#include using namespace std; const long long MOD = 998244353; const long long R = 249561089; //3/4 int main(){ int N; cin >> N; vector prime(N + 1, true); for (int i = 2; i <= N; i++){ if (prime[i]){ for (int j = i * 2; j <= N; j += i){ prime[j] = false; } } } vector mobius(N + 1, 1); for (int i = 2; i <= N; i++){ if (prime[i]){ for (int j = i; j <= N; j += i){ mobius[j] *= -1; } } } for (int i = 2; i * i <= N; i++){ for (int j = i * i; j <= N; j += i * i){ mobius[j] = 0; } } vector pow2(N + 1); pow2[0] = 1; for (int i = 0; i < N; i++){ pow2[i + 1] = pow2[i] * 2 % MOD; } vector A(N + 2, 0); for (int i = 1; i <= N; i++){ A[i] = mobius[i]; } A[N + 1] = 0; for (int i = 1; i <= N; i++){ A[N + 1] -= mobius[i]; } for (int i = 1; i <= N + 1; i++){ if (A[i] < 0){ A[i] += MOD; } A[i] *= pow2[N / i]; A[i] %= MOD; } vector powR(N + 1); powR[0] = 1; for (int i = 0; i < N; i++){ powR[i + 1] = powR[i] * R % MOD; } vector C = A; for (int i = 2; i <= N; i++){ if (prime[i]){ for (int j = 1; j * i <= N + 1; j++){ C[j * i] += C[j]; C[j * i] %= MOD; } } } for (int i = 1; i <= N + 1; i++){ C[i] *= C[i]; C[i] %= MOD; } for (int i = 2; i <= N; i++){ if (prime[i]){ for (int j = (N + 1) / i; j >= 1; j--){ C[j * i] -= C[j]; C[j * i] += MOD; C[j * i] %= MOD; } } } long long sum = 0; for (int i = 1; i <= N + 1; i++){ sum += A[i]; } sum %= MOD; sum *= sum; sum %= MOD; for (int i = 1; i <= N; i++){ sum += MOD - C[i]; sum %= MOD; } long long ans = 0; for (int i = 1; i <= N; i++){ ans += C[i] * powR[N / i] % MOD; } ans += sum; ans %= MOD; cout << ans << endl; }