Problem: Kavi has 2n points lying on the OX axis, i-th of which is located at x = i.

Kavi considers all ways to split these 2n points into n pairs. Among those, he is interested in good pairings, which are defined as follows:

Consider n segments with ends at the points in correspondent pairs. The pairing is called good, if for every 2 different segments A and B among those, at least one of the following holds:

  * One of the segments A and B lies completely inside the other. 
  * A and B have the same length. 



Consider the following example:

<image>

A is a good pairing since the red segment lies completely inside the blue segment.

B is a good pairing since the red and the blue segment have the same length.

C is not a good pairing since none of the red or blue segments lies inside the other, neither do they have the same size.

Kavi is interested in the number of good pairings, so he wants you to find it for him. As the result can be large, find this number modulo 998244353.

Two pairings are called different, if some two points are in one pair in some pairing and in different pairs in another.

Input

The single line of the input contains a single integer n (1≤ n ≤ 10^6).

Output

Print the number of good pairings modulo 998244353.

Examples

Input


1


Output


1

Input


2


Output


3

Input


3


Output


6

Input


100


Output


688750769

Note

The good pairings for the second example are: 

<image>

In the third example, the good pairings are: 

<image>

Solution (in CPP):

Solution:
// author: erray
#include <bits/stdc++.h>
 
using namespace std;

// modular template by tourist
template <typename T>
T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a; swap(a, m);
    u -= t * v; swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T>
class Modular {
 public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}
  template <typename U>
  Modular(const U& x) {
    value = normalize(x);
  }

  template <typename U>
  static Type normalize(const U& x) {
    Type v;
    if (-mod() <= x && x < mod()) v = static_cast<Type>(x);
    else v = static_cast<Type>(x % mod());
    if (v < 0) v += mod();
    return v;
  }

  const Type& operator()() const { return value; }
  template <typename U>
  explicit operator U() const { return static_cast<U>(value); }
  constexpr static Type mod() { return T::value; }

  Modular& operator+=(const Modular& other) { if ((value += other.value) >= mod()) value -= mod(); return *this; }
  Modular& operator-=(const Modular& other) { if ((value -= other.value) < 0) value += mod(); return *this; }
  template <typename U> Modular& operator+=(const U& other) { return *this += Modular(other); }
  template <typename U> Modular& operator-=(const U& other) { return *this -= Modular(other); }
  Modular& operator++() { return *this += 1; }
  Modular& operator--() { return *this -= 1; }
  Modular operator++(int) { Modular result(*this); *this += 1; return result; }
  Modular operator--(int) { Modular result(*this); *this -= 1; return result; }
  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int>::value, Modular>::type& operator*=(const Modular& rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x), d, m;
    asm(
      "divl %4; \n\t"
      : "=a" (d), "=d" (m)
      : "d" (xh), "a" (xl), "r" (mod())
    );
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }
  template <typename U = T>
  typename enable_if<is_same<typename Modular<U>::Type, int64_t>::value, Modular>::type& operator*=(const Modular& rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) * rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }
  template <typename U = T>
  typename enable_if<!is_integral<typename Modular<U>::Type>::value, Modular>::type& operator*=(const Modular& rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular& operator/=(const Modular& other) { return *this *= Modular(inverse(other.value, mod())); }

  template <typename U>
  friend const Modular<U>& abs(const Modular<U>& v) { return v; }

  template <typename U>
  friend bool operator==(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend bool operator<(const Modular<U>& lhs, const Modular<U>& rhs);

  template <typename U>
  friend std::istream& operator>>(std::istream& stream, Modular<U>& number);

 private:
  Type value;
};

template <typename T> bool operator==(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value == rhs.value; }
template <typename T, typename U> bool operator==(const Modular<T>& lhs, U rhs) { return lhs == Modular<T>(rhs); }
template <typename T, typename U> bool operator==(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) == rhs; }

template <typename T> bool operator!=(const Modular<T>& lhs, const Modular<T>& rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(const Modular<T>& lhs, U rhs) { return !(lhs == rhs); }
template <typename T, typename U> bool operator!=(U lhs, const Modular<T>& rhs) { return !(lhs == rhs); }

template <typename T> bool operator<(const Modular<T>& lhs, const Modular<T>& rhs) { return lhs.value < rhs.value; }

template <typename T> Modular<T> operator+(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) += rhs; }
template <typename T, typename U> Modular<T> operator+(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) += rhs; }

template <typename T> Modular<T> operator-(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) -= rhs; }
template <typename T, typename U> Modular<T> operator-(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) -= rhs; }

template <typename T> Modular<T> operator*(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) *= rhs; }
template <typename T, typename U> Modular<T> operator*(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) *= rhs; }

template <typename T> Modular<T> operator/(const Modular<T>& lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(const Modular<T>& lhs, U rhs) { return Modular<T>(lhs) /= rhs; }
template <typename T, typename U> Modular<T> operator/(U lhs, const Modular<T>& rhs) { return Modular<T>(lhs) /= rhs; }

template<typename T, typename U>
Modular<T> power(const Modular<T>& a, const U& b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1) res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename T>
bool IsZero(const Modular<T>& number) {
  return number() == 0;
}

template <typename T>
string to_string(const Modular<T>& number) {
  return to_string(number());
}

template <typename T>
std::ostream& operator<<(std::ostream& stream, const Modular<T>& number) {
  return stream << number();
}

template <typename T>
std::istream& operator>>(std::istream& stream, Modular<T>& number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}

/*
using ModType = int;
struct VarMod { static ModType value; };
ModType VarMod::value;
ModType& md = VarMod::value;
using Mint = Modular<VarMod>;
*/

constexpr int md = 998244353;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
template<typename A, typename B> string to_string(const pair<A, B>& p);
template<typename A, typename B, typename C> string to_string(const tuple<A, B, C>& t);
template<typename A, typename B, typename C, typename D> string to_string(const tuple<A, B, C, D>& t);

string to_string(const string& s) {
  return '"' + s + '"';
}

string to_string(const char& c) {
  return string("'") + c + "'";
}

string to_string(const char *c) {
  return to_string(string(c));
}

string to_string(const bool& b) {
  return (b ? "true" : "false");
}

string to_string(const vector<bool>& v) {
  string res = "{";
  for (int i = 0; i < (int) v.size(); ++i) {
    if (i > 0) {
      res += ", ";
    }
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}

template<size_t T> string to_string(const bitset<T>& bs) {
  return bs.to_string();
}

template<typename T> string to_string(queue<T> q) {
  string res = "{";
  size_t sz = q.size();
  while (sz--) {
    T cur = q.front();
    q.pop();
    q.push(cur);
    if ((int) res.size() > 1) {
      res += ", ";
    }
    res += to_string(cur);
  }
  res += "}";
  return res;
}

template<typename T, class C> string to_string(priority_queue<T, vector<T>, C> pq) {
  vector<T> tmp;
  string res = "{";
  while (!pq.empty()) {
    T cur = pq.top();
    pq.pop();
    if ((int) res.size() > 1) {
      res += ", ";
    }
    res += to_string(cur);
    tmp.push_back(cur);
  }
  for (auto el : tmp) {
    pq.push(el);
  }
  res += "}";
  return res;
}

template<typename T> string to_string(const T& v) {
  string res = "{";
  for (auto &el : v) {
    if ((int) res.size() > 1) {
      res += ", ";
    }
    res += to_string(el);
  }
  res += "}";
  return res;
}

template<typename A, typename B> string to_string(const pair<A, B>& p) {
  return '(' + to_string(p.first) + ", " + to_string(p.second) + ')';
}
template<typename A, typename B, typename C> string to_string(const tuple<A, B, C>& t) {
  return '(' + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ')';
}
template<typename A, typename B, typename C, typename D> string to_string(const tuple<A, B, C, D>& t) {
  return '(' + to_string(get<0>(t)) + ", " + to_string(get<1>(t)) + ", " + to_string(get<2>(t)) + ", " + to_string(get<3>(t)) + ')';
}

void debug_out(int size, bool first, string name) {
  vector<string> tmp = {name};
  vector<int> tmp2 = {size, first};
  cerr << endl;
}

constexpr int buffer_size = 255;

template<typename Head, typename... Tail> void debug_out(int size, bool first, string name, Head H, Tail... T) {
  string tmp;
  int off = 0;
  while ((!name.empty() && name[0] != ',') || off != 0) {
    tmp += name[0];
    name.erase(name.begin());
    char c = tmp.back();
    if (c == '{' || c == '(') {
      ++off;
    } else if (c == '}' || c == ')'){
      --off;
    }
  }
  if (!name.empty()) {
    name.erase(name.begin());
  }
  if (tmp[0] == ' ') {
    tmp.erase(tmp.begin());
  }

  string buff = to_string(H);
  if ((int) buff.size() + size + (int) tmp.size() > buffer_size - 5 && !first) {
    cerr << '\n';
    size = 0;
  }
  cerr << '[' << tmp << ": " << buff << "] ";
  debug_out(((int) buff.size() + size + (int) tmp.size() + 5) % buffer_size, false, name, T...);
}

#ifdef DEBUG
#define debug(...) cerr << "-> ", debug_out(3, true, string(#__VA_ARGS__), __VA_ARGS__)
#define here cerr << "-> " << __LINE__ << endl
#else
#define debug(...) void(37)
#define here void(37)
#endif
 
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  int n;
  cin >> n;
  vector<Mint> dp(n + 1);
  dp[1] = 1;
  Mint pref = 1;
  for (int i = 1; i <= n; ++i) {
    for (int j = i * 2; j <= n; j += i) {
      dp[j]++;
    }   
    dp[i] += pref;
    if (i == 1) {
      --dp[i];
    }
    pref += dp[i];
  }
  cout << dp[n] << '\n';
}