結果
問題 | No.2995 The Ruler Sequence Concatenation |
ユーザー |
👑 |
提出日時 | 2024-12-21 00:11:23 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 15 ms / 1,000 ms |
コード長 | 31,451 bytes |
コンパイル時間 | 4,501 ms |
コンパイル使用メモリ | 279,356 KB |
実行使用メモリ | 6,816 KB |
最終ジャッジ日時 | 2024-12-21 00:11:29 |
合計ジャッジ時間 | 4,943 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 9 |
ソースコード
// #pragma GCC target("avx2")// #pragma GCC optimize("O3")// #pragma GCC optimize("unroll-loops")// #define INTERACTIVE#include <bits/stdc++.h>using namespace std;namespace templates {// typeusing ll = long long;using ull = unsigned long long;using Pii = pair<int, int>;using Pil = pair<int, ll>;using Pli = pair<ll, int>;using Pll = pair<ll, ll>;template <class T>using pq = priority_queue<T>;template <class T>using qp = priority_queue<T, vector<T>, greater<T>>;// clang-format off#define vec(T, A, ...) vector<T> A(__VA_ARGS__);#define vvec(T, A, h, ...) vector<vector<T>> A(h, vector<T>(__VA_ARGS__));#define vvvec(T, A, h1, h2, ...) vector<vector<vector<T>>> A(h1, vector<vector<T>>(h2, vector<T>(__VA_ARGS__)));// clang-format on// for loop#define fori1(a) for (ll _ = 0; _ < (a); _++)#define fori2(i, a) for (ll i = 0; i < (a); i++)#define fori3(i, a, b) for (ll i = (a); i < (b); i++)#define fori4(i, a, b, c) for (ll i = (a); ((c) > 0 || i > (b)) && ((c) < 0 || i < (b)); i += (c))#define overload4(a, b, c, d, e, ...) e#define fori(...) overload4(__VA_ARGS__, fori4, fori3, fori2, fori1)(__VA_ARGS__)// declare and input// clang-format off#define INT(...) int __VA_ARGS__; inp(__VA_ARGS__);#define LL(...) ll __VA_ARGS__; inp(__VA_ARGS__);#define STRING(...) string __VA_ARGS__; inp(__VA_ARGS__);#define CHAR(...) char __VA_ARGS__; inp(__VA_ARGS__);#define DOUBLE(...) double __VA_ARGS__; STRING(str___); __VA_ARGS__ = stod(str___);#define VEC(T, A, n) vector<T> A(n); inp(A);#define VVEC(T, A, n, m) vector<vector<T>> A(n, vector<T>(m)); inp(A);// clang-format on// const valueconst ll MOD1 = 1000000007;const ll MOD9 = 998244353;const double PI = acos(-1);// other macro#if !defined(RIN__LOCAL) && !defined(INTERACTIVE)#define endl "\n"#endif#define spa ' '#define len(A) ll(A.size())#define all(A) begin(A), end(A)// functionvector<char> stoc(string &S) {int n = S.size();vector<char> ret(n);for (int i = 0; i < n; i++) ret[i] = S[i];return ret;}string ctos(vector<char> &S) {int n = S.size();string ret = "";for (int i = 0; i < n; i++) ret += S[i];return ret;}template <class T>auto min(const T &a) {return *min_element(all(a));}template <class T>auto max(const T &a) {return *max_element(all(a));}template <class T, class S>auto clamp(T &a, const S &l, const S &r) {return (a > r ? r : a < l ? l : a);}template <class T, class S>inline bool chmax(T &a, const S &b) {return (a < b ? a = b, 1 : 0);}template <class T, class S>inline bool chmin(T &a, const S &b) {return (a > b ? a = b, 1 : 0);}template <class T, class S>inline bool chclamp(T &a, const S &l, const S &r) {auto b = clamp(a, l, r);return (a != b ? a = b, 1 : 0);}template <typename T>T sum(vector<T> &A) {T tot = 0;for (auto a : A) tot += a;return tot;}template <typename T>vector<T> compression(vector<T> X) {sort(all(X));X.erase(unique(all(X)), X.end());return X;}// input and outputnamespace io {// __int128_tstd::istream &operator>>(std::istream &is, __int128_t &value) {std::string str;is >> str;value = 0;int sign = 1;for (size_t i = 0; i < str.size(); i++) {if (i == 0 && str[i] == '-') {sign = -1;continue;}value = value * 10 + str[i] - '0';}value *= sign;return is;}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;}// vector<T>template <typename T>istream &operator>>(istream &is, vector<T> &A) {for (auto &a : A) is >> a;return is;}template <typename T>ostream &operator<<(ostream &os, vector<T> &A) {for (size_t i = 0; i < A.size(); i++) {os << A[i];if (i != A.size() - 1) os << ' ';}return os;}// vector<vector<T>>template <typename T>istream &operator>>(istream &is, vector<vector<T>> &A) {for (auto &a : A) is >> a;return is;}template <typename T>ostream &operator<<(ostream &os, vector<vector<T>> &A) {for (size_t i = 0; i < A.size(); i++) {os << A[i];if (i != A.size() - 1) os << endl;}return os;}// pair<S, T>template <typename S, typename T>istream &operator>>(istream &is, pair<S, T> &A) {is >> A.first >> A.second;return is;}template <typename S, typename T>ostream &operator<<(ostream &os, pair<S, T> &A) {os << A.first << ' ' << A.second;return os;}// vector<pair<S, T>>template <typename S, typename T>istream &operator>>(istream &is, vector<pair<S, T>> &A) {for (size_t i = 0; i < A.size(); i++) {is >> A[i];}return is;}template <typename S, typename T>ostream &operator<<(ostream &os, vector<pair<S, T>> &A) {for (size_t i = 0; i < A.size(); i++) {os << A[i];if (i != A.size() - 1) os << endl;}return os;}// tupletemplate <typename T, size_t N>struct TuplePrint {static ostream &print(ostream &os, const T &t) {TuplePrint<T, N - 1>::print(os, t);os << ' ' << get<N - 1>(t);return os;}};template <typename T>struct TuplePrint<T, 1> {static ostream &print(ostream &os, const T &t) {os << get<0>(t);return os;}};template <typename... Args>ostream &operator<<(ostream &os, const tuple<Args...> &t) {TuplePrint<decltype(t), sizeof...(Args)>::print(os, t);return os;}// io functionsvoid FLUSH() {cout << flush;}void print() {cout << endl;}template <class Head, class... Tail>void print(Head &&head, Tail &&...tail) {cout << head;if (sizeof...(Tail)) cout << spa;print(std::forward<Tail>(tail)...);}template <typename T, typename S>void prisep(vector<T> &A, S sep) {int n = A.size();for (int i = 0; i < n; i++) {cout << A[i];if (i != n - 1) cout << sep;}cout << endl;}template <typename T, typename S>void priend(T A, S end) {cout << A << end;}template <typename T>void prispa(T A) {priend(A, spa);}template <typename T, typename S>bool printif(bool f, T A, S B) {if (f)print(A);elseprint(B);return f;}template <class... T>void inp(T &...a) {(cin >> ... >> a);}} // namespace iousing namespace io;// read graphvector<vector<int>> read_edges(int n, int m, bool direct = false, int indexed = 1) {vector<vector<int>> edges(n, vector<int>());for (int i = 0; i < m; i++) {INT(u, v);u -= indexed;v -= indexed;edges[u].push_back(v);if (!direct) edges[v].push_back(u);}return edges;}vector<vector<int>> read_tree(int n, int indexed = 1) {return read_edges(n, n - 1, false, indexed);}template <typename T = long long>vector<vector<pair<int, T>>> read_wedges(int n, int m, bool direct = false, int indexed = 1) {vector<vector<pair<int, T>>> edges(n, vector<pair<int, T>>());for (int i = 0; i < m; i++) {INT(u, v);T w;inp(w);u -= indexed;v -= indexed;edges[u].push_back({v, w});if (!direct) edges[v].push_back({u, w});}return edges;}template <typename T = long long>vector<vector<pair<int, T>>> read_wtree(int n, int indexed = 1) {return read_wedges<T>(n, n - 1, false, indexed);}// yes / nonamespace yesno {// yesinline bool yes(bool f = true) {cout << (f ? "yes" : "no") << endl;return f;}inline bool Yes(bool f = true) {cout << (f ? "Yes" : "No") << endl;return f;}inline bool YES(bool f = true) {cout << (f ? "YES" : "NO") << endl;return f;}// noinline bool no(bool f = true) {cout << (!f ? "yes" : "no") << endl;return f;}inline bool No(bool f = true) {cout << (!f ? "Yes" : "No") << endl;return f;}inline bool NO(bool f = true) {cout << (!f ? "YES" : "NO") << endl;return f;}// possibleinline bool possible(bool f = true) {cout << (f ? "possible" : "impossible") << endl;return f;}inline bool Possible(bool f = true) {cout << (f ? "Possible" : "Impossible") << endl;return f;}inline bool POSSIBLE(bool f = true) {cout << (f ? "POSSIBLE" : "IMPOSSIBLE") << endl;return f;}// impossibleinline bool impossible(bool f = true) {cout << (!f ? "possible" : "impossible") << endl;return f;}inline bool Impossible(bool f = true) {cout << (!f ? "Possible" : "Impossible") << endl;return f;}inline bool IMPOSSIBLE(bool f = true) {cout << (!f ? "POSSIBLE" : "IMPOSSIBLE") << endl;return f;}// Alice Bobinline bool Alice(bool f = true) {cout << (f ? "Alice" : "Bob") << endl;return f;}inline bool Bob(bool f = true) {cout << (f ? "Bob" : "Alice") << endl;return f;}// Takahashi Aokiinline bool Takahashi(bool f = true) {cout << (f ? "Takahashi" : "Aoki") << endl;return f;}inline bool Aoki(bool f = true) {cout << (f ? "Aoki" : "Takahashi") << endl;return f;}} // namespace yesnousing namespace yesno;} // namespace templatesusing namespace templates;template <int MOD>struct Modint {int x;Modint() : x(0) {}Modint(int64_t y) {if (y >= 0)x = y % MOD;elsex = (y % MOD + MOD) % MOD;}Modint &operator+=(const Modint &p) {x += p.x;if (x >= MOD) x -= MOD;return *this;}Modint &operator-=(const Modint &p) {x -= p.x;if (x < 0) x += MOD;return *this;}Modint &operator*=(const Modint &p) {x = int(1LL * x * p.x % MOD);return *this;}Modint &operator/=(const Modint &p) {*this *= p.inverse();return *this;}Modint &operator%=(const Modint &p) {assert(p.x == 0);return *this;}Modint operator-() const {return Modint(-x);}Modint &operator++() {x++;if (x == MOD) x = 0;return *this;}Modint &operator--() {if (x == 0) x = MOD;x--;return *this;}Modint operator++(int) {Modint result = *this;++*this;return result;}Modint operator--(int) {Modint result = *this;--*this;return result;}friend Modint operator+(const Modint &lhs, const Modint &rhs) {return Modint(lhs) += rhs;}friend Modint operator-(const Modint &lhs, const Modint &rhs) {return Modint(lhs) -= rhs;}friend Modint operator*(const Modint &lhs, const Modint &rhs) {return Modint(lhs) *= rhs;}friend Modint operator/(const Modint &lhs, const Modint &rhs) {return Modint(lhs) /= rhs;}friend Modint operator%(const Modint &lhs, const Modint &rhs) {assert(rhs.x == 0);return Modint(lhs);}bool operator==(const Modint &p) const {return x == p.x;}bool operator!=(const Modint &p) const {return x != p.x;}bool operator<(const Modint &rhs) const {return x < rhs.x;}bool operator<=(const Modint &rhs) const {return x <= rhs.x;}bool operator>(const Modint &rhs) const {return x > rhs.x;}bool operator>=(const Modint &rhs) const {return x >= rhs.x;}Modint inverse() const {int a = x, b = MOD, u = 1, v = 0, t;while (b > 0) {t = a / b;a -= t * b;u -= t * v;std::swap(a, b);std::swap(u, v);}return Modint(u);}Modint pow(int64_t k) const {Modint ret(1);Modint y(x);while (k > 0) {if (k & 1) ret *= y;y *= y;k >>= 1;}return ret;}std::pair<int, int> to_frac(int max_n = 1000) const {int y = x;for (int i = 1; i <= max_n; i++) {if (y <= max_n) {return {y, i};} else if (MOD - y <= max_n) {return {-(MOD - y), i};}y = (y + x) % MOD;}return {-1, -1};}friend std::ostream &operator<<(std::ostream &os, const Modint &p) {return os << p.x;}friend std::istream &operator>>(std::istream &is, Modint &p) {int64_t y;is >> y;p = Modint<MOD>(y);return (is);}static int get_mod() {return MOD;}};struct Arbitrary_Modint {int x;static int MOD;static void set_mod(int mod) {MOD = mod;}Arbitrary_Modint() : x(0) {}Arbitrary_Modint(int64_t y) {if (y >= 0)x = y % MOD;elsex = (y % MOD + MOD) % MOD;}Arbitrary_Modint &operator+=(const Arbitrary_Modint &p) {x += p.x;if (x >= MOD) x -= MOD;return *this;}Arbitrary_Modint &operator-=(const Arbitrary_Modint &p) {x -= p.x;if (x < 0) x += MOD;return *this;}Arbitrary_Modint &operator*=(const Arbitrary_Modint &p) {x = int(1LL * x * p.x % MOD);return *this;}Arbitrary_Modint &operator/=(const Arbitrary_Modint &p) {*this *= p.inverse();return *this;}Arbitrary_Modint &operator%=(const Arbitrary_Modint &p) {assert(p.x == 0);return *this;}Arbitrary_Modint operator-() const {return Arbitrary_Modint(-x);}Arbitrary_Modint &operator++() {x++;if (x == MOD) x = 0;return *this;}Arbitrary_Modint &operator--() {if (x == 0) x = MOD;x--;return *this;}Arbitrary_Modint operator++(int) {Arbitrary_Modint result = *this;++*this;return result;}Arbitrary_Modint operator--(int) {Arbitrary_Modint result = *this;--*this;return result;}friend Arbitrary_Modint operator+(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {return Arbitrary_Modint(lhs) += rhs;}friend Arbitrary_Modint operator-(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {return Arbitrary_Modint(lhs) -= rhs;}friend Arbitrary_Modint operator*(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {return Arbitrary_Modint(lhs) *= rhs;}friend Arbitrary_Modint operator/(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {return Arbitrary_Modint(lhs) /= rhs;}friend Arbitrary_Modint operator%(const Arbitrary_Modint &lhs, const Arbitrary_Modint &rhs) {assert(rhs.x == 0);return Arbitrary_Modint(lhs);}bool operator==(const Arbitrary_Modint &p) const {return x == p.x;}bool operator!=(const Arbitrary_Modint &p) const {return x != p.x;}bool operator<(const Arbitrary_Modint &rhs) {return x < rhs.x;}bool operator<=(const Arbitrary_Modint &rhs) {return x <= rhs.x;}bool operator>(const Arbitrary_Modint &rhs) {return x > rhs.x;}bool operator>=(const Arbitrary_Modint &rhs) {return x >= rhs.x;}Arbitrary_Modint inverse() const {int a = x, b = MOD, u = 1, v = 0, t;while (b > 0) {t = a / b;a -= t * b;u -= t * v;std::swap(a, b);std::swap(u, v);}return Arbitrary_Modint(u);}Arbitrary_Modint pow(int64_t k) const {Arbitrary_Modint ret(1);Arbitrary_Modint y(x);while (k > 0) {if (k & 1) ret *= y;y *= y;k >>= 1;}return ret;}friend std::ostream &operator<<(std::ostream &os, const Arbitrary_Modint &p) {return os << p.x;}friend std::istream &operator>>(std::istream &is, Arbitrary_Modint &p) {int64_t y;is >> y;p = Arbitrary_Modint(y);return (is);}static int get_mod() {return MOD;}};int Arbitrary_Modint::MOD = 998244353;using modint9 = Modint<998244353>;using modint1 = Modint<1000000007>;using modint = Arbitrary_Modint;using mint = modint9;template <typename T>T modinv(T a, T MOD) {T b = MOD;T u = 1;T v = 0;while (b > 0) {T t = a / b;a -= t * b;u -= t * v;std::swap(a, b);std::swap(u, v);}if (a != 1) return -1;if (u < 0) u += MOD;return u;}template <typename T>std::vector<T> berlekampMessy(const std::vector<T> &A) {int n = A.size();std::vector<T> B(1, -1);std::vector<T> C(1, -1);T y = 1;for (int j = 1; j <= n; j++) {int l = C.size();int m = B.size();T x = 0;for (int i = 0; i < l; i++) {x += C[i] * A[j - l + i];}B.push_back(0);m++;if (x == 0) continue;T freq = x / y;if (l < m) {std::vector<T> D(m - l, T(0));D.insert(D.end(), C.begin(), C.end());for (int i = 0; i < m; i++) {D[m - 1 - i] -= freq * B[m - 1 - i];}std::swap(B, C);std::swap(C, D);y = x;} else {for (int i = 0; i < m; i++) {C[l - 1 - i] -= freq * B[m - 1 - i];}}}std::reverse(C.begin(), C.end());for (auto &c : C) c = -c;return C;}/*return x^n mod f引数: f_reversed: f(x)の係数(逆順, f_reversed[0] = 1)*/template <typename T>std::vector<T> monomial_mod_polynomial(long long n, const std::vector<T> &f_reversed) {assert(!f_reversed.empty() and f_reversed[0] == 1);int K = f_reversed.size() - 1;if (!K) return {};int D = 64 - __builtin_clzll(n);std::vector<T> ret(K, 0);ret[0] = 1;auto self_conv = [](std::vector<T> &x) -> std::vector<T> {int d = x.size();std::vector<T> ret(2 * d - 1);for (int i = 0; i < d; i++) {ret[2 * i] += x[i] * x[i];for (int j = 0; j < i; j++) ret[i + j] += 2 * x[i] * x[j];}return ret;};for (int d = D - 1; d >= 0; d--) {ret = self_conv(ret);for (int i = 2 * K - 2; i >= K; i--) {for (int j = 1; j <= K; j++) {ret[i - j] -= ret[i] * f_reversed[j];}}ret.resize(K);if ((n >> d) & 1) {std::vector<T> c(K);c[0] = -ret[K - 1] * f_reversed[K];for (int i = 1; i < K; i++) {c[i] = ret[i - 1] - ret[K - 1] * f_reversed[K - i];}ret = c;}}return ret;}template <typename T>T guess_kth_term(const std::vector<T> &A, long long k, bool debug = false) {assert(k >= 0);if (k < int(A.size())) return A[k];const auto F = berlekampMessy(A);if (debug) {std::cerr << "F.size() = " << F.size() << "\n" << std::flush;}const auto G = monomial_mod_polynomial<T>(k, F);T ret = 0;for (size_t i = 0; i < G.size(); i++) ret += G[i] * A[i];return ret;}using mint2 = Modint<998244352>;template <typename type>struct Matrix {int n, m;std::vector<std::vector<type>> A;Matrix() = default;Matrix(int n, int m) : n(n), m(m), A(n, std::vector<type>(m, 0)) {}Matrix(int n) : n(n), m(n), A(n, std::vector<type>(n, 0)) {}Matrix(std::vector<std::vector<type>> A) : n(A.size()), m(A[0].size()), A(A) {}inline const std::vector<type> &operator[](int k) const {return (A.at(k));}inline std::vector<type> &operator[](int k) {return (A.at(k));}Matrix T() {Matrix<type> B(m, n);for (int i = 0; i < m; i++)for (int j = 0; j < n; j++) {B.A[i][j] = A[j][i];}return B;}Matrix &operator=(const std::vector<std::vector<type>> &B) {n = B.size();m = B[0].size();A = B;return *this;}Matrix &operator+=(const Matrix &B) {assert(n == int(B.A.size()));assert(m == int(B.A[0].size()));for (int i = 0; i < n; i++)for (int j = 0; j < m; j++) {this->A[i][j] += B[i][j];}return *this;}Matrix &operator-=(const Matrix &B) {assert(n == int(B.A.size()));assert(m == int(B.A[0].size()));for (int i = 0; i < n; i++)for (int j = 0; j < m; j++) {this->A[i][j] -= B[i][j];}return *this;}Matrix &operator*=(const Matrix &B) {int k = B[0].size();assert(m == int(B.A.size()));std::vector<std::vector<type>> C(n, std::vector<type>(k, 0));for (int i = 0; i < n; i++)for (int j = 0; j < k; j++) {for (int l = 0; l < m; l++) {C[i][j] += this->A[i][l] * B[l][j];}}std::swap(this->A, C);this->m = k;return *this;}std::vector<type> operator*(const std::vector<type> &x) {assert(m == int(x.size()));std::vector<type> ret(n, 0);for (int i = 0; i < n; i++)for (int j = 0; j < m; j++) ret[i] += this->A[i][j] * x[j];return ret;}template <typename Ti>Matrix &operator*=(const Ti x) {for (auto &row : A) {for (auto &e : row) {e *= x;}}return *this;}Matrix operator-() {return (Matrix(*this) *= -1);}Matrix operator+(const Matrix &B) const {return (Matrix(*this) += B);}Matrix operator-(const Matrix &B) const {return (Matrix(*this) -= B);}Matrix operator*(const Matrix &B) const {return (Matrix(*this) *= B);}type det() {auto arr = A;assert(n == m);type ret = 1;for (int i = 0; i < n; i++) {if (arr[i][i] == 0) {bool ng = true;for (int j = i + 1; j < n; j++) {if (arr[j][i] == 0) continue;swap(arr[i], arr[j]);ret *= -1;ng = false;break;}if (ng) return 0;}ret *= arr[i][i];type inv = type(1) / arr[i][i];for (int j = i; j < n; j++) arr[i][j] *= inv;for (int j = i + 1; j < n; j++) {type x = arr[j][i];for (int k = i; k < n; k++) {arr[j][k] -= arr[i][k] * x;}}}return ret;}void I() {assert(n == m);for (int i = 0; i < n; i++) {for (int j = 0; j < m; j++) {if (i == j)A[i][j] = 1;elseA[i][j] = 0;}}}Matrix<type> inv() {assert(n == m);Matrix<type> ret(n);ret.I();auto &B = ret.A;auto arr = A;for (int j = 0; j < n; j++) {int ii = -1;for (int i = j; i < n; i++) {if (arr[i][j] != 0) {ii = i;break;}}if (ii == -1) {return {};}swap(arr[j], arr[ii]);swap(B[j], B[ii]);ii = j;type inv = type(1) / arr[ii][j];for (int jj = 0; jj < n; jj++) {B[ii][jj] *= inv;arr[ii][jj] *= inv;}for (int i = 0; i < n; i++) {if (i == ii) continue;type t = arr[i][j];for (int jj = 0; jj < n; jj++) {arr[i][jj] -= arr[ii][jj] * t;B[i][jj] -= B[ii][jj] * t;}}}return ret;}int choose_pivot(int h, int c) const {for (int j = h; j < n; j++) {if (A[j][c] != type(0)) return j;}return -1;}int rank() const {auto arr = *this;if (arr.n < arr.m) {arr = arr.T();}int ret = 0;for (int i = 0; i < arr.m; i++) {int j = arr.choose_pivot(ret, i);if (j == -1) continue;swap(arr[ret], arr[j]);type inv = type(1) / arr[ret][i];for (int k = i; k < arr.m; k++) {arr[ret][k] *= inv;}for (int j = ret + 1; j < arr.n; j++) {type x = arr[j][i];for (int k = i; k < arr.m; k++) {arr[j][k] -= arr[ret][k] * x;}}ret++;}return ret;}Matrix<type> pow(long long k) {assert(n == m);Matrix<type> B(n);B.I();Matrix<type> A(*this);while (k) {if (k & 1) B *= A;A *= A;k >>= 1;}return B;}friend std::ostream &operator<<(std::ostream &os, const Matrix &p) {for (int i = 0; i < p.n; i++) {for (auto &x : p.A[i]) {os << x << " ";}if (i != p.n - 1) {os << "\n";}}return (os);}friend std::istream &operator>>(std::istream &is, Matrix &p) {for (auto &row : p.A) {for (auto &x : row) {is >> x;}}return (is);}};template <typename T>Matrix<T> Matrix_exp(Matrix<T> A, Matrix<T> B, long long k) {assert(A.A.size() == A[0].size());assert(A.A.size() == B.A.size());assert(B.A[0].size() == 1u);while (k > 0) {if (k & 1) B = A * B;A *= A;k >>= 1;}return B;}template <typename T>std::vector<T> Matrix_exp(Matrix<T> A, std::vector<T> B, long long k) {assert(A.A.size() == A[0].size());assert(A.A.size() == B.size());while (k > 0) {if (k & 1) {B = A * B;}A *= A;k >>= 1;}return B;}void solve() {LL(n);if (n <= 1000) {mint now = 1;int length = 1;fori(i, 2, n + 1) {auto x = i;int le = 0;while (x) {x /= 10;le++;}mint nex = now;nex += i * mint(10).pow(length);nex += now * mint(10).pow(length + le);length = 2 * length + le;length %= 998244352;now = nex;}print(now);return;}mint now = 1;int length = 1;fori(i, 2, 1000) {auto x = i;int le = 0;while (x) {x /= 10;le++;}mint nex = now;nex += i * mint(10).pow(length);nex += now * mint(10).pow(length + le);length = 2 * length + le;length %= 998244352;now = nex;}ll x = 1000;n++;int le = 4;while (x < n) {ll y = x * 10;chmin(y, n);vec(mint, A, 500);mint2 bef_length = length;fori(i, x, x + 500) {mint nex = now;nex += i * mint(10).pow(length);nex += now * mint(10).pow(length + le);length = 2 * length + le;length %= 998244352;now = nex;A[i - x] = now;}now = guess_kth_term(A, y - x - 1, true);Matrix<mint2> B({{2, le},{0, 1},});B = B.pow(y - x);length = (B[0][0] * bef_length + B[0][1]).x;le++;x = y;}print(now);}int main() {#ifndef INTERACTIVEstd::cin.tie(0)->sync_with_stdio(0);#endif// std::cout << std::fixed << std::setprecision(12);int t;t = 1;// std::cin >> t;while (t--) solve();return 0;}// // #pragma GCC target("avx2")// // #pragma GCC optimize("O3")// // #pragma GCC optimize("unroll-loops")// // #define INTERACTIVE//// #include "kyopro-cpp/template.hpp"//// #include "misc/Modint.hpp"// using mint = modint9;// #include "polynomial/guess_kth_term.hpp"// using mint2 = Modint<998244352>;// #include "matrix/Matrix_exp.hpp"//// void solve() {// LL(n);//// if (n <= 1000) {// mint now = 1;// int length = 1;// fori(i, 2, n + 1) {// auto x = i;// int le = 0;// while (x) {// x /= 10;// le++;// }//// mint nex = now;// nex += i * mint(10).pow(length);// nex += now * mint(10).pow(length + le);// length = 2 * length + le;// length %= 998244352;//// now = nex;// }//// print(now);// return;// }//// mint now = 1;// int length = 1;// fori(i, 2, 1000) {// auto x = i;// int le = 0;// while (x) {// x /= 10;// le++;// }//// mint nex = now;// nex += i * mint(10).pow(length);// nex += now * mint(10).pow(length + le);// length = 2 * length + le;// length %= 998244352;//// now = nex;// }//// ll x = 1000;// n++;// int le = 4;// while (x < n) {// ll y = x * 10;// chmin(y, n);//// vec(mint, A, 500);// mint2 bef_length = length;// fori(i, x, x + 500) {// mint nex = now;// nex += i * mint(10).pow(length);// nex += now * mint(10).pow(length + le);// length = 2 * length + le;// length %= 998244352;//// now = nex;// A[i - x] = now;// }//// now = guess_kth_term(A, y - x - 1, true);//// Matrix<mint2> B({// {2, le},// {0, 1},// });// B = B.pow(y - x);// length = (B[0][0] * bef_length + B[0][1]).x;//// le++;// x = y;// }// print(now);// }//// int main() {// #ifndef INTERACTIVE// std::cin.tie(0)->sync_with_stdio(0);// #endif// // std::cout << std::fixed << std::setprecision(12);// int t;// t = 1;// // std::cin >> t;// while (t--) solve();// return 0;// }