#include #include #include #include #include #include #include #include #include #include #include #include #include using namespace atcoder; using namespace std; #define rep(i,a,b) for(ll i=a;i=b;--i) #define fore(i, a) for(auto& i : a) #define pi 3.141592653589793238 typedef long long ll; typedef pair pp; typedef vector vl; typedef vector vu; typedef vector vvl; typedef vector vp; typedef vector vvp; typedef priority_queue > pq; vl kaijou; void kaijou_set(ll m) {kaijou.push_back(1); rep(i, 1, 1000009)kaijou.push_back((kaijou[i-1] * i) % m); return;} ll C(ll a, ll b, ll m) {if(a T bisect(T ok, T bad, F pred) {if(!pred(ok))return ok; while (bad - ok > 1) {T mid = ok + (bad - ok) / 2; (pred(mid) ? ok : bad) = mid;} return bad;} bool chmin(ll &a, ll b) {if (a > b) {a = b;return true;} return false;} bool chmax(ll &a, ll b) {if (a < b) {a = b;return true;} return false;} void YESNO(bool b) { cout << (b ? "YES" : "NO") << endl; } void YesNo(bool b) { cout << (b ? "Yes" : "No") << endl; } ll gcd(ll x, ll y) {if(y == 0)return x; return gcd(y, x % y); } ll RU(ll a, ll b) {return a / b + (a % b && (a ^ b) >= 0); } ll minus_mod(ll a,ll m){return a < 0 ? (a + RU(abs(a), m) * m) % m : a % m; } ll mod=998244353; ll mof=1000000007; vector pri; void pri_set() { if(!pri.empty()) return; bool sos[1000009]; for (int i = 2; i < 1000009; ++i) sos[i] = true; sos[1] = false; sos[0] = false; for (int i = 2; i < 1000009; ++i) { if (sos[i]) { for (ll j = 2; i * j < 1000009; j++) sos[i * j] = false; pri.push_back(i); } } return; } vector> prime_factorize(long long m) { long long M = m; vector> ans; pri_set(); for (int i = 0; i < pri.size(); ++i) { if (M % pri[i] == 0) ans.push_back(make_pair(pri[i], 0)); while (M % pri[i] == 0) { M /= pri[i]; ++ans[ans.size() - 1].second; } } if (M > 1) ans.push_back(make_pair(M, 1)); return ans; } void dfs(ll val, ll dep, vector &ans, vector> prime) { if (dep == prime.size()) { ans.push_back(val); return; } ll so = 1; for (int i = 0; i <= prime[dep].second; ++i) { dfs(val * so, dep + 1, ans, prime); so *= prime[dep].first; } return; } vector div_enum(long long m) { vector ans; vector> prime = prime_factorize(m); dfs(1, 0, ans, prime); sort(ans.begin(), ans.end()); return ans; } int main() { ll n;cin>>n; pri_set(); vl cnt(pri.size()); rep(i,0,pri.size()){ ll nkari=n; cnt[i]=0; ll m=pri[i]; while(m<=n){ cnt[i]+=n/m; m*=pri[i]; } } ll ans=0; rep(i,1,mof){ //i回割れるbがいくつあるか ll anskari=1; rep(j,0,cnt.size()){ ll lim=cnt[j]/i;//素因数jを含ませていい回数 if(lim==0)break; anskari*=lim+1; anskari%=mod; } anskari+=mod-1;anskari%=mod; if(anskari==0)break; ans+=anskari;ans%=mod; } cout<