#line 1 "Verify/verify-yuki/yuki_336-barrett.test.cpp" #define PROBLEM "https://yukicoder.me/problems/no/336" #line 2 "Template.hpp" //https://tatyam.hatenablog.com/entry/2019/12/15/003634 #include using namespace std; using ll=long long; template using pq=priority_queue,greater>; using pll=pair; const ll LINF=1LL<<60; #define _overload3(_1,_2,_3,name,...) name #define _overload4(_1,_2,_3,_4,name,...) name #define _rep1(i,n) for(ll i=0; i<(n); i++) #define _rep2(i,a,b) for(ll i=(a); i<(b); i++) #define _rep3(i,a,b,c) for(ll i=(a); i<(b); i+=(c)) #define rep(...) _overload4(__VA_ARGS__,_rep3,_rep2,_rep1)(__VA_ARGS__) #define _rrep1(i,n) for(ll i=(n); i-->0;) #define _rrep2(i,a,b) for(ll i=(b); i-->(a);) #define rrep(...) _overload3(__VA_ARGS__,_rrep2,_rrep1)(__VA_ARGS__) #define each(i,...) for(auto&& i:__VA_ARGS__) #define all(i) begin(i),end(i) #define rall(i) rbegin(i),rend(i) template bool chmin(T &a,const T &b){if(a>b){a=b;return true;}else return false;} template bool chmax(T &a,const T &b){if(a ll sum(const T &a){return accumulate(all(a),0LL);} template auto min(const T &a){return *min_element(all(a));} template auto max(const T &a){return *max_element(all(a));} inline int scan(){ return getchar(); } inline void scan(int &a){ scanf("%d", &a); } inline void scan(unsigned &a){ scanf("%u", &a); } inline void scan(long &a){ scanf("%ld", &a); } inline void scan(long long &a){ scanf("%lld", &a); } inline void scan(unsigned long long &a){ scanf("%llu", &a); } inline void scan(char &a){ cin >> a; } inline void scan(float &a){ scanf("%f", &a); } inline void scan(double &a){ scanf("%lf", &a); } inline void scan(long double &a){ scanf("%Lf", &a); } inline void scan(vector &vec){ for(unsigned i = 0; i < vec.size(); i++) { int a; scan(a); vec[i] = a; } } inline void scan(char a[]){ scanf("%s", a); } inline void scan(string &a){ cin >> a; } template inline void scan(vector &vec); template inline void scan(array &vec); template inline void scan(pair &p); template inline void scan(T (&vec)[size]); template inline void scan(vector &vec){ for(auto &i : vec) scan(i); } template inline void scan(deque &vec){ for(auto &i : vec) scan(i); } template inline void scan(array &vec){ for(auto &i : vec) scan(i); } template inline void scan(pair &p){ scan(p.first); scan(p.second); } template inline void scan(T (&vec)[size]){ for(auto &i : vec) scan(i); } template inline void scan(T &a){ cin >> a; } inline void in(){} template inline void in(Head &head, Tail&... tail){ scan(head); in(tail...); } inline void print(){ putchar(' '); } inline void print(const bool &a){ printf("%d", a); } inline void print(const int &a){ printf("%d", a); } inline void print(const unsigned &a){ printf("%u", a); } inline void print(const long &a){ printf("%ld", a); } inline void print(const long long &a){ printf("%lld", a); } inline void print(const unsigned long long &a){ printf("%llu", a); } inline void print(const char &a){ printf("%c", a); } inline void print(const char a[]){ printf("%s", a); } inline void print(const float &a){ printf("%.15f", a); } inline void print(const double &a){ printf("%.15f", a); } inline void print(const long double &a){ printf("%.15Lf", a); } inline void print(const string &a){ for(auto&& i : a) print(i); } template inline void print(const vector &vec); template inline void print(const array &vec); template inline void print(const pair &p); template inline void print(const T (&vec)[size]); template inline void print(const vector &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } } template inline void print(const deque &vec){ if(vec.empty()) return; print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } } template inline void print(const array &vec){ print(vec[0]); for(auto i = vec.begin(); ++i != vec.end(); ){ putchar(' '); print(*i); } } template inline void print(const pair &p){ print(p.first); putchar(' '); print(p.second); } template inline void print(const T (&vec)[size]){ print(vec[0]); for(auto i = vec; ++i != end(vec); ){ putchar(' '); print(*i); } } template inline void print(const T &a){ cout << a; } inline int out(){ putchar('\n'); return 0; } template inline int out(const T &t){ print(t); putchar('\n'); return 0; } template inline int out(const Head &head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } using ld=long double; using ull=unsigned long long; using uint=unsigned int; using pii=pair; using pdd=pair; using tuplis=array; #define vec(type,name,...) vector name(__VA_ARGS__); #define vv(type,name,h,...)vector> name(h,vector(__VA_ARGS__)); #define INT(...) int __VA_ARGS__; in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__; in(__VA_ARGS__) #define ULL(...) ull __VA_ARGS__; in(__VA_ARGS__) #define STR(...) string __VA_ARGS__; in(__VA_ARGS__) #define CHR(...) char __VA_ARGS__; in(__VA_ARGS__) #define LD(...) ld __VA_ARGS__; in(__VA_ARGS__) #define VEC(type,name,size) vector name(size); in(name) #define VV(type, name, h, w) vector> name(h, vector(w)); in(name) template ld dsum(const T &a){return accumulate(all(a),0.0L);} const int INF=INT_MAX>>1; const ll MINF=1LL<<40; const ld DINF=numeric_limits::infinity(); const int MODD=1000000007; const int MOD=998244353; const ld EPS=1e-9; const ld PI=3.1415926535897932; const ll four[]={0,1,0,-1,0}; const ll eight[]={0,1,1,0,-1,-1,1,-1,0}; ll intpow(ll a,ll b){ll ret=1;while(b){if(b&1)ret*=a;a*=a;b>>=1;}return ret;} int Yes(bool i=true){return out(i?"Yes":"No");} int No(bool i=true){return out(i?"No":"Yes");} #define len(x) ((int)(x).size()) #define fi first #define se second #line 2 "Math/BarrettModint.hpp" template struct BarrettModint{ static constexpr uint32_t _phi(){ uint32_t prime_fact=N; uint32_t ret=N; for(int i=2; i*i>64; if(x-ret*N<0){ return x-(ret-1)*N; } return x-ret*N; } constexpr BarrettModint()noexcept{ x=0; } constexpr BarrettModint(int64_t val)noexcept{ x=((val%N)+N)%N; } constexpr uint64_t val()noexcept{ return x; } friend ostream &operator<<(ostream &os,BarrettModint &b){ return os<=N)x-=N; return *this; } constexpr BarrettModint operator-=(BarrettModint rhs)noexcept{ x-=rhs.x; if(x<0)x+=N; return *this; } constexpr BarrettModint operator*=(BarrettModint rhs)noexcept{ x=_get_mod(x*rhs.x); return *this; } constexpr BarrettModint operator/=(BarrettModint rhs){ (*this)*=rhs.inv(); return *this; } constexpr BarrettModint& operator++(){ (*this)+=1; return *this; } constexpr BarrettModint& operator--(){ (*this)-=1; return *this; } constexpr BarrettModint operator++(int){ (*this)+=1; return *this; } constexpr BarrettModint operator--(int){ (*this)-=1; return *this; } constexpr bool operator==(BarrettModint rhs)noexcept{ return (x>=N?x-N:x)==(rhs.x>=N?rhs.x-N:rhs.x); } constexpr bool operator!=(BarrettModint rhs)noexcept{ return (x>=N?x-N:x)!=(rhs.x>=N?rhs.x-N:rhs.x); } constexpr BarrettModint inv(){ BarrettModint ret=(*this).pow(inv_power); assert(ret*(*this)==1); return ret; } constexpr BarrettModint pow(uint64_t x)noexcept{ BarrettModint ret=1; BarrettModint bin=(*this); while(x){ if(x&1)ret*=bin; bin*=bin; x>>=1; } return ret; } }; template struct ArbitraryBarrettModint{ static uint32_t _phi(uint32_t N){ uint32_t prime_fact=N; uint32_t ret=N; for(int i=2; i*i>64; if(x-ret*N<0){ return x-(ret-1)*N; } return x-ret*N; } ArbitraryBarrettModint()noexcept{ x=0; } ArbitraryBarrettModint(int64_t val)noexcept{ x=((val%N)+N)%N; } uint64_t val()noexcept{ return x; } friend ostream &operator<<(ostream &os,ArbitraryBarrettModint &b){ return os<=N)x-=N; return *this; } ArbitraryBarrettModint operator-=(ArbitraryBarrettModint rhs)noexcept{ x-=rhs.x; if(x<0)x+=N; return *this; } ArbitraryBarrettModint operator*=(ArbitraryBarrettModint rhs)noexcept{ x=_get_mod(x*rhs.x); return *this; } ArbitraryBarrettModint operator/=(ArbitraryBarrettModint rhs){ (*this)*=rhs.inv(); return *this; } ArbitraryBarrettModint& operator++(){ (*this)+=1; return *this; } ArbitraryBarrettModint& operator--(){ (*this)-=1; return *this; } ArbitraryBarrettModint operator++(int){ (*this)+=1; return *this; } ArbitraryBarrettModint operator--(int){ (*this)-=1; return *this; } bool operator==(ArbitraryBarrettModint rhs)noexcept{ return (x>=N?x-N:x)==(rhs.x>=N?rhs.x-N:rhs.x); } bool operator!=(ArbitraryBarrettModint rhs)noexcept{ return (x>=N?x-N:x)!=(rhs.x>=N?rhs.x-N:rhs.x); } ArbitraryBarrettModint inv(){ ArbitraryBarrettModint ret=(*this).pow(inv_power); assert(ret*(*this)==1); return ret; } ArbitraryBarrettModint pow(uint64_t x)noexcept{ ArbitraryBarrettModint ret=1; ArbitraryBarrettModint bin=(*this); while(x){ if(x&1)ret*=bin; bin*=bin; x>>=1; } return ret; } }; templateuint64_t ArbitraryBarrettModint::N; templateuint64_t ArbitraryBarrettModint::Nr; templateuint32_t ArbitraryBarrettModint::inv_power; template inline void print(BarrettModint a){ cout << a; } template inline void print(ArbitraryBarrettModint a){ cout << a; } #line 4 "Verify/verify-yuki/yuki_336-barrett.test.cpp" using mint=BarrettModint; void solve(){ LL(N); if(N<=2){ out(0);return; } vec(mint,dp,1,2); rep(i,1,N){ vec(mint,ndp,i+1,0); if(i&1){ mint now=0; rep(j,i){ now+=dp[j]; ndp[j+1]=now; } } else{ mint now=0; rrep(j,i){ now+=dp[j]; ndp[j]=now; } } dp=move(ndp); } mint ans=0; each(i,dp){ ans+=i; } out(ans); } int main(){ solve(); return 0; }