#include #include namespace neguse {} using namespace std; using namespace atcoder; using namespace neguse; typedef long long ll; typedef long double ld; typedef pair pii; typedef pair pll; typedef vector vi; typedef vector vll; typedef vector vld; typedef vector vvi; typedef vector vvll; typedef vector vs; typedef vector vpii; typedef vector vpll; #define _overload3(_1, _2, _3, name, ...) name #define _rep(i, n) repi(i, 0, n) #define repi(i, a, b) for (int i = int(a); i < int(b); ++i) #define rep(...) _overload3(__VA_ARGS__, repi, _rep, )(__VA_ARGS__) #define _rrep(i, n) rrepi(i, n - 1, -1) #define rrepi(i, a, b) for (int i = int(a); i > int(b); --i) #define rrep(...) _overload3(__VA_ARGS__, rrepi, _rrep)(__VA_ARGS__) #define _each1(i, v) for (auto &i : v) #define _each2(i, j, v) for (auto &[i, j] : v) #define each(...) _overload3(__VA_ARGS__, _each2, _each1, )(__VA_ARGS__) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() #define SUM(x) accumulate(all(x), 0LL) #define MAX(x) *max_element(all(x)) #define MIN(x) *min_element(all(x)) #define ACC(x, acc) partial_sum(all(x), acc.begin()+1) #define SORT(x) sort(all(x)) #define RSORT(x) sort(rall(x)) #define REVERSE(x) reverse(all(x)) #define dump(x) cerr << #x << " = " << (x) << '\n' #define print(x) cout << (x) << '\n' #define yes(f) cout << ((f) ? "Yes" : "No") << '\n' #define ge(v, x) (int)(lower_bound(all(v), x) - v.begin()) #define gt(v, x) (int)(upper_bound(all(v), x) - v.begin()) #define le(v, x) (int)(upper_bound(all(v), x) - v.begin()) - 1 #define lt(v, x) (int)(lower_bound(all(v), x) - v.begin()) - 1 template bool chmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; } template bool chmin(T &a, const T &b) { return a > b ? a = b, 1 : 0; } ostream &operator<<(ostream &os, const modint998244353 &a) { return os << a.val(); } ostream &operator<<(ostream &os, const modint1000000007 &a) { return os << a.val(); } istream &operator>>(istream &is, modint998244353 &a) { int64_t t; is >> t; a = t; return is; } istream &operator>>(istream &is, modint1000000007 &a) { int64_t t; is >> t; a = t; return is; } template ostream &operator<<(ostream &os, const pair &p) { return os << '(' << p.first << ", " << p.second << ')'; } template istream &operator>>(istream &is, pair &p) { return is >> p.first >> p.second; } template istream &operator>>(istream &is, vector &v) { for (T &x : v) is >> x; return is; } template ostream &operator<<(ostream &os, const vector &v) { for (const T &x : v) os << x << ' '; return os; } template ostream &operator<<(ostream &os, const vector> &v) { for (const vector &x : v) os << x << '\n'; return os; } #include #include #include namespace neguse { std::vector divisor(long long n, bool sorted = true) { std::vector res; for (long long i = 1; i*i <= n; i++) { if (n % i == 0) { res.push_back(i); if (i*i != n) res.push_back(n/i); } } if (sorted) std::sort(res.begin(), res.end()); return res; } std::map prime_factor(long long n) { std::map res; for (long long i = 2; i*i <= n; i++) { while (n % i == 0) { res[i]++; n /= i; } } if (n != 1) res[n] = 1; return res; } std::vector spf(int n) { std::vector spf(n+1); for (int i = 0; i <= n; i++) spf[i] = i; for (int i = 2; i*i <= n; i++) { if (spf[i] != i) continue; for (int j = i*i; j <= n; j += i) { if (spf[j] == j) spf[j] = i; } } return spf; } std::map fast_prime_factor(int n, const std::vector& spf) { std::map res; while (n != 1) { res[spf[n]]++; n /= spf[n]; } return res; } bool is_prime(long long n) { if (n <= 1) return false; for (long long i = 2; i*i <= n; i++) { if (n % i == 0) return false; } return true; } std::vector prime_table(int n) { std::vector is_prime(n+1, true); if (n >= 0) is_prime[0] = false; if (n >= 1) is_prime[1] = false; for (int i = 2; i*i <= n; i++) { if (!is_prime[i]) continue; for (int j = i*2; j <= n; j += i) { is_prime[j] = false; } } return is_prime; } } int main() { int N; cin >> N; auto p = prime_table(N); vi primes; rep(i, N+1) if (p[i]) primes.push_back(i); map cnt; for (auto p: primes) { for (ll i = p; i <= N; i *= p) cnt[p] += N / i; } using mint = modint998244353; vector A(cnt[2]+1, 1); for (auto [p, c]: cnt) { rep(k, 1, c+1) A[k] *= 1 + c/k; } mint ans = 0; for (auto a: A) ans += a - 1; cout << ans << endl; return 0; }