#include <bits/stdc++.h>
using namespace std;
template <class T>
struct AffineSegmentTree {
  int sz;
  std::vector<T> sum, mult, add;
  void push(int ind, int L, int R) {
    sum[ind] *= mult[ind];
    sum[ind] += (R - L + 1) * add[ind];
    if (L != R) {
      mult[2 * ind] *= mult[ind];
      mult[2 * ind + 1] *= mult[ind];
      add[2 * ind] *= mult[ind];
      add[2 * ind] += add[ind];
      add[2 * ind + 1] *= mult[ind];
      add[2 * ind + 1] += add[ind];
    }
    add[ind] = 0;
    mult[ind] = 1;
  }
  void init(int n) {
    sz = 1;
    while (sz < n) sz *= 2;
    mult.assign(2 * sz, 1);
    sum.assign(2 * sz, 0);
    add.assign(2 * sz, 0);
  }
  void pull(int ind) { sum[ind] = sum[2 * ind] + sum[2 * ind + 1]; }
  void upd(int t, int lo, int hi, T inc, int ind = 1, int L = 0, int R = -1) {
    if (R == -1) R += sz;
    push(ind, L, R);
    if (hi < L || R < lo) return;
    if (lo <= L && R <= hi) {
      if (t == 0)
        add[ind] = inc;
      else
        mult[ind] = inc;
      push(ind, L, R);
      return;
    }
    int M = (L + R) / 2;
    upd(t, lo, hi, inc, 2 * ind, L, M);
    upd(t, lo, hi, inc, 2 * ind + 1, M + 1, R);
    pull(ind);
  }
  T qsum(int lo, int hi, int ind = 1, int L = 0, int R = -1) {
    if (R == -1) R += sz;
    push(ind, L, R);
    if (lo > R || L > hi) return 0;
    if (lo <= L && R <= hi) return sum[ind];
    int M = (L + R) / 2;
    return qsum(lo, hi, 2 * ind, L, M) + qsum(lo, hi, 2 * ind + 1, M + 1, R);
  }
};
template <int MOD, int RT>
struct Mint {
  static const int mod = MOD;
  static constexpr Mint rt() { return RT; }
  int v;
  explicit operator int() const { return v; }
  Mint() { v = 0; }
  Mint(long long _v) {
    v = int((-MOD <= _v && _v < MOD) ? _v : _v % MOD);
    if (v < 0) v += MOD;
  }
  friend bool operator==(const Mint &a, const Mint &b) { return a.v == b.v; }
  friend bool operator!=(const Mint &a, const Mint &b) { return !(a == b); }
  friend bool operator<(const Mint &a, const Mint &b) { return a.v < b.v; }
  friend bool operator>(const Mint &a, const Mint &b) { return a.v > b.v; }
  friend bool operator<=(const Mint &a, const Mint &b) { return a.v <= b.v; }
  friend bool operator>=(const Mint &a, const Mint &b) { return a.v >= b.v; }
  friend std::istream &operator>>(std::istream &in, Mint &a) {
    long long x;
    std::cin >> x;
    a = Mint(x);
    return in;
  }
  friend std::ostream &operator<<(std::ostream &os, const Mint &a) {
    return os << a.v;
  }
  Mint &operator+=(const Mint &m) {
    if ((v += m.v) >= MOD) v -= MOD;
    return *this;
  }
  Mint &operator-=(const Mint &m) {
    if ((v -= m.v) < 0) v += MOD;
    return *this;
  }
  Mint &operator*=(const Mint &m) {
    v = (long long)v * m.v % MOD;
    return *this;
  }
  Mint &operator/=(const Mint &m) { return (*this) *= inv(m); }
  friend Mint pow(Mint a, long long p) {
    Mint ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1) ans *= a;
    return ans;
  }
  friend Mint inv(const Mint &a) {
    assert(a.v != 0);
    return pow(a, MOD - 2);
  }
  Mint operator-() const { return Mint(-v); }
  Mint &operator++() { return *this += 1; }
  Mint &operator--() { return *this -= 1; }
  friend Mint operator+(Mint a, const Mint &b) { return a += b; }
  friend Mint operator-(Mint a, const Mint &b) { return a -= b; }
  friend Mint operator*(Mint a, const Mint &b) { return a *= b; }
  friend Mint operator/(Mint a, const Mint &b) { return a /= b; }
};
template <class T>
struct IntervalUnion {
  const T INF = std::numeric_limits<T>::max();
  std::set<std::pair<T, T>> le, ri;
  void reset() {
    le.clear();
    ri.clear();
  }
  std::vector<std::pair<T, T>> insert(std::pair<T, T> x) {
    std::set<std::pair<T, T>> bad;
    std::vector<std::pair<T, T>> ret;
    std::pair<T, T> use1 = {x.first, -INF}, use2 = {x.second, INF};
    auto it1 = le.lower_bound(use1);
    auto it2 = ri.lower_bound(use2);
    if (it2 != ri.end()) {
      T lo = it2->second, hi = it2->first;
      if (lo <= x.first && x.second <= hi) {
        ret.emplace_back(lo, hi);
        T mn = x.first, mx = x.second;
        for (auto &b : ret) {
          le.erase(b);
          ri.erase({b.second, b.first});
          mn = std::min(mn, b.first);
          mx = std::max(mx, b.second);
        }
        le.emplace(mn, mx);
        ri.emplace(mx, mn);
        return ret;
      }
    }
    if (it1 != le.end()) {
      while (it1 != le.end()) {
        auto val = (*it1);
        if (val.first <= x.second)
          bad.insert(val);
        else
          break;
        it1 = next(it1);
      }
    }
    if (it2 != ri.begin()) {
      it2 = prev(it2);
      while (true) {
        auto val = *it2;
        if (val.first >= x.first)
          bad.emplace(val.second, val.first);
        else
          break;
        if (it2 == ri.begin()) break;
        it2 = prev(it2);
      }
    }
    for (auto &b : bad) ret.emplace_back(b);
    T mn = x.first, mx = x.second;
    for (auto &b : ret) {
      le.erase(b);
      ri.erase({b.second, b.first});
      mn = std::min(mn, b.first);
      mx = std::max(mx, b.second);
    }
    le.emplace(mn, mx);
    ri.emplace(mx, mn);
    return ret;
  }
};
using mi = Mint<998244353, 5>;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, q;
  cin >> n >> q;
  vector<IntervalUnion<int>> iu(n);
  AffineSegmentTree<mi> seg;
  seg.init(n);
  while (q--) {
    int t;
    cin >> t;
    if (t == 1) {
      int l, r, x;
      cin >> l >> r >> x;
      --l, --r, --x;
      vector<pair<int, int>> use = iu[x].insert({l, r});
      for (auto &y : use) {
        seg.upd(1, max(l, y.first), min(r, y.second), 2);
      }
      if (!use.empty()) {
        for (int i = 0; i < use.size() + 1; ++i) {
          if (i == 0) {
            seg.upd(0, l, use[i].first - 1, 1);
          } else if (i != use.size()) {
            seg.upd(0, use[i - 1].second + 1, use[i].first - 1, 1);
          } else {
            seg.upd(0, use[i - 1].second + 1, r, 1);
          }
        }
      } else {
        seg.upd(0, l, r, 1);
      }
    } else {
      int l, r;
      cin >> l >> r;
      --l, --r;
      cout << seg.qsum(l, r) << '\n';
    }
  }
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

In the School of Magic in Dirtpolis a lot of interesting objects are studied on Computer Science lessons.

Consider, for example, the magic multiset. If you try to add an integer to it that is already presented in the multiset, each element in the multiset duplicates. For example, if you try to add the integer 2 to the multiset \{1, 2, 3, 3\}, you will get \{1, 1, 2, 2, 3, 3, 3, 3\}. 

If you try to add an integer that is not presented in the multiset, it is simply added to it. For example, if you try to add the integer 4 to the multiset \{1, 2, 3, 3\}, you will get \{1, 2, 3, 3, 4\}.

Also consider an array of n initially empty magic multisets, enumerated from 1 to n.

You are to answer q queries of the form "add an integer x to all multisets with indices l, l + 1, …, r" and "compute the sum of sizes of multisets with indices l, l + 1, …, r". The answers for the second type queries can be large, so print the answers modulo 998244353.

Input

The first line contains two integers n and q (1 ≤ n, q ≤ 2 ⋅ 10^{5}) — the number of magic multisets in the array and the number of queries, respectively.

The next q lines describe queries, one per line. Each line starts with an integer t (1 ≤ t ≤ 2) — the type of the query. If t equals 1, it is followed by three integers l, r, x (1 ≤ l ≤ r ≤ n, 1 ≤ x ≤ n) meaning that you should add x to all multisets with indices from l to r inclusive. If t equals 2, it is followed by two integers l, r (1 ≤ l ≤ r ≤ n) meaning that you should compute the sum of sizes of all multisets with indices from l to r inclusive.

Output

For each query of the second type print the sum of sizes of multisets on the given segment.

The answers can be large, so print them modulo 998244353.

Examples

Input

4 4
1 1 2 1
1 1 2 2
1 1 4 1
2 1 4


Output

10


Input

3 7
1 1 1 3
1 1 1 3
1 1 1 2
1 1 1 1
2 1 1
1 1 1 2
2 1 1


Output

4
8

Note

In the first example after the first two queries the multisets are equal to [\{1, 2\},\{1, 2\},\{\},\{\}], after the third query they are equal to [\{1, 1, 2, 2\},\{1, 1, 2, 2\},\{1\},\{1\}].

In the second example the first multiset evolves as follows: 

\{\} → \{3\} → \{3, 3\} → \{2, 3, 3\} → \{1, 2, 3, 3\} → \{1, 1, 2, 2, 3, 3, 3, 3\}. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class T>
struct AffineSegmentTree {
  int sz;
  std::vector<T> sum, mult, add;
  void push(int ind, int L, int R) {
    sum[ind] *= mult[ind];
    sum[ind] += (R - L + 1) * add[ind];
    if (L != R) {
      mult[2 * ind] *= mult[ind];
      mult[2 * ind + 1] *= mult[ind];
      add[2 * ind] *= mult[ind];
      add[2 * ind] += add[ind];
      add[2 * ind + 1] *= mult[ind];
      add[2 * ind + 1] += add[ind];
    }
    add[ind] = 0;
    mult[ind] = 1;
  }
  void init(int n) {
    sz = 1;
    while (sz < n) sz *= 2;
    mult.assign(2 * sz, 1);
    sum.assign(2 * sz, 0);
    add.assign(2 * sz, 0);
  }
  void pull(int ind) { sum[ind] = sum[2 * ind] + sum[2 * ind + 1]; }
  void upd(int t, int lo, int hi, T inc, int ind = 1, int L = 0, int R = -1) {
    if (R == -1) R += sz;
    push(ind, L, R);
    if (hi < L || R < lo) return;
    if (lo <= L && R <= hi) {
      if (t == 0)
        add[ind] = inc;
      else
        mult[ind] = inc;
      push(ind, L, R);
      return;
    }
    int M = (L + R) / 2;
    upd(t, lo, hi, inc, 2 * ind, L, M);
    upd(t, lo, hi, inc, 2 * ind + 1, M + 1, R);
    pull(ind);
  }
  T qsum(int lo, int hi, int ind = 1, int L = 0, int R = -1) {
    if (R == -1) R += sz;
    push(ind, L, R);
    if (lo > R || L > hi) return 0;
    if (lo <= L && R <= hi) return sum[ind];
    int M = (L + R) / 2;
    return qsum(lo, hi, 2 * ind, L, M) + qsum(lo, hi, 2 * ind + 1, M + 1, R);
  }
};
template <int MOD, int RT>
struct Mint {
  static const int mod = MOD;
  static constexpr Mint rt() { return RT; }
  int v;
  explicit operator int() const { return v; }
  Mint() { v = 0; }
  Mint(long long _v) {
    v = int((-MOD <= _v && _v < MOD) ? _v : _v % MOD);
    if (v < 0) v += MOD;
  }
  friend bool operator==(const Mint &a, const Mint &b) { return a.v == b.v; }
  friend bool operator!=(const Mint &a, const Mint &b) { return !(a == b); }
  friend bool operator<(const Mint &a, const Mint &b) { return a.v < b.v; }
  friend bool operator>(const Mint &a, const Mint &b) { return a.v > b.v; }
  friend bool operator<=(const Mint &a, const Mint &b) { return a.v <= b.v; }
  friend bool operator>=(const Mint &a, const Mint &b) { return a.v >= b.v; }
  friend std::istream &operator>>(std::istream &in, Mint &a) {
    long long x;
    std::cin >> x;
    a = Mint(x);
    return in;
  }
  friend std::ostream &operator<<(std::ostream &os, const Mint &a) {
    return os << a.v;
  }
  Mint &operator+=(const Mint &m) {
    if ((v += m.v) >= MOD) v -= MOD;
    return *this;
  }
  Mint &operator-=(const Mint &m) {
    if ((v -= m.v) < 0) v += MOD;
    return *this;
  }
  Mint &operator*=(const Mint &m) {
    v = (long long)v * m.v % MOD;
    return *this;
  }
  Mint &operator/=(const Mint &m) { return (*this) *= inv(m); }
  friend Mint pow(Mint a, long long p) {
    Mint ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1) ans *= a;
    return ans;
  }
  friend Mint inv(const Mint &a) {
    assert(a.v != 0);
    return pow(a, MOD - 2);
  }
  Mint operator-() const { return Mint(-v); }
  Mint &operator++() { return *this += 1; }
  Mint &operator--() { return *this -= 1; }
  friend Mint operator+(Mint a, const Mint &b) { return a += b; }
  friend Mint operator-(Mint a, const Mint &b) { return a -= b; }
  friend Mint operator*(Mint a, const Mint &b) { return a *= b; }
  friend Mint operator/(Mint a, const Mint &b) { return a /= b; }
};
template <class T>
struct IntervalUnion {
  const T INF = std::numeric_limits<T>::max();
  std::set<std::pair<T, T>> le, ri;
  void reset() {
    le.clear();
    ri.clear();
  }
  std::vector<std::pair<T, T>> insert(std::pair<T, T> x) {
    std::set<std::pair<T, T>> bad;
    std::vector<std::pair<T, T>> ret;
    std::pair<T, T> use1 = {x.first, -INF}, use2 = {x.second, INF};
    auto it1 = le.lower_bound(use1);
    auto it2 = ri.lower_bound(use2);
    if (it2 != ri.end()) {
      T lo = it2->second, hi = it2->first;
      if (lo <= x.first && x.second <= hi) {
        ret.emplace_back(lo, hi);
        T mn = x.first, mx = x.second;
        for (auto &b : ret) {
          le.erase(b);
          ri.erase({b.second, b.first});
          mn = std::min(mn, b.first);
          mx = std::max(mx, b.second);
        }
        le.emplace(mn, mx);
        ri.emplace(mx, mn);
        return ret;
      }
    }
    if (it1 != le.end()) {
      while (it1 != le.end()) {
        auto val = (*it1);
        if (val.first <= x.second)
          bad.insert(val);
        else
          break;
        it1 = next(it1);
      }
    }
    if (it2 != ri.begin()) {
      it2 = prev(it2);
      while (true) {
        auto val = *it2;
        if (val.first >= x.first)
          bad.emplace(val.second, val.first);
        else
          break;
        if (it2 == ri.begin()) break;
        it2 = prev(it2);
      }
    }
    for (auto &b : bad) ret.emplace_back(b);
    T mn = x.first, mx = x.second;
    for (auto &b : ret) {
      le.erase(b);
      ri.erase({b.second, b.first});
      mn = std::min(mn, b.first);
      mx = std::max(mx, b.second);
    }
    le.emplace(mn, mx);
    ri.emplace(mx, mn);
    return ret;
  }
};
using mi = Mint<998244353, 5>;
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n, q;
  cin >> n >> q;
  vector<IntervalUnion<int>> iu(n);
  AffineSegmentTree<mi> seg;
  seg.init(n);
  while (q--) {
    int t;
    cin >> t;
    if (t == 1) {
      int l, r, x;
      cin >> l >> r >> x;
      --l, --r, --x;
      vector<pair<int, int>> use = iu[x].insert({l, r});
      for (auto &y : use) {
        seg.upd(1, max(l, y.first), min(r, y.second), 2);
      }
      if (!use.empty()) {
        for (int i = 0; i < use.size() + 1; ++i) {
          if (i == 0) {
            seg.upd(0, l, use[i].first - 1, 1);
          } else if (i != use.size()) {
            seg.upd(0, use[i - 1].second + 1, use[i].first - 1, 1);
          } else {
            seg.upd(0, use[i - 1].second + 1, r, 1);
          }
        }
      } else {
        seg.upd(0, l, r, 1);
      }
    } else {
      int l, r;
      cin >> l >> r;
      --l, --r;
      cout << seg.qsum(l, r) << '\n';
    }
  }
  return 0;
}

```