deg) ret.resize(deg, mint(0));return ret;}if (__int128_t(i + 1) * k >= deg) return FPS(deg, mint(0));}return FPS(deg, mint(0));}static void *ntt_ptr;static void set_fft();FPS &operator*=(const FPS &r);void ntt();void intt();void ntt_doubling();static int ntt_pr();FPS inv(int deg = -1) const;FPS exp(int deg = -1) const;};template <typename mint>void *FormalPowerSeries<mint>::ntt_ptr = nullptr;template <typename mint>void FormalPowerSeries<mint>::set_fft() {if (!ntt_ptr) ntt_ptr = new NTT<mint>;}template <typename mint>FormalPowerSeries<mint> &FormalPowerSeries<mint>::operator*=(const FormalPowerSeries<mint> &r) {if (this->empty() || r.empty()) {this->clear();return *this;}set_fft();auto ret = static_cast<NTT<mint> *>(ntt_ptr)->multiply(*this, r);return *this = FormalPowerSeries<mint>(ret.begin(), ret.end());}template <typename mint>void FormalPowerSeries<mint>::ntt() {set_fft();static_cast<NTT<mint> *>(ntt_ptr)->ntt(*this);}template <typename mint>void FormalPowerSeries<mint>::intt() {set_fft();static_cast<NTT<mint> *>(ntt_ptr)->intt(*this);}template <typename mint>void FormalPowerSeries<mint>::ntt_doubling() {set_fft();static_cast<NTT<mint> *>(ntt_ptr)->ntt_doubling(*this);}template <typename mint>int FormalPowerSeries<mint>::ntt_pr() {set_fft();return static_cast<NTT<mint> *>(ntt_ptr)->pr;}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::inv(int deg) const {assert((*this)[0] != mint(0));if (deg == -1) deg = (int)this->size();FormalPowerSeries<mint> res(deg);res[0] = {mint(1) / (*this)[0]};for (int d = 1; d < deg; d <<= 1) {FormalPowerSeries<mint> f(2 * d), g(2 * d);for (int j = 0; j < min((int)this->size(), 2 * d); j++)f[j] = (*this)[j];for (int j = 0; j < d; j++)g[j] = res[j];f.ntt();g.ntt();for (int j = 0; j < 2 * d; j++)f[j] *= g[j];f.intt();for (int j = 0; j < d; j++)f[j] = 0;f.ntt();for (int j = 0; j < 2 * d; j++)f[j] *= g[j];f.intt();for (int j = d; j < min(2 * d, deg); j++)res[j] = -f[j];}return res.pre(deg);}template <typename mint>FormalPowerSeries<mint> FormalPowerSeries<mint>::exp(int deg) const {using fps = FormalPowerSeries<mint>;assert((*this).size() == 0 || (*this)[0] == mint(0));if (deg == -1) deg = this->size();fps inv;inv.reserve(deg + 1);inv.push_back(mint(0));inv.push_back(mint(1));auto inplace_integral = [&](fps &F) -> void {const int n = (int)F.size();auto mod = mint::get_mod();while ((int)inv.size() <= n) {int i = inv.size();inv.push_back((-inv[mod % i]) * (mod / i));}F.insert(begin(F), mint(0));for (int i = 1; i <= n; i++)F[i] *= inv[i];};auto inplace_diff = [](fps &F) -> void {if (F.empty()) return;F.erase(begin(F));mint coeff = 1, one = 1;for (int i = 0; i < (int)F.size(); i++) {F[i] *= coeff;coeff += one;}};fps b{1, 1 < (int)this->size() ? (*this)[1] : 0}, c{1}, z1, z2{1, 1};for (int m = 2; m < deg; m *= 2) {auto y = b;y.resize(2 * m);y.ntt();z1 = z2;fps z(m);for (int i = 0; i < m; ++i)z[i] = y[i] * z1[i];z.intt();fill(begin(z), begin(z) + m / 2, mint(0));z.ntt();for (int i = 0; i < m; ++i)z[i] *= -z1[i];z.intt();c.insert(end(c), begin(z) + m / 2, end(z));z2 = c;z2.resize(2 * m);z2.ntt();fps x(begin(*this), begin(*this) + min<int>(this->size(), m));x.resize(m);inplace_diff(x);x.push_back(mint(0));x.ntt();for (int i = 0; i < m; ++i)x[i] *= y[i];x.intt();x -= b.diff();x.resize(2 * m);for (int i = 0; i < m - 1; ++i)x[m + i] = x[i], x[i] = mint(0);x.ntt();for (int i = 0; i < 2 * m; ++i)x[i] *= z2[i];x.intt();x.pop_back();inplace_integral(x);for (int i = m; i < min<int>(this->size(), 2 * m); ++i)x[i] += (*this)[i];fill(begin(x), begin(x) + m, mint(0));x.ntt();for (int i = 0; i < 2 * m; ++i)x[i] *= y[i];x.intt();b.insert(end(b), begin(x) + m, end(x));}return fps{begin(b), begin(b) + deg};}template <typename mint>mint LinearRecurrence(long long k, FormalPowerSeries<mint> Q,FormalPowerSeries<mint> P) {Q.shrink();mint ret = 0;if (P.size() >= Q.size()) {auto R = P / Q;P -= R * Q;P.shrink();if (k < (int)R.size()) ret += R[k];}if ((int)P.size() == 0) return ret;FormalPowerSeries<mint>::set_fft();if (FormalPowerSeries<mint>::ntt_ptr == nullptr) {P.resize((int)Q.size() - 1);while (k) {auto Q2 = Q;for (int i = 1; i < (int)Q2.size(); i += 2)Q2[i] = -Q2[i];auto S = P * Q2;auto T = Q * Q2;if (k & 1) {for (int i = 1; i < (int)S.size(); i += 2)P[i >> 1] = S[i];for (int i = 0; i < (int)T.size(); i += 2)Q[i >> 1] = T[i];} else {for (int i = 0; i < (int)S.size(); i += 2)P[i >> 1] = S[i];for (int i = 0; i < (int)T.size(); i += 2)Q[i >> 1] = T[i];}k >>= 1;}return ret + P[0];} else {int N = 1;while (N < (int)Q.size())N <<= 1;P.resize(2 * N);Q.resize(2 * N);P.ntt();Q.ntt();vector<mint> S(2 * N), T(2 * N);vector<int> btr(N);for (int i = 0, logn = __builtin_ctz(N); i < (1 << logn); i++) {btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (logn - 1));}mint dw = mint(FormalPowerSeries<mint>::ntt_pr()).inverse().pow((mint::get_mod() - 1) / (2 * N));while (k) {mint inv2 = mint(2).inverse();// even degree of Q(x)Q(-x)T.resize(N);for (int i = 0; i < N; i++)T[i] = Q[(i << 1) | 0] * Q[(i << 1) | 1];S.resize(N);if (k & 1) {// odd degree of P(x)Q(-x)for (auto &i : btr) {S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] -P[(i << 1) | 1] * Q[(i << 1) | 0]) *inv2;inv2 *= dw;}} else {// even degree of P(x)Q(-x)for (int i = 0; i < N; i++) {S[i] = (P[(i << 1) | 0] * Q[(i << 1) | 1] +P[(i << 1) | 1] * Q[(i << 1) | 0]) *inv2;}}swap(P, S);swap(Q, T);k >>= 1;if (k < N) break;P.ntt_doubling();Q.ntt_doubling();}P.intt();Q.intt();return ret + (P * (Q.inv()))[k];}}template <typename mint>mint kitamasa(long long N, FormalPowerSeries<mint> Q,FormalPowerSeries<mint> a) {assert(!Q.empty() && Q[0] != 0);if (N < (int)a.size()) return a[N];assert((int)a.size() >= int(Q.size()) - 1);auto P = a.pre((int)Q.size() - 1) * Q;P.resize(Q.size() - 1);return LinearRecurrence<mint>(N, Q, P);}template <typename mint>vector<mint> BerlekampMassey(const vector<mint> &s) {const int N = (int)s.size();vector<mint> b, c;b.reserve(N + 1);c.reserve(N + 1);b.push_back(mint(1));c.push_back(mint(1));mint y = mint(1);for (int ed = 1; ed <= N; ed++) {int l = int(c.size()), m = int(b.size());mint x = 0;for (int i = 0; i < l; i++)x += c[i] * s[ed - l + i];b.emplace_back(mint(0));m++;if (x == mint(0)) continue;mint freq = x / y;if (l < m) {auto tmp = c;c.insert(begin(c), m - l, mint(0));for (int i = 0; i < m; i++)c[m - 1 - i] -= freq * b[m - 1 - i];b = tmp;y = x;} else {for (int i = 0; i < m; i++)c[l - 1 - i] -= freq * b[m - 1 - i];}}reverse(begin(c), end(c));return c;}template <typename mint>mint nth_term(long long n, const vector<mint> &s) {// https://nyaannyaan.github.io/library/fps/nth-term.hpp.html// verify: https://atcoder.jp/contests/npcapc_2024/submissions/55211058// 線形漸化式の最初の数項が与えられた時に n 番目の項を求める。具体的な漸化式は与える必要がない// k-項間線形漸化式の場合 2k 項以上の数列が必要？// Berlekamp-Massey で O(k^2) で具体的な線形漸化式を与えることができる// その後、Bostan-Mori で O(k log k log n) で n 番目の項を求めることができるusing fps = FormalPowerSeries<mint>;auto bm = BerlekampMassey<mint>(s);return kitamasa(n, fps{begin(bm), end(bm)}, fps{begin(s), end(s)});}using mint = LazyMontgomeryModInt<998244353>;signed main() {int n;cin >> n;int K = 100;vector dp(K + 1, vector(K + 1, vector(3, mint(0))));dp[1][0][0] = mint(2) / 5;dp[1][1][1] = mint(2) / 5;dp[1][1][2] = mint(1) / 5;for (int i = 1; i < K; i++) {rep(j, K + 1) {rep(b, 3) {mint val = dp[i][j][b];if (val == 0) continue;if (b == 0) {dp[i + 1][j][0] += val / mint(2);dp[i + 1][j + 1][1] += val / mint(2);} else if (b == 1) {mint p = mint(1) / 3;dp[i + 1][j][0] += val * p;dp[i + 1][j + 1][1] += val * p;dp[i + 1][j + 1][2] += val * p;} else {mint p = mint(1) / 3;dp[i + 1][j + 1][2] += val * p;dp[i + 1][j + 1][1] += val * p * 2;}}}}vector<mint> ans;for (int i = 1; i <= K; i++) {mint ex = 0;rep(j, K + 1) {rep(l, 3) {ex += dp[i][j][l] * j;}}ans.push_back(ex);}cout << nth_term(n - 1, ans) << endl;}