#include <bits/stdc++.h>
using namespace std;
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cerr << ' ' << H;
  dbg_out(T...);
}
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(int64_t v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(uint64_t v) {
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(int v) : _m_int(int64_t(v)) {}
  _m_int(unsigned v) : _m_int(uint64_t(v)) {}
  explicit operator int() const { return val; }
  explicit operator unsigned() const { return val; }
  explicit operator int64_t() const { return val; }
  explicit operator uint64_t() const { return val; }
  explicit operator double() const { return val; }
  explicit operator long double() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val -= MOD - other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return unsigned(x % m);
    unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod(uint64_t(val) * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  friend bool operator==(const _m_int &a, const _m_int &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const _m_int &a, const _m_int &b) {
    return a.val != b.val;
  }
  friend bool operator<(const _m_int &a, const _m_int &b) {
    return a.val < b.val;
  }
  friend bool operator>(const _m_int &a, const _m_int &b) {
    return a.val > b.val;
  }
  friend bool operator<=(const _m_int &a, const _m_int &b) {
    return a.val <= b.val;
  }
  friend bool operator>=(const _m_int &a, const _m_int &b) {
    return a.val >= b.val;
  }
  static const int SAVE_INV = int(1e6) + 5;
  static _m_int save_inv[SAVE_INV];
  static void prepare_inv() {
    for (int64_t p = 2; p * p <= MOD; p += p % 2 + 1) assert(MOD % p != 0);
    save_inv[0] = 0;
    save_inv[1] = 1;
    for (int i = 2; i < SAVE_INV; i++)
      save_inv[i] = save_inv[MOD % i] * (MOD - MOD / i);
  }
  _m_int inv() const {
    if (save_inv[1] == 0) prepare_inv();
    if (val < SAVE_INV) return save_inv[val];
    _m_int product = 1;
    int v = val;
    while (v >= SAVE_INV) {
      product *= MOD - MOD / v;
      v = MOD % v;
    }
    return product * save_inv[v];
  }
  _m_int pow(int64_t p) const {
    if (p < 0) return inv().pow(-p);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      p >>= 1;
      if (p > 0) a *= a;
    }
    return result;
  }
  friend ostream &operator<<(ostream &os, const _m_int &m) {
    return os << m.val;
  }
};
template <const int &MOD>
_m_int<MOD> _m_int<MOD>::save_inv[_m_int<MOD>::SAVE_INV];
const int MOD = 998244353;
using mint = _m_int<MOD>;
const int MXN = 1e5 + 5, INF = 1e9 + 5;
void solve() {
  int N;
  cin >> N;
  vector<int> loc(N + 1), teleport(N + 1), state(N + 1);
  for (int i = 1; i <= N; i++) cin >> loc[i] >> teleport[i] >> state[i];
  loc[0] = loc[1];
  teleport[0] = teleport[1];
  state[0] = state[1];
  vector<int> closest(N + 1);
  for (int i = 1; i <= N; i++)
    closest[i] =
        upper_bound(loc.begin() + 1, loc.end(), teleport[i]) - loc.begin();
  closest[0] = closest[1];
  vector<mint> time_taken(N + 1, 0);
  mint ans = loc[1];
  for (int i = 1; i <= N; i++) {
    time_taken[i] = loc[closest[i]] - teleport[i] + time_taken[i - 1] -
                    time_taken[closest[i] - 1];
    ans += loc[i] - loc[i - 1];
    if (state[i] == 1) ans += time_taken[i];
    if (i < N) time_taken[i] += loc[i + 1] - loc[i];
    time_taken[i] += time_taken[i - 1];
  }
  cout << ans + 1;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int TC = 1;
  while (TC--) solve();
}

### Prompt

Your task is to create a cpp solution to the following problem:

An ant moves on the real line with constant speed of 1 unit per second. It starts at 0 and always moves to the right (so its position increases by 1 each second).

There are n portals, the i-th of which is located at position x_i and teleports to position y_i < x_i. Each portal can be either active or inactive. The initial state of the i-th portal is determined by s_i: if s_i=0 then the i-th portal is initially inactive, if s_i=1 then the i-th portal is initially active. When the ant travels through a portal (i.e., when its position coincides with the position of a portal): 

  * if the portal is inactive, it becomes active (in this case the path of the ant is not affected); 
  * if the portal is active, it becomes inactive and the ant is instantly teleported to the position y_i, where it keeps on moving as normal. 



How long (from the instant it starts moving) does it take for the ant to reach the position x_n + 1? It can be shown that this happens in a finite amount of time. Since the answer may be very large, compute it modulo 998 244 353.

Input

The first line contains the integer n (1≤ n≤ 2⋅ 10^5) — the number of portals.

The i-th of the next n lines contains three integers x_i, y_i and s_i (1≤ y_i < x_i≤ 10^9, s_i∈\{0,1\}) — the position of the i-th portal, the position where the ant is teleported when it travels through the i-th portal (if it is active), and the initial state of the i-th portal.

The positions of the portals are strictly increasing, that is x_1<x_2<⋅⋅⋅<x_n. It is guaranteed that the 2n integers x_1,   x_2,   ...,   x_n,   y_1,   y_2,   ...,   y_n are all distinct.

Output

Output the amount of time elapsed, in seconds, from the instant the ant starts moving to the instant it reaches the position x_n+1. Since the answer may be very large, output it modulo 998 244 353.

Examples

Input


4
3 2 0
6 5 1
7 4 0
8 1 1


Output


23


Input


1
454971987 406874902 1


Output


503069073


Input


5
243385510 42245605 0
644426565 574769163 0
708622105 208990040 0
786625660 616437691 0
899754846 382774619 0


Output


899754847


Input


5
200000000 100000000 1
600000000 400000000 0
800000000 300000000 0
900000000 700000000 1
1000000000 500000000 0


Output


3511295

Note

Explanation of the first sample: The ant moves as follows (a curvy arrow denotes a teleporting, a straight arrow denotes normal movement with speed 1 and the time spent during the movement is written above the arrow). $$$ 0 \stackrel{6}{\longrightarrow} 6 \leadsto 5 \stackrel{3}{\longrightarrow} 8 \leadsto 1 \stackrel{2}{\longrightarrow} 3 \leadsto 2 \stackrel{4}{\longrightarrow} 6 \leadsto 5 \stackrel{2}{\longrightarrow} 7 \leadsto 4 \stackrel{2}{\longrightarrow} 6 \leadsto 5 \stackrel{4}{\longrightarrow} 9  Notice that the total time is 6+3+2+4+2+2+4=23$$$.

Explanation of the second sample: The ant moves as follows (a curvy arrow denotes a teleporting, a straight arrow denotes normal movement with speed 1 and the time spent during the movement is written above the arrow). $$$ 0 \stackrel{454971987}{\longrightarrow} 454971987 \leadsto 406874902 \stackrel{48097086}{\longrightarrow} 454971988  Notice that the total time is 454971987+48097086=503069073$$$.

Explanation of the third sample: Since all portals are initially off, the ant will not be teleported and will go straight from 0 to x_n+1=899754846+1=899754847.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
void dbg_out() { cerr << endl; }
template <typename Head, typename... Tail>
void dbg_out(Head H, Tail... T) {
  cerr << ' ' << H;
  dbg_out(T...);
}
template <const int &MOD>
struct _m_int {
  int val;
  _m_int(int64_t v = 0) {
    if (v < 0) v = v % MOD + MOD;
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(uint64_t v) {
    if (v >= MOD) v %= MOD;
    val = int(v);
  }
  _m_int(int v) : _m_int(int64_t(v)) {}
  _m_int(unsigned v) : _m_int(uint64_t(v)) {}
  explicit operator int() const { return val; }
  explicit operator unsigned() const { return val; }
  explicit operator int64_t() const { return val; }
  explicit operator uint64_t() const { return val; }
  explicit operator double() const { return val; }
  explicit operator long double() const { return val; }
  _m_int &operator+=(const _m_int &other) {
    val -= MOD - other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  _m_int &operator-=(const _m_int &other) {
    val -= other.val;
    if (val < 0) val += MOD;
    return *this;
  }
  static unsigned fast_mod(uint64_t x, unsigned m = MOD) {
    return unsigned(x % m);
    unsigned x_high = unsigned(x >> 32), x_low = unsigned(x);
    unsigned quot, rem;
    asm("divl %4\n" : "=a"(quot), "=d"(rem) : "d"(x_high), "a"(x_low), "r"(m));
    return rem;
  }
  _m_int &operator*=(const _m_int &other) {
    val = fast_mod(uint64_t(val) * other.val);
    return *this;
  }
  _m_int &operator/=(const _m_int &other) { return *this *= other.inv(); }
  friend _m_int operator+(const _m_int &a, const _m_int &b) {
    return _m_int(a) += b;
  }
  friend _m_int operator-(const _m_int &a, const _m_int &b) {
    return _m_int(a) -= b;
  }
  friend _m_int operator*(const _m_int &a, const _m_int &b) {
    return _m_int(a) *= b;
  }
  friend _m_int operator/(const _m_int &a, const _m_int &b) {
    return _m_int(a) /= b;
  }
  _m_int &operator++() {
    val = val == MOD - 1 ? 0 : val + 1;
    return *this;
  }
  _m_int &operator--() {
    val = val == 0 ? MOD - 1 : val - 1;
    return *this;
  }
  _m_int operator++(int) {
    _m_int before = *this;
    ++*this;
    return before;
  }
  _m_int operator--(int) {
    _m_int before = *this;
    --*this;
    return before;
  }
  _m_int operator-() const { return val == 0 ? 0 : MOD - val; }
  friend bool operator==(const _m_int &a, const _m_int &b) {
    return a.val == b.val;
  }
  friend bool operator!=(const _m_int &a, const _m_int &b) {
    return a.val != b.val;
  }
  friend bool operator<(const _m_int &a, const _m_int &b) {
    return a.val < b.val;
  }
  friend bool operator>(const _m_int &a, const _m_int &b) {
    return a.val > b.val;
  }
  friend bool operator<=(const _m_int &a, const _m_int &b) {
    return a.val <= b.val;
  }
  friend bool operator>=(const _m_int &a, const _m_int &b) {
    return a.val >= b.val;
  }
  static const int SAVE_INV = int(1e6) + 5;
  static _m_int save_inv[SAVE_INV];
  static void prepare_inv() {
    for (int64_t p = 2; p * p <= MOD; p += p % 2 + 1) assert(MOD % p != 0);
    save_inv[0] = 0;
    save_inv[1] = 1;
    for (int i = 2; i < SAVE_INV; i++)
      save_inv[i] = save_inv[MOD % i] * (MOD - MOD / i);
  }
  _m_int inv() const {
    if (save_inv[1] == 0) prepare_inv();
    if (val < SAVE_INV) return save_inv[val];
    _m_int product = 1;
    int v = val;
    while (v >= SAVE_INV) {
      product *= MOD - MOD / v;
      v = MOD % v;
    }
    return product * save_inv[v];
  }
  _m_int pow(int64_t p) const {
    if (p < 0) return inv().pow(-p);
    _m_int a = *this, result = 1;
    while (p > 0) {
      if (p & 1) result *= a;
      p >>= 1;
      if (p > 0) a *= a;
    }
    return result;
  }
  friend ostream &operator<<(ostream &os, const _m_int &m) {
    return os << m.val;
  }
};
template <const int &MOD>
_m_int<MOD> _m_int<MOD>::save_inv[_m_int<MOD>::SAVE_INV];
const int MOD = 998244353;
using mint = _m_int<MOD>;
const int MXN = 1e5 + 5, INF = 1e9 + 5;
void solve() {
  int N;
  cin >> N;
  vector<int> loc(N + 1), teleport(N + 1), state(N + 1);
  for (int i = 1; i <= N; i++) cin >> loc[i] >> teleport[i] >> state[i];
  loc[0] = loc[1];
  teleport[0] = teleport[1];
  state[0] = state[1];
  vector<int> closest(N + 1);
  for (int i = 1; i <= N; i++)
    closest[i] =
        upper_bound(loc.begin() + 1, loc.end(), teleport[i]) - loc.begin();
  closest[0] = closest[1];
  vector<mint> time_taken(N + 1, 0);
  mint ans = loc[1];
  for (int i = 1; i <= N; i++) {
    time_taken[i] = loc[closest[i]] - teleport[i] + time_taken[i - 1] -
                    time_taken[closest[i] - 1];
    ans += loc[i] - loc[i - 1];
    if (state[i] == 1) ans += time_taken[i];
    if (i < N) time_taken[i] += loc[i + 1] - loc[i];
    time_taken[i] += time_taken[i - 1];
  }
  cout << ans + 1;
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  int TC = 1;
  while (TC--) solve();
}

```