#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(ll i = 0 ; i < n ; i++) #define drep(i,n) for(ll i = n-1 ; i >= 0 ; i--) #define crep(i,x,n) for(ll 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 ll max_n = 1030002; using namespace std; ll mod=998244353; ll binpow(ll a, ll b) { a %= mod; ll res = 1; while (b) { if (b%2) res = res * a % mod; a = a * a % mod; b /= 2; } return res % mod; } ll gcd(ll x , ll y){ return y == 0 ? x : gcd(y,x%y); } ll prod(ll a , ll b){ a%=mod; b%=mod; return ((a*b)%mod); } ll add(ll a , ll b){ a%=mod; b%=mod; return (a+b)%mod; } vec(pii) primefact[max_n]; unordered_mapmp; void merg(ll x,ll y) { unordered_map nmp; for(auto p:primefact[x]) { nmp[p.fi]=p.se; } for(auto p:primefact[y]) { if(nmp.find(p.fi)==nmp.end())nmp[p.fi]=p.se; else nmp[p.fi]+=p.se; } for(auto p : nmp) { mp[p.fi]=max(mp[p.fi],p.se); } } int main(){ fcin; ll n; cin>>n; crep(i,1,n) { ll x=i,y=x; for(ll j=2;j<=sqrt(x);j++) { while(y%j==0) { ll 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); } ll ans=1; // crep(i,1,n) { // for(auto p : a[i]) { // mp[p.fi]=max(mp[p.fi],p.se); // } // } for(auto p : mp) { ans = prod(ans,binpow(p.fi,p.se)); } cout << ans << "\n"; /* */ return 0; }