結果
問題 | No.2904 Distinct Multisets in a Way |
ユーザー |
![]() |
提出日時 | 2024-09-27 20:27:16 |
言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 19 ms / 2,000 ms |
コード長 | 31,213 bytes |
コンパイル時間 | 1,615 ms |
コンパイル使用メモリ | 122,084 KB |
実行使用メモリ | 6,948 KB |
最終ジャッジ日時 | 2024-09-27 20:27:20 |
合計ジャッジ時間 | 3,228 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge5 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 42 |
ソースコード
#include <cstdio>#include <cctype>#include <cstdint>#include <string>namespace nachia{struct CInStream{private:static const unsigned int INPUT_BUF_SIZE = 1 << 17;unsigned int p = INPUT_BUF_SIZE;static char Q[INPUT_BUF_SIZE];public:using MyType = CInStream;char seekChar(){if(p == INPUT_BUF_SIZE){size_t len = fread(Q, 1, INPUT_BUF_SIZE, stdin);if(len != INPUT_BUF_SIZE) Q[len] = '\0';p = 0;}return Q[p];}void skipSpace(){ while(isspace(seekChar())) p++; }private:template<class T, int sp = 1>T nextUInt(){if constexpr (sp) skipSpace();T buf = 0;while(true){char tmp = seekChar();if('9' < tmp || tmp < '0') break;buf = buf * 10 + (tmp - '0');p++;}return buf;}public:uint32_t nextU32(){ return nextUInt<uint32_t>(); }int32_t nextI32(){skipSpace();if(seekChar() == '-'){p++; return (int32_t)(-nextUInt<uint32_t, 0>());}return (int32_t)nextUInt<uint32_t, 0>();}uint64_t nextU64(){ return nextUInt<uint64_t>();}int64_t nextI64(){skipSpace();if(seekChar() == '-'){p++; return (int64_t)(-nextUInt<int64_t, 0>());}return (int64_t)nextUInt<int64_t, 0>();}template<class T>T nextInt(){skipSpace();if(seekChar() == '-'){p++;return - nextUInt<T, 0>();}return nextUInt<T, 0>();}char nextChar(){ skipSpace(); char buf = seekChar(); p++; return buf; }std::string nextToken(){skipSpace();std::string buf;while(true){char ch = seekChar();if(isspace(ch) || ch == '\0') break;buf.push_back(ch);p++;}return buf;}MyType& operator>>(unsigned int& dest){ dest = nextU32(); return *this; }MyType& operator>>(int& dest){ dest = nextI32(); return *this; }MyType& operator>>(unsigned long& dest){ dest = nextU64(); return *this; }MyType& operator>>(long& dest){ dest = nextI64(); return *this; }MyType& operator>>(unsigned long long& dest){ dest = nextU64(); return *this; }MyType& operator>>(long long& dest){ dest = nextI64(); return *this; }MyType& operator>>(std::string& dest){ dest = nextToken(); return *this; }MyType& operator>>(char& dest){ dest = nextChar(); return *this; }} cin;struct FastOutputTable{char LZ[1000][4] = {};char NLZ[1000][4] = {};constexpr FastOutputTable(){using u32 = uint_fast32_t;for(u32 d=0; d<1000; d++){LZ[d][0] = ('0' + d / 100 % 10);LZ[d][1] = ('0' + d / 10 % 10);LZ[d][2] = ('0' + d / 1 % 10);LZ[d][3] = '\0';}for(u32 d=0; d<1000; d++){u32 i = 0;if(d >= 100) NLZ[d][i++] = ('0' + d / 100 % 10);if(d >= 10) NLZ[d][i++] = ('0' + d / 10 % 10);if(d >= 1) NLZ[d][i++] = ('0' + d / 1 % 10);NLZ[d][i++] = '\0';}}};struct COutStream{private:using u32 = uint32_t;using u64 = uint64_t;using MyType = COutStream;static const u32 OUTPUT_BUF_SIZE = 1 << 17;static char Q[OUTPUT_BUF_SIZE];static constexpr FastOutputTable TB = FastOutputTable();u32 p = 0;static constexpr u32 P10(u32 d){ return d ? P10(d-1)*10 : 1; }static constexpr u64 P10L(u32 d){ return d ? P10L(d-1)*10 : 1; }template<class T, class U> static void Fil(T& m, U& l, U x){ m = l/x; l -= m*x; }void next_dig9(u32 x){u32 y;Fil(y, x, P10(6));nextCstr(TB.LZ[y]);Fil(y, x, P10(3));nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);}public:void nextChar(char c){Q[p++] = c;if(p == OUTPUT_BUF_SIZE){ fwrite(Q, p, 1, stdout); p = 0; }}void nextEoln(){ nextChar('\n'); }void nextCstr(const char* s){ while(*s) nextChar(*(s++)); }void nextU32(uint32_t x){u32 y = 0;if(x >= P10(9)){Fil(y, x, P10(9));nextCstr(TB.NLZ[y]); next_dig9(x);}else if(x >= P10(6)){Fil(y, x, P10(6));nextCstr(TB.NLZ[y]);Fil(y, x, P10(3));nextCstr(TB.LZ[y]); nextCstr(TB.LZ[x]);}else if(x >= P10(3)){Fil(y, x, P10(3));nextCstr(TB.NLZ[y]); nextCstr(TB.LZ[x]);}else if(x >= 1) nextCstr(TB.NLZ[x]);else nextChar('0');}void nextI32(int32_t x){if(x >= 0) nextU32(x);else{ nextChar('-'); nextU32((u32)-x); }}void nextU64(uint64_t x){u32 y = 0;if(x >= P10L(18)){Fil(y, x, P10L(18));nextU32(y);Fil(y, x, P10L(9));next_dig9(y); next_dig9(x);}else if(x >= P10L(9)){Fil(y, x, P10L(9));nextU32(y); next_dig9(x);}else nextU32(x);}void nextI64(int64_t x){if(x >= 0) nextU64(x);else{ nextChar('-'); nextU64((u64)-x); }}template<class T>void nextInt(T x){if(x < 0){ nextChar('-'); x = -x; }if(!(0 < x)){ nextChar('0'); return; }std::string buf;while(0 < x){buf.push_back('0' + (int)(x % 10));x /= 10;}for(int i=(int)buf.size()-1; i>=0; i--){nextChar(buf[i]);}}void writeToFile(bool flush = false){fwrite(Q, p, 1, stdout);if(flush) fflush(stdout);p = 0;}COutStream(){ Q[0] = 0; }~COutStream(){ writeToFile(); }MyType& operator<<(unsigned int tg){ nextU32(tg); return *this; }MyType& operator<<(unsigned long tg){ nextU64(tg); return *this; }MyType& operator<<(unsigned long long tg){ nextU64(tg); return *this; }MyType& operator<<(int tg){ nextI32(tg); return *this; }MyType& operator<<(long tg){ nextI64(tg); return *this; }MyType& operator<<(long long tg){ nextI64(tg); return *this; }MyType& operator<<(const std::string& tg){ nextCstr(tg.c_str()); return *this; }MyType& operator<<(const char* tg){ nextCstr(tg); return *this; }MyType& operator<<(char tg){ nextChar(tg); return *this; }} cout;char CInStream::Q[INPUT_BUF_SIZE];char COutStream::Q[OUTPUT_BUF_SIZE];} // namespace nachia#include <vector>#include <algorithm>#include <cassert>#include <iostream>#include <utility>namespace nachia{template<unsigned int MOD>struct PrimitiveRoot{using u64 = unsigned long long;static constexpr u64 powm(u64 a, u64 i) {u64 res = 1, aa = a;while(i){if(i & 1) res = res * aa % MOD;aa = aa * aa % MOD;i /= 2;}return res;}static constexpr bool ExamineVal(unsigned int g){unsigned int t = MOD - 1;for(u64 d=2; d*d<=t; d++) if(t % d == 0){if(powm(g, (MOD - 1) / d) == 1) return false;while(t % d == 0) t /= d;}if(t != 1) if(powm(g, (MOD - 1) / t) == 1) return false;return true;}static constexpr unsigned int GetVal(){for(unsigned int x=2; x<MOD; x++) if(ExamineVal(x)) return x;return 0;}static const unsigned int val = GetVal();};} // namespace nachianamespace nachia{template<class Modint>class Comb{private:std::vector<Modint> F;std::vector<Modint> iF;public:void extend(int newN){int prevN = (int)F.size() - 1;if(prevN >= newN) return;F.resize(newN+1);iF.resize(newN+1);for(int i=prevN+1; i<=newN; i++) F[i] = F[i-1] * Modint::raw(i);iF[newN] = F[newN].inv();for(int i=newN; i>prevN; i--) iF[i-1] = iF[i] * Modint::raw(i);}Comb(int n = 1){F.assign(2, Modint(1));iF.assign(2, Modint(1));extend(n);}Modint factorial(int n) const { return F[n]; }Modint invFactorial(int n) const { return iF[n]; }Modint invOf(int n) const { return iF[n] * F[n-1]; }Modint comb(int n, int r) const {if(n < 0 || n < r || r < 0) return Modint(0);return F[n] * iF[r] * iF[n-r];}Modint invComb(int n, int r) const {if(n < 0 || n < r || r < 0) return Modint(0);return iF[n] * F[r] * F[n-r];}Modint perm(int n, int r) const {if(n < 0 || n < r || r < 0) return Modint(0);return F[n] * iF[n-r];}Modint invPerm(int n, int r) const {if(n < 0 || n < r || r < 0) return Modint(0);return iF[n] * F[n-r];}Modint operator()(int n, int r) const { return comb(n,r); }};} // namespace nachianamespace nachia{int Popcount(unsigned long long c) noexcept {#ifdef __GNUC__return __builtin_popcountll(c);#elsec = (c & (~0ull/3)) + ((c >> 1) & (~0ull/3));c = (c & (~0ull/5)) + ((c >> 2) & (~0ull/5));c = (c & (~0ull/17)) + ((c >> 4) & (~0ull/17));c = (c * (~0ull/257)) >> 56;return c;#endif}// please ensure x != 0int MsbIndex(unsigned long long x) noexcept {#ifdef __GNUC__return 63 - __builtin_clzll(x);#elseusing u64 = unsigned long long;int q = (x >> 32) ? 32 : 0;auto m = x >> q;constexpr u64 hi = 0x8888'8888;constexpr u64 mi = 0x1111'1111;m = (((m | ~(hi - (m & ~hi))) & hi) * mi) >> 35;m = (((m | ~(hi - (x & ~hi))) & hi) * mi) >> 31;q += (m & 0xf) << 2;q += 0x3333'3333'2222'1100 >> (((x >> q) & 0xf) << 2) & 0xf;return q;#endif}// please ensure x != 0int LsbIndex(unsigned long long x) noexcept {#ifdef __GNUC__return __builtin_ctzll(x);#elsereturn MsbIndex(x & -x);#endif}}namespace nachia {template<class mint>struct NttInterface{template<class Iter>void Butterfly(Iter, int) const {}template<class Iter>void IButterfly(Iter, int) const {}template<class Iter>void BitReversal(Iter a, int N) const {for(int i=0, j=0; j<N; j++){if(i < j) std::swap(a[i], a[j]);for(int k = N>>1; k > (i^=k); k>>=1);}}};} // namespace nachia#include <iterator>#include <array>namespace nachia{constexpr int bsf_constexpr(unsigned int n) {int x = 0;while (!(n & (1 << x))) x++;return x;}template <class mint>struct NttFromAcl : NttInterface<mint> {using u32 = unsigned int;using u64 = unsigned long long;static int ceil_pow2(int n) {int x = 0;while ((1U << x) < (u32)(n)) x++;return x;}struct fft_info {static constexpr u32 g = nachia::PrimitiveRoot<mint::mod()>::val;static constexpr int rank2 = bsf_constexpr(mint::mod()-1);std::array<mint, rank2+1> root;std::array<mint, rank2+1> iroot;std::array<mint, std::max(0, rank2-1)> rate2;std::array<mint, std::max(0, rank2-1)> irate2;std::array<mint, std::max(0, rank2-2)> rate3;std::array<mint, std::max(0, rank2-2)> irate3;fft_info(){root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2);iroot[rank2] = root[rank2].inv();for(int i=rank2-1; i>=0; i--){root[i] = root[i+1] * root[i+1];iroot[i] = iroot[i+1] * iroot[i+1];}mint prod = 1, iprod = 1;for(int i=0; i<=rank2-2; i++){rate2[i] = root[i+2] * prod;irate2[i] = iroot[i+2] * iprod;prod *= iroot[i+2];iprod *= root[i+2];}prod = 1; iprod = 1;for(int i=0; i<=rank2-3; i++){rate3[i] = root[i+3] * prod;irate3[i] = iroot[i+3] * iprod;prod *= iroot[i+3];iprod *= root[i+3];}}};template<class RandomAccessIterator>void Butterfly(RandomAccessIterator a, int n) const {int h = ceil_pow2(n);static const fft_info info;int len = 0;while(len < h){if(h-len == 1){int p = 1 << (h-len-1);mint rot = 1;for(int s=0; s<(1<<len); s++){int offset = s << (h-len);for(int i=0; i<p; i++){auto l = a[i+offset];auto r = a[i+offset+p] * rot;a[i+offset] = l+r;a[i+offset+p] = l-r;}if(s+1 != (1<<len)) rot *= info.rate2[LsbIndex(~(u32)(s))];}len++;} else {int p = 1 << (h-len-2);mint rot = 1, imag = info.root[2];for(int s=0; s<(1<<len); s++){mint rot2 = rot * rot;mint rot3 = rot2 * rot;int offset = s << (h-len);for(int i=0; i<p; i++){auto mod2 = 1ULL * mint::mod() * mint::mod();auto a0 = 1ULL * a[i+offset].val();auto a1 = 1ULL * a[i+offset+p].val() * rot.val();auto a2 = 1ULL * a[i+offset+2*p].val() * rot2.val();auto a3 = 1ULL * a[i+offset+3*p].val() * rot3.val();auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val();auto na2 = mod2 - a2;a[i+offset] = a0 + a2 + a1 + a3;a[i+offset+1*p] = a0 + a2 + (2 * mod2 - (a1 + a3));a[i+offset+2*p] = a0 + na2 + a1na3imag;a[i+offset+3*p] = a0 + na2 + (mod2 - a1na3imag);}if(s+1 != (1<<len)) rot *= info.rate3[LsbIndex(~(u32)(s))];}len += 2;}}}template<class RandomAccessIterator>void IButterfly(RandomAccessIterator a, int n) const {int h = ceil_pow2(n);static const fft_info info;constexpr int MOD = mint::mod();int len = h;while(len){if(len == 1){int p = 1 << (h-len);mint irot = 1;for(int s=0; s<(1<<(len-1)); s++){int offset = s << (h-len+1);for(int i=0; i<p; i++){auto l = a[i+offset];auto r = a[i+offset+p];a[i+offset] = l+r;a[i+offset+p] = (u64)(MOD + l.val() - r.val()) * irot.val();}if(s+1 != (1<<(len-1))) irot *= info.irate2[LsbIndex(~(u32)(s))];}len--;} else {int p = 1 << (h-len);mint irot = 1, iimag = info.iroot[2];for(int s=0; s<(1<<(len-2)); s++){mint irot2 = irot * irot;mint irot3 = irot2 * irot;int offset = s << (h-len+2);for(int i=0; i<p; i++){auto a0 = 1ULL * a[i+offset+0*p].val();auto a1 = 1ULL * a[i+offset+1*p].val();auto a2 = 1ULL * a[i+offset+2*p].val();auto a3 = 1ULL * a[i+offset+3*p].val();auto a2na3iimag = 1ULL * mint((MOD + a2 - a3) * iimag.val()).val();a[i+offset] = a0 + a1 + a2 + a3;a[i+offset+1*p] = (a0 + (MOD - a1) + a2na3iimag) * irot.val();a[i+offset+2*p] = (a0 + a1 + (MOD - a2) + (MOD - a3)) * irot2.val();a[i+offset+3*p] = (a0 + (MOD - a1) + (MOD - a2na3iimag)) * irot3.val();}if(s+1 != (1<<(len-2))) irot *= info.irate3[LsbIndex(~(u32)(s))];}len -= 2;}}}};} // namespace nachianamespace nachia {template<class Elem, class NttInst = NttFromAcl<Elem>>struct FpsNtt {public:using Fps = FpsNtt;using ElemTy = Elem;static constexpr unsigned int MOD = Elem::mod();static constexpr int CONV_THRES = 30;static const NttInst nttInst;static const unsigned int zeta = nachia::PrimitiveRoot<MOD>::GetVal();private:using u32 = unsigned int;static Elem ZeroElem() noexcept { return Elem(0); }static Elem OneElem() noexcept { return Elem(1); }static Comb<Elem> comb;std::vector<Elem> a;int RSZ(int& sz) const { return sz = (sz < 0 ? size() : sz); }public:int size() const noexcept { return a.size(); }Elem& operator[](int x) noexcept { return a[x]; }const Elem& operator[](int x) const noexcept { return a[x]; }Elem getCoeff(int x) const noexcept { return (0 <= x && x < size()) ? a[x] : ZeroElem(); }static Comb<Elem>& GetComb() { return comb; }static int BestNttSize(int x) noexcept { assert(x); return 1 << MsbIndex(x*2-1); }Fps move(){ return std::move(*this); }Fps& set(int i, Elem c){ a[i] = c; return *this; }Fps& removeLeadingZeros(){int newsz = size();while(newsz && a[newsz-1].val() == 0) newsz--;a.resize(newsz);if((int)a.capacity() / 4 > newsz) a.shrink_to_fit();return *this;}FpsNtt(){}FpsNtt(int sz) : a(sz, ZeroElem()) {}FpsNtt(int sz, Elem e) : a(sz, e) {}FpsNtt(std::vector<Elem>&& src) : a(std::move(src)) {}FpsNtt(const std::vector<Elem>& src) : a(src) {}Fps& ntt() {capSize(BestNttSize(size()));nttInst.Butterfly(a.begin(), size());return *this;}Fps& intt() {nttInst.IButterfly(a.begin(), a.size());return times(Elem::raw(size()).inv());}Fps nttDouble(Fps vanilla) const {int n = size();assert(n == (n&-n)); // n is a power of 2Elem q = Elem::raw(zeta).pow((Elem::mod() - 1) / (n*2));Elem qq = OneElem();for(int i=0; i<n; i++){ vanilla[i] *= qq; qq *= q; }vanilla.ntt();Fps res = clip(0, n*2);for(int i=0; i<n; i++) res[n+i] = vanilla[i];return res;}Fps nttDouble() const { return nttDouble(clip().intt().move()); }// Fps res(resSz);// for(int j=0; j<resSz-destL && j+srcL < srcR; j++) res[j+destL] = a.getCoeff(j+srcL)// if srcR is unspecified -> srcR = max(srcL, size());// if resSz is unspecified -> resSz = destL + srcR - srcLFps clip(int srcL, int srcR = -1, int destL = 0, int resSz = -1) const {srcR = RSZ(srcR);if(resSz < 0) resSz = destL + srcR - srcL;int rj = std::min(std::min(srcR, size()) - srcL, resSz - destL);Fps res(resSz);for(int j=std::max(0, -srcL); j<rj; j++) res[j+destL] = a[j+srcL];return res;}Fps clip() const { return *this; }Fps& capSize(int l, int r) {if(r <= (int)size()) a.resize(r);if(size() <= l) a.resize(l, ZeroElem());return *this;}Fps& capSize(int z){ a.resize(RSZ(z), ZeroElem()); return *this; }Fps& times(Elem x){ for(int i=0; i<size(); i++){ a[i] *= x; } return *this; }Fps& timesFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.factorial(i); } return *this; }Fps& timesInvFactorial(int z = -1){ comb.extend(RSZ(z)); for(int i=0; i<z; i++){ a[i] *= comb.invFactorial(i); } return *this; }Fps& clrRange(int l, int r){ for(int i=l; i<r; i++){ a[i] = ZeroElem(); } return *this; }Fps& negate(){ for(auto& e : a){ e = -e; } return *this; }Fps& mulEach(const Fps& other, int maxi = -1){maxi = std::min(RSZ(maxi), std::min(size(), other.size()));for(int i=0; i<maxi; i++) a[i] *= other[i];return *this;}Fps& reverse(int sz = -1){ RSZ(sz); std::reverse(a.begin(), a.begin() + sz); return *this; }static Fps convolution(const Fps& a, const Fps& b, int sz = -1){if(std::min(a.size(), b.size()) <= CONV_THRES){if(a.size() > b.size()) return convolution(b, a, sz);if(sz < 0) sz = std::max(0, a.size() + b.size() - 1);std::vector<Elem> res(sz);for(int i=0; i<a.size(); i++) for(int j=0; j<b.size() && i+j<sz; j++) res[i+j] += a[i] * b[j];return res;}int Z = BestNttSize(a.size() + b.size() - 1);return a.clip(0, Z).ntt().mulEach(b.clip(0, Z).ntt()).intt().capSize(sz).move();}Fps convolve(const Fps& r, int sz = -1) const { return convolution(*this, r, sz); }// 1// ----- = 1 + f + f^2 + f^3 + ...// 1-fFps powerSum(int sz) const {RSZ(sz);if(sz == 0) return {};int q = std::min(sz, 32);Fps x = Fps(q).set(0, OneElem()).move();for(int i=1; i<q; i++) for(int j=1; j<=std::min(i,(int)a.size()-1); j++) x[i] += x[i-j] * a[j];while(x.size() < sz){int hN = x.size(), N = hN*2;Fps a = x.clip(0, N).ntt().move();Fps b = clip(0, N).ntt().mulEach(a).intt().clrRange(0,hN).ntt().mulEach(a).intt().move();for(int i=0; i<hN; i++) b[i] = x[i];std::swap(b, x);}return x.capSize(sz).move();}Fps inv(int sz = -1) const {RSZ(sz);Elem iA0 = a[0].inv();return clip(0, std::min(sz, size())).times(-iA0).set(0, ZeroElem()).powerSum(sz).times(iA0).move();}Fps& difference(){if(size() == 0) return *this;for(int i=0; i+1<size(); i++) a[i] = a[i+1] * Elem::raw(i+1);return capSize(size()-1);}Fps& integral(){if(size() == 0) return capSize(1);capSize(size()+1);comb.extend(size());for(int i=size()-1; i>=1; i--) a[i] = a[i-1] * comb.invOf(i);return set(0, ZeroElem());}Fps& EgfToOgf(){comb.extend(size());for(int i=0; i<size(); i++) a[i] *= comb.factorial(i);return *this;}Fps& OgfToEgf(){comb.extend(size());for(int i=0; i<size(); i++) a[i] *= comb.invFactorial(i);return *this;}Fps log(int sz = -1){RSZ(sz);assert(sz != 0);assert(a[0].val() == 1);return convolution(inv(sz), clip().difference(), sz-1).integral();}Fps exp(int sz = -1){RSZ(sz);Fps res = Fps(1).set(0, OneElem());while(res.size() < sz){auto z = res.size();auto tmp = res.capSize(z*2).log().set(0, -OneElem()).move();for(int i=0; i<z*2 && i<size(); i++) tmp[i] -= a[i];auto resntt = res.clip().ntt().mulEach(tmp.ntt()).intt().move();for(int i=z; i<z*2; i++) res[i] = -resntt[i];}return res.capSize(0, sz).move();}Fps pow(unsigned long long k, int sz = -1){int n = RSZ(sz);if(k == 0) return Fps(n).set(0, OneElem()).move();int ctz = 0;while(ctz<n && a[ctz].val() == 0) ctz++;if((unsigned long long)ctz >= (n-1) / k + 1) return Fps(n);Elem a0 = a[ctz];return clip(ctz, ctz+n-ctz*k).times(a0.inv()).log().times(Elem(k)).exp().times(a0.pow(k)).clip(0, -1, ctz*k);}auto begin(){ return a.begin(); }auto end(){ return a.end(); }auto begin() const { return a.begin(); }auto end() const { return a.end(); }std::string toString(std::string beg = "[ ", std::string delim = " ", std::string en = " ]") const {std::string res = beg;bool f = false;for(auto x : a){ if(f){ res += delim; } f = true; res += std::to_string(x.val()); }res += en;return res;}std::vector<Elem> getVectorMoved(){ return std::move(a); }Fps& operator+=(const Fps& r){capSize(std::max(size(), r.size()));for(int i=0; i<r.size(); i++) a[i] += r[i];return *this;}Fps& operator-=(const Fps& r){capSize(std::max(size(), r.size()));for(int i=0; i<r.size(); i++) a[i] -= r[i];return *this;}Fps operator+(const Fps& r) const { return (clip(0, std::max(size(), r.size())) += r).move(); }Fps operator-(const Fps& r) const { return (clip(0, std::max(size(), r.size())) -= r).move(); }Fps operator-() const { return (clip().negate()).move(); }Fps operator*(const Fps& r) const { return convolve(r).removeLeadingZeros().move(); }Fps& operator*=(const Fps& r){ return (*this) = operator*(r); }Fps& operator*=(Elem m){ return times(m); }Fps operator*(Elem m) const { return (clip() *= m).move(); }Elem eval(Elem x) const {Elem res = 0;for(int i=size()-1; i>=0; i--) res = res * x + a[i];return res;}};template<class Elem, class NttInst> Comb<Elem> FpsNtt<Elem, NttInst>::comb;template<class Elem, class NttInst> const NttInst FpsNtt<Elem, NttInst>::nttInst;} // namespace nachianamespace nachia{template<class Modint>class SparsePolynomialFp{public:struct Term{int index;Modint coeff;};std::vector<Term> a;bool m_good;private:void refine(){if(m_good) return;std::sort(a.begin(), a.end(), [](const Term& l, const Term& r){ return l.index < r.index; });int p = -1;for(size_t i=0; i<a.size(); i++){if(a[i].index < 0) continue;if(p < 0 || a[p].index != a[i].index) a[++p] = a[i];else a[p].coeff += a[i].coeff;if(a[p].coeff.val() == 0) p--;}a.resize(p+1);m_good = false;}static std::vector<Modint> InvTable(int n) {if(n == 0) return {};std::vector<Modint> res(n);res[0] = Modint::raw(1);for(int i=1; i<n; i++) res[i] = res[i-1] * Modint::raw(i);res[n-1] = res[n-1].inv();for(int i=n-1; i>=1; i--){Modint x = res[i];res[i] = x * res[i-1];res[i-1] = x * Modint::raw(i);}return res;}Term uniconst() {refine();int i = lowestIndex(-1);if(i < 0) return { -1, Modint(0) };Term res = a[0];Modint a0inv = res.coeff.inv();shift(-i); times(a0inv);return res;}public:int lowestIndex(int whenEmpty = 1001001001){refine();return a.empty() ? whenEmpty : a.front().index;}void shift(int width){refine();for(auto& b : a) b.index += width;}void times(Modint t){if(t.val() == 0){ a.clear(); }for(auto& b : a) b.coeff *= t;}SparsePolynomialFp difference() const {SparsePolynomialFp res;res.a.reserve(a.size());for(auto& b : a){if(b.index == 0){ continue; }res.a.push_back({ b.index - 1, b.coeff * b.index });}return res;}std::vector<Modint> asVector(int n) const {std::vector<Modint> res(n);for(auto& term : a) if(term.index < n){res[term.index] += term.coeff;}return res;}void divInplace(std::vector<Modint>& target){auto b = *this; b.refine();assert(b.lowestIndex() == 0);int n = target.size();Modint invA0 = b.a.front().coeff.inv();for(auto& t : b.a) t.coeff *= invA0;for(auto& x : target) x *= invA0;for(int u=0; u<n; u++){for(int i=1; i<(int)b.a.size(); i++){auto& tm = b.a[i];if(u < tm.index) break;target[u] -= target[u - tm.index] * tm.coeff;}}}std::vector<Modint> exp(int n) const {assert(lowestIndex() > 0);refine();std::vector<Modint> res = InvTable(n);if(n == 0) return res;auto fp = difference();fp.shift(1);for(int i=1; i<n; i++){Modint buf;for(auto b : fp.a){if(i < b.index) break;buf += b.coeff * res[i - b.index];}res[i] *= buf;}return res;}std::vector<Modint> pow(int n, unsigned long long i) const {const Modint Zero = Modint(0);auto pown = Modint(i);SparsePolynomialFp f = *this;Term li = f.uniconst();if(i == 0){std::vector<Modint> res(n, Zero);if(n > 0) res[0] = Modint(1);return res;}if(n == 0 || li.index < 0 || (li.index > 0 && n / li.index <= i)){return std::vector<Modint>(n, Zero);}int k = f.a.size() - 1;std::vector<int> fi(k);std::vector<Modint> fc(k);std::vector<Modint> fdc(k);for(int i=0; i<k; i++){fi[i] = f.a[i+1].index;fc[i] = f.a[i+1].coeff;fdc[i] = fc[i] * Modint::raw(fi[i]);}int shp = (int)(li.index * i);std::vector<Modint> F = InvTable(n-shp);// f F' = n f' FF[0] = Modint(1);int t = 0;for(int i=1; i<n-shp; i++){Modint fd_F = Zero;if(t < k && fi[t] <= i) t++;for(int j=0; j<t; j++) fd_F += fdc[j] * F[i-fi[j]];Modint f_Fd = Zero;for(int j=0; j<t; j++) f_Fd += fc[j] * F[i-fi[j]] * Modint::raw(i-fi[j]);F[i] *= fd_F * pown - f_Fd;}F.resize(n, Zero);auto q = li.coeff.pow(i);for(int i=0; i<n-shp; i++) F[i] *= q;if(shp != 0){for(int i=n-shp-1; i>=0; i--) F[i+shp] = F[i];for(int i=0; i<shp; i++) F[i] = Zero;}return F;}};} // namespace nachianamespace nachia{// ax + by = gcd(a,b)// return ( x, - )std::pair<long long, long long> ExtGcd(long long a, long long b){long long x = 1, y = 0;while(b){long long u = a / b;std::swap(a-=b*u, b);std::swap(x-=y*u, y);}return std::make_pair(x, a);}} // namespace nachianamespace nachia{template<unsigned int MOD>struct StaticModint{private:using u64 = unsigned long long;unsigned int x;public:using my_type = StaticModint;template< class Elem >static Elem safe_mod(Elem x){if(x < 0){if(0 <= x+MOD) return x + MOD;return MOD - ((-(x+MOD)-1) % MOD + 1);}return x % MOD;}StaticModint() : x(0){}StaticModint(const my_type& a) : x(a.x){}StaticModint& operator=(const my_type&) = default;template< class Elem >StaticModint(Elem v) : x(safe_mod(v)){}unsigned int operator*() const noexcept { return x; }my_type& operator+=(const my_type& r) noexcept { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }my_type operator+(const my_type& r) const noexcept { my_type res = *this; return res += r; }my_type& operator-=(const my_type& r) noexcept { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }my_type operator-(const my_type& r) const noexcept { my_type res = *this; return res -= r; }my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }my_type& operator*=(const my_type& r)noexcept { x = (u64)x * r.x % MOD; return *this; }my_type operator*(const my_type& r) const noexcept { my_type res = *this; return res *= r; }my_type pow(unsigned long long i) const noexcept {my_type a = *this, res = 1;while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }return res;}my_type inv() const { return my_type(ExtGcd(x, MOD).first); }unsigned int val() const noexcept { return x; }static constexpr unsigned int mod() { return MOD; }static my_type raw(unsigned int val) noexcept { auto res = my_type(); res.x = val; return res; }my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }my_type operator/(const my_type& r) const { return operator*(r.inv()); }};} // namespace nachiaint main(){using nachia::cin;using nachia::cout;using Modint = nachia::StaticModint<998244353>;using Sparce = nachia::SparsePolynomialFp<Modint>;int n; cin >> n;int N = n+1;long long M = n;Sparce f;f.a.push_back({0,Modint::raw(1)});f.a.push_back({1,Modint::raw(1)});f.a.push_back({2,Modint::raw(1)});auto ar = f.pow(N, M);auto ans = ar[n];ans = (ans - 1) / 2;cout << ans.val() << '\n';return 0;}