#include <bits/stdc++.h>
using namespace std;
const long long MOD = 998244353;
const long long R = 249561089; //3/4
int main(){
  int N;
  cin >> N;
  vector<bool> 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<int> 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<long long> pow2(N + 1);
  pow2[0] = 1;
  for (int i = 0; i < N; i++){
    pow2[i + 1] = pow2[i] * 2 % MOD;
  }
  vector<long long> 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<long long> powR(N + 1);
  powR[0] = 1;
  for (int i = 0; i < N; i++){
    powR[i + 1] = powR[i] * R % MOD;
  }
  vector<long long> 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;
}