#include #include #ifndef IO_HPP #define IO_HPP #include #include #include #include #include #include #include #include #include using namespace std; templateistream &operator>>(istream&,pair&); templateistream &operator>>(istream&,tuple&a); templateistream &operator>>(istream&is,vector&a); templateistream &operator>>(istream&is,array&a); template istream &operator>>(istream&is,pair&a){ is>>a.first>>a.second; return is; } template void read_tuple(istream&is,tuple&a){ if constexpr(pos>::value){ is>>get(a); read_tuple(is,a); } } template istream &operator>>(istream&is,tuple&a){ read_tuple<0>(is,a); return is; } template istream &operator>>(istream&is,vector&a){ for(T&x:a)is>>x; return is; } template istream &operator>>(istream&is,array&a){ for(T&x:a)is>>x; return is; } templateostream &operator<<(ostream&os,const pair&); templateostream &operator<<(ostream&os,const tuple&); templateostream &operator<<(ostream&os,const vector&); templateostream &operator<<(ostream&os,priority_queue); templateostream &operator<<(ostream&os,queue); templateostream &operator<<(ostream&os,deque); templateostream &operator<<(ostream&os,stack); templateostream &operator<<(ostream&os,const array&); templateostream &operator<<(ostream&os,const map&); templateostream &operator<<(ostream&os,const unordered_map&); templateostream &operator<<(ostream&os,const set&); templateostream &operator<<(ostream&os,const multiset&); templateostream &operator<<(ostream&os,const unordered_set&); template ostream &operator<<(ostream&os,const pair&a){ os< void write_tuple(ostream&os,const tuple&a){ if constexpr(pos>::value){ if constexpr(pos>0)os<<' '; os<(a); write_tuple(os,a); } } template ostream &operator<<(ostream&os,const tuple&a){ write_tuple<0>(os,a); return os; } template ostream &operator<<(ostream&os,const vector&a){ os<<'{'; for(int i=0;i<(int)a.size();i++){ os< ostream &operator<<(ostream&os,priority_queuea){ os<<'{'; if(!a.empty()){ os< ostream &operator<<(ostream&os,queuea){ os<<'{'; if(!a.empty()){ os< ostream &operator<<(ostream&os,dequea){ os<<'{'; if(!a.empty()){ os< ostream &operator<<(ostream&os,stacka){ os<<'{'; if(!a.empty()){ os< ostream &operator<<(ostream&os,const array&a){ os<<'{'; for(int i=0;i<(int)a.size();i++){ os< ostream &operator<<(ostream&os,const map&a){ if(a.empty()){ os<<"{}"; return os; } auto itr=a.begin(); os<<"{["<first<<","<second<<']'; while(++itr!=a.end())os<<",["<first<<','<second<<']'; os<<'}'; return os; } template ostream &operator<<(ostream&os,const unordered_map&a){ if(a.empty()){ os<<"{}"; return os; } auto itr=a.begin(); os<<"{["<first<<","<second<<']'; while(++itr!=a.end())os<<",["<first<<','<second<<']'; os<<'}'; return os; } template ostream &operator<<(ostream&os,const set&a){ if(a.empty()){ os<<"{}"; return os; } auto itr=a.begin(); os<<'{'<<*itr; while(++itr!=a.end())os<<','<<*itr; os<<'}'; return os; } template ostream &operator<<(ostream&os,const multiset&a){ if(a.empty()){ os<<"{}"; return os; } auto itr=a.begin(); os<<'{'<<*itr; while(++itr!=a.end())os<<','<<*itr; os<<'}'; return os; } template ostream &operator<<(ostream&os,const unordered_set&a){ if(a.empty()){ os<<"{}"; return os; } auto itr=a.begin(); os<<'{'<<*itr; while(++itr!=a.end())os<<','<<*itr; os<<'}'; return os; } #endif using namespace std; using ll=long long; using ull=unsigned long long; using P=pair; templateusing minque=priority_queue,greater>; templatebool chmax(T &a,const T &b){return (abool chmin(T &a,const T &b){return (a>b?(a=b,true):false);} templatevoid operator++(pair&a,int){a.first++,a.second++;} templatevoid operator--(pair&a,int){a.first--,a.second--;} templatevoid operator++(vector&a,int){for(auto &i:a)i++;} templatevoid operator--(vector&a,int){for(auto &i:a)i--;} using vref=typename vector::reference; vref operator|=(vref a,bool b){a=a|b;return a;} vref operator&=(vref a,bool b){a=a&b;return a;} vref operator^=(vref a,bool b){a=a^b;return a;} #define overload3(_1,_2,_3,name,...) name #define rep1(i,n) for(int i=0;i<(int)(n);i++) #define rep2(i,l,r) for(int i=(int)(l);i<(int)(r);i++) #define rep(...) overload3(__VA_ARGS__,rep2,rep1)(__VA_ARGS__) #define reps(i,l,r) rep2(i,l,r) #define all(x) x.begin(),x.end() #define pcnt(x) __builtin_popcountll(x) #define fin(x) return cout<<(x)<<'\n',static_cast(0) #define yn(x) cout<<((x)?"Yes\n":"No\n") #define uniq(x) sort(all(x)),x.erase(unique(all(x)),x.end()) template inline int fkey(vector&z,T key){return lower_bound(z.begin(),z.end(),key)-z.begin();} ll myceil(ll a,ll b){return (a+b-1)/b;} template auto vec(const int (&d)[n],const T &init=T()){ if constexpr (id(d,init)); else return init; } #ifdef LOCAL #include #define SWITCH(a,b) (a) #else #define debug(...) static_cast(0) #define debugg(...) static_cast(0) #define SWITCH(a,b) (b) #endif struct Timer{ clock_t start; Timer(){ start=clock(); ios::sync_with_stdio(false); cin.tie(nullptr); cout<>testcase; for(int i=0;i #include #include constexpr bool isprime_constexpr(unsigned long long n){ if(n==998244353)return true; if(n==1000000007)return true; if(n<64)return 2891462833508853932ll>>n&1; if(n%2==0)return false; unsigned long long d=n-1; int s=0; while(!(d&1))d>>=1,s++; int q=63; while(!(d>>q))q--; unsigned long long r=n; for(int i=0;i<5;i++)r*=2-r*n; auto redc=[&r,&n](__uint128_t x)->unsigned long long { x=(x+__uint128_t((unsigned long long)x*-r)*n)>>64; return x>=n?x-n:x; }; __uint128_t r2=-__uint128_t(n)%n; unsigned long long one=redc(r2); for(unsigned long long base:{2,325,9375,28178,450775,9780504,1795265022}){ if(base%n==0)continue; unsigned long long a=base=redc((base%n)*r2); for(int i=q-1;i>=0;i--){ a=redc(__uint128_t(a)*a); if(d>>i&1)a=redc(__uint128_t(a)*base); } if(a==one)continue; for(int i=1;a!=n-one;i++){ if(i>=s)return false; a=redc(__uint128_t(a)*a); } } return true; } constexpr std::pairext_gcd(long long a,long long b){ if(b==0)return std::make_pair(1,0); auto [x,y]=ext_gcd(b,a%b); std::swap(x,y); return std::make_pair(x,y-a/b*x); } template constexpr std::pair inv_mod(T a,T b){ a%=b; if(a<0)a+=b; if(a==0)return std::make_pair(b,0); T s=b,t=a; T m0=0,m1=1; while(t){ T u=s/t; s-=t*u; m0-=m1*u; std::swap(s,t); std::swap(m0,m1); } if(m0<0)m0+=b/s; return std::make_pair(s,m0); } template struct modint{ static_assert(1<=m&&m<(1ull<<63)); using value_type=std::conditional_t<((m>>31)==0),uint32_t,uint64_t>; using mul_type=std::conditional_t<((m>>31)==0),uint64_t,__uint128_t>; private: value_type v; static constexpr value_type umod=m; constexpr modint sqrt_impl()const{ if(this->val()<=1)return *this; if(umod%8==1){ modint b=2; while(b.pow((umod-1)/2).val()==1)b++; value_type m2=umod-1; int e=0; while(m2%2==0)m2>>=1,e++; modint x=this->pow((m2-1)/2); modint y=(*this)*x*x; x*=*this; modint z=b.pow(m2); while(y.val()!=1){ int j=0; modint t=y; while(t.val()!=1)t*=t,j++; z=z.pow((value_type(1))<<(e-j-1)); x*=z; z*=z; y*=z; e=j; } return x; } else if(umod%8==5){ modint res=this->pow((umod+3)/8); if((res*res).val()==this->val())return res; else return res*modint(2).pow((umod-1)/4); } else return this->pow((umod+1)/4); } template||std::is_same_v,std::nullptr_t> =nullptr> static constexpr value_type take_mod(U x){ if constexpr(std::numeric_limits::max()>61)+(x&umod); if(res>=umod)res-=umod; return res; } if constexpr(umod==(1ull<<61)-(1ull<<24)+1){ value_type high=x>>61,low=x&((1ull<<61)-1); mul_type t=low+(mul_type(high)<<24)-high; high=t>>61,low=t&((1ull<<61)-1); low=low+(mul_type(high)<<24)-high; if(low>=umod)low-=umod; return low; } return x%umod; } public: constexpr modint():v(0){} template||std::is_same_v,std::nullptr_t> =nullptr> constexpr modint(U x){ x%=std::make_signed_t(umod); v=x>=0?x:x+umod; } template||std::is_same_v,std::nullptr_t> =nullptr> constexpr modint(U x):v(take_mod(x)){} static constexpr value_type mod(){return umod;} static constexpr modint zero(){return raw(0);} static constexpr modint one(){ if constexpr(m==1)return raw(0); else return raw(1); } template static constexpr modint raw(U x){ modint res; res.v=x; return res; } constexpr std::make_signed_t val()const{return v;} constexpr modint &operator+=(const modint&b){ this->v+=b.v; if(this->v>=umod)this->v-=umod; return *this; } constexpr modint &operator-=(const modint&b){ this->v-=b.v; if(this->v>=umod)this->v+=umod; return *this; } constexpr modint &operator*=(const modint&b){ this->v=take_mod(mul_type(this->v)*mul_type(b.v)); return *this; } constexpr modint &operator/=(const modint&b){return *this*=b.inv();} constexpr modint operator+()const{return *this;} constexpr modint operator-()const{return modint()-*this;} friend constexpr modint operator+(const modint&a,const modint&b){return modint(a)+=b;} friend constexpr modint operator-(const modint&a,const modint&b){return modint(a)-=b;} friend constexpr modint operator*(const modint&a,const modint&b){return modint(a)*=b;} friend constexpr modint operator/(const modint&a,const modint&b){return modint(a)/=b;} constexpr auto operator<=>(const modint&)const=default; constexpr modint operator++(int){ modint res=*this; this->v++; if(this->v==umod)this->v=0; return res; } constexpr modint operator--(int){ modint res=*this; if(this->v==0)this->v=umod; this->v--; return res; } template constexpr modint pow(U k)const{ if constexpr(std::is_signed_v){ assert(0<=k); } modint res=1,a(*this); while(k){ if(k&1)res*=a; a*=a; k>>=1; } return res; } constexpr modint inv()const{ if constexpr(isprime_constexpr(umod)){ if(std::is_constant_evaluated()){ if(v==0){ throw "no inverse"; } } else assert(v!=0); return pow(umod-2); } else{ modint res; auto [g,x]=inv_mod>(this->v,umod); if(std::is_constant_evaluated()){ if(g!=1){ throw "no inverse"; } } else assert(g==1); res.v=x; return res; } } std::optionalsqrt()const{ if(this->val()<=1||this->pow((umod-1)/2)==1)return std::make_optional(this->sqrt_impl()); else return std::nullopt; } friend std::istream &operator>>(std::istream&is,modint&b){ long long a; is>>a; b=modint(a); return is; } friend std::ostream &operator<<(std::ostream&os,const modint&b){ os< struct std::hash>{ std::size_t operator()(modintx)const{ return std::hash::value_type>(x.val()); } }; using mint998=modint<998244353>; using mint107=modint<1000000007>; using mint61=modint<2305843009213693951>; using mint6124=modint<2305843009196916737>; struct is_modint_impl{ template static auto check(T&&x)->decltype(x.mod(),std::true_type{}); template static auto check(...)->std::false_type; }; template struct is_modint:public decltype(is_modint_impl::check(std::declval())){}; template inline constexpr bool is_modint_v=is_modint::value; struct is_dynamic_modint_impl{ template static auto check(T&&x)->decltype(x.set_mod((typename T::value_type)0),std::true_type{}); template static auto check(...)->std::false_type; }; template struct is_dynamic_modint:public decltype(is_dynamic_modint_impl::check(std::declval())){}; template inline constexpr bool is_dynamic_modint_v=is_dynamic_modint::value; template inline constexpr bool is_static_modint_v=is_modint_v&&!is_dynamic_modint_v; struct is_uso_modint_impl{ template static auto check(T&&x)->decltype(x.uso(),std::true_type{}); template static auto check(...)->std::false_type; }; template struct is_uso_modint:public decltype(is_uso_modint_impl::check(std::declval())){}; template inline constexpr bool is_uso_modint_v=is_uso_modint::value; template struct F{ private: static int capacity; static std::vectorfact,factinv,inv; public: static void resize(int n){ if(capacity>=n)return; fact.resize(n+1),factinv.resize(n+1),inv.resize(n+1); for(int i=capacity+1;i<=n;i++){ fact[i]=fact[i-1]*T::raw(i); if constexpr(is_uso_modint_v)inv[i]=T(1)/T(i); else inv[i]=-inv[T::mod()%i]*(T::mod()/i); factinv[i]=factinv[i-1]*inv[i]; } capacity=n; } static T C(int n,int k){ if(n static T O(INT...k){ int n=0; for(int i:std::initializer_list{k...}){ if(i<0)return 0; n+=i; } resize(n); T ret=fact[n]; for(int i:std::initializer_list{k...})ret*=factinv[i]; return ret; } static T rising_factorial(int x,int n){ assert(n>=0); if(x>0){ resize(x+n-1); return fact[x+n-1]*factinv[x-1]; } else if(x+n>0)return T(); else{ resize(-x); T res=fact[-x]*factinv[-x-n]; if(n&1)res=-res; return res; } } static T falling_factorial(int x,int n){return rising_factorial(x-n+1,n);} }; templateint F::capacity=1; templatestd::vectorF::fact{1,1}; templatestd::vectorF::factinv{1,1}; templatestd::vectorF::inv{0,1}; using mint=mint998; void SOLVE(){ int n; cin>>n; vector>dp(3,vector(n+1)); dp[1][0]=1; rep(i,n){ vector>ndp(3,vector(n+1)); rep(j,3)rep(k,n+1)if(dp[j][k].val()){ if(j+1<3)ndp[j+1][k]+=dp[j][k]; if(j>=1&&k+1<=n)ndp[0][k+1]+=dp[j][k]; } dp=move(ndp); } mint ans=0; rep(i,2)rep(j,n+1)ans+=dp[i][j]*F::factorial(j)*F::factorial(n-j); cout<