#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include //eolibraries #define lnf 3999999999999999999 #define inf 999999999 #define PI 3.14159265359 #define endl "\n" #define fi first #define se second #define pb push_back #define eb emplace_back #define ll long long #define all(c) (c).begin(),(c).end() #define sz(c) (ll)(c).size() #define mkp(a,b) make_pair(a,b) #define make_unique(a) sort(all(a)),a.erase(unique(all(a)),a.end()) #define rsz(a,n) a.resize(n) #define pii pair #define rep(i,n) for(int i = 0 ; i < n ; i++) #define drep(i,n) for(int i = n-1 ; i >= 0 ; i--) #define crep(i,x,n) for(int i = x ; i < n ; i++) #define vi vector #define vec(s) vector #define rsz(a,n) a.resize(n) #define rszv(a,n,v) a.resize(n,v) #define fcin ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0); //eodefine const int max_n = 103002; using namespace std; const int mod=998244353; struct mint { ll x; mint(ll x=0):x(x%mod){} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this; } mint operator+(const mint a) const { mint res(*this); return res+=a; } mint operator-(const mint a) const { mint res(*this); return res-=a; } mint operator*(const mint a) const { mint res(*this); return res*=a; } }; mint binpow(int a, int b) { mint res = 1; while (b) { if (b%2) res = res * a; a = a * a; b /= 2; } return res; } vec(pii) primefact[max_n]; int nmp[max_n],mp[max_n]; void merg(int x,int y) { for(auto p:primefact[x]) { nmp[p.fi]=0; } for(auto p:primefact[y]) { nmp[p.fi]=0; } for(auto p:primefact[x]) { nmp[p.fi]=p.se; } for(auto p:primefact[y]) { nmp[p.fi]+=p.se; } for(auto p :primefact[x]) mp[p.fi]=max(mp[p.fi],nmp[p.fi]); for(auto p :primefact[y]) mp[p.fi]=max(mp[p.fi],nmp[p.fi]); } int main(){ fcin; int n; cin>>n; crep(i,1,n) { int x=i,y=x; for(int j=2;j<=sqrt(x);j++) { while(y%j==0) { int cnt=0; while(y%j==0) {y/=j; cnt++;} primefact[i].pb({j,cnt}); } } if(y!=1) primefact[i].pb({y,1}); } crep(i,1,n) { merg(i,n-i); } mint ans=1; crep(i,1,max_n-3){ if(mp[i]==0)continue; ans *= binpow(i,mp[i]); } cout << ans.x << "\n"; /* */ return 0; }