#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define X first #define Y second #define pb push_back #define rep(X,Y) for (int (X) = 0;(X) < (int)(Y);++(X)) #define reps(X,S,Y) for (int (X) = (int)(S);(X) < (int)(Y);++(X)) #define rrep(X,Y) for (int (X) = (int)(Y)-1;(X) >=0;--(X)) #define rreps(X,S,Y) for (int (X) = (int)(Y)-1;(X) >= (int)(S);--(X)) #define repe(X,Y) for ((X) = 0;(X) < (Y);++(X)) #define peat(X,Y) for (;(X) < (Y);++(X)) #define all(X) (X).begin(),(X).end() #define rall(X) (X).rbegin(),(X).rend() #define eb emplace_back #define UNIQUE(X) (X).erase(unique(all(X)),(X).end()) #define Endl endl #define NL <<"\n" #define cauto const auto using namespace std; using ll=long long; using pii=pair; using pll=pair; template using vv=vector>; template inline bool MX(T &l,const T &r){return l inline bool MN(T &l,const T &r){return l>r?l=r,1:0;} //#undef NUIP #ifdef NUIP #include "benri.h" #else #define out(args...) #endif void ouT(ll x,int d=3){auto re=to_string(x);if((int)re.size()>d) re=x>0?"oo":"-oo";cout<vector table(int n, T v){ return vector(n, v);} template auto table(int n, Args... args){auto val = table(args...); return vector(n, move(val));} #endif template pair operator+(const pair &p,const pair &q){ return {p.X+q.X,p.Y+q.Y};} template pair& operator+=(pair &p,const pair &q){ p.X+=q.X; p.Y+=q.Y; return p;} template pair operator-(const pair &p,const pair &q){ return {p.X-q.X,p.Y-q.Y};} template pair& operator-=(pair &p,const pair &q){ p.X-=q.X; p.Y-=q.Y; return p;} template istream& operator>>(istream &is, pair &p){ is>>p.X>>p.Y; return is;} template T read(){ T re; cin>>re; return move(re);} template T read(const T &dec){ T re; cin>>re; return re-dec;} template vector readV(const int sz){ vector re(sz); for(auto &x:re) x=read(); return move(re);} template vector readV(const int sz, const T &dec){ vector re(sz); for(auto &x:re) x=read(dec); return move(re);} vv readG(const int &n,const int &m){ vv g(n); rep(_,m){ cauto a=read(1),b=read(1); g[a].pb(b); g[b].pb(a);} return move(g);} vv readG(const int &n){ return readG(n,n-1);} #define TT cauto TTT=read();rep(_,TTT) const ll MOD=998244353; ll modpow_(ll r,ll n,ll m=MOD){ ll re=1,d=r%m; if(n<0)(n%=m-1)+=m-1; for(;n;n/=2){ if(n&1)(re*=d)%=m; (d*=d)%=m; } return re; } template struct ModInt{ int v; ModInt(int v=0):v(v){} ModInt operator+(const ModInt &n)const{return v+n.v=mod) v-=mod; return *this;} ModInt& operator-=(const ModInt &n){v-=n.v; if(v<0) v+=mod; return *this;} ModInt& operator*=(const ModInt &n){v=ll(v)*n.v%mod; return *this;} ModInt& operator/=(const ModInt &n){v=ll(v)*modpow_(n.v,-1,mod)%mod; return *this;} ModInt& operator+=(const ll &n){v+=n; if(v>=mod) v-=mod; return *this;} ModInt& operator-=(const ll &n){v-=n; if(v<0) v+=mod; return *this;} ModInt& operator*=(const ll &n){v=ll(v)*n%mod; return *this;} ModInt& operator/=(const ll &n){v=ll(v)*modpow_(n,-1,mod)%mod; return *this;} bool operator==(const ModInt &n)const{return v==n.v;}; bool operator!=(const ModInt &n)const{return v!=n.v;}; ModInt& operator++(){ return operator+=(1); } ModInt& operator--(){ return operator-=(1); } ModInt operator++(int i){ ModInt tmp(*this); operator++(); return tmp; } ModInt operator--(int i){ ModInt tmp(*this); operator--(); return tmp; } }; #ifdef NUIP class MINT_FRAC____{ public: unordered_map dict; MINT_FRAC____(int n){ rep(p,n+1)reps(q,1,n+1)if(__gcd(p,q)==1){ dict[1ll*p*modpow_(q,-1)%MOD]=pii(p,q); dict[MOD-1ll*p*modpow_(q,-1)%MOD]=pii(-p,q); } } } Il1Il1Il1(1000); template ostream& operator<<(ostream &os,const ModInt &n){if(Il1Il1Il1.dict.count(n.v)) os< ostream& operator<<(ostream &os,const ModInt &n){return os< ModInt operator+(const ll &n,const ModInt &m){return m.v+n ModInt operator-(const ll &n,const ModInt &m){return n-m.v<0 ? n-m.v+mod : n-m.v;} template ModInt operator*(const ll &n,const ModInt &m){return ll(m.v)*(n%mod)%mod;} template ModInt operator/(const ll &n,const ModInt &m){return ModInt(n%mod)/m;} typedef ModInt mint; template ModInt modpow(ModInt r,ll n){ ModInt re(1); if(n<0)(n%=mod-1)+=mod-1; for(;n;n/=2){if(n&1) re*=r; r*=r;} return re;} vector fact,finv,inv; mint comb(ll n,ll r){ if(n &re,int n){ re.resize(n+1); re[1]=1; for(int i=2;i<=n;++i)re[i]=re[MOD%i]*(MOD-MOD/i);} void Facts(vector &re,int n){ re.resize(n+1); re[0]=1; rep(i,n)re[i+1]=re[i]*(i+1);} void Factinvs(vector &re,const vector &inv,int n){ re.resize(n+1); re[0]=1; rep(i,n)re[i+1]=re[i]*inv[i+1];} public: Doralion(int n){ Modinvs(inv,n); Facts(fact,n); Factinvs(finv,inv,n);} } doralion(1123456); using pmm=pair; mint modpow(ll r,ll n){ return modpow_(r,n);} vector primes,prime; class PRPRPR{ public: PRPRPR(int PRIME_MAX){ prime.resize(PRIME_MAX); for(int i=2;i facts[1123456]; int main(){ ios_base::sync_with_stdio(false); cin.tie(0); cout<> cnts; reps(i,1,n+1)for(cauto [p,c]:facts[i]) cnts[p].emplace(c); mint prod=1; for(cauto &[p,st]:cnts){ cauto t=st.top(); rep(_,t) prod*=p; } ll mx=0; for(cauto p:primes)if(p<=n) mx=p; if(0)rreps(i,1,n+1){ if(i<=mx) break; ll prod=1; for(cauto &[p,c]:facts[i]){ int dif=cnts[p].top(); if(dif!=c) continue; cnts[p].pop(); if(cnts[p].size()) dif-=cnts[p].top(); cnts[p].emplace(c); if(dif) prod*=p; } MX(mx,prod); } cout<