CF1552F.Telepanting

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 $y_i \lt x_i$. 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 $998\,244\,353$.

一只蚂蚁在实数轴上以恒定速度 $1$ 单位/秒移动。它从位置 $0$ 出发，始终向右移动（即其位置每秒增加 $1$）。

共有 $n$ 个传送门，其中第 $i$ 个传送门位于位置 $x_i$，并传送到位置 $y_i \lt x_i$。每个传送门可以处于激活或未激活状态。第 $i$ 个传送门的初始状态由 $s_i$ 决定：若 $s_i = 0$，则该传送门初始为未激活；若 $s_i = 1$，则该传送门初始为激活。当蚂蚁经过某个传送门（即其位置恰好等于该传送门的位置）时：

• 若该传送门处于未激活状态，则它变为激活状态（此时蚂蚁的运动路径不受影响）；
• 若该传送门处于激活状态，则它变为未激活状态，且蚂蚁立即被传送到位置 $y_i$，之后继续按常规方式向右移动。

从蚂蚁开始移动的时刻起，它需要多长时间才能到达位置 $x_n + 1$？可以证明该过程必在有限时间内完成。由于答案可能非常大，请对 $998\,244\,353$ 取模输出结果。

The first line contains the integer $n$ ($1\le n\le 2\cdot 10^5$) — the number of portals.

The $i$-th of the next $n$ lines contains three integers $x_i$, $y_i$ and $s_i$ ($1\le y_i \lt x_i\le 10^9$, $s_i\in{0,1}$) — 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 $x_1 \lt x_2 \lt \cdots \lt x_n$. It is guaranteed that the $2n$ integers $x_1, \, x_2, \, \dots, \, x_n, \, y_1, \, y_2, \, \dots, \, y_n$ are all distinct.

第一行包含一个整数 $n$（$1\le n\le 2\cdot 10^5$）—— 表示传送门的数量。

接下来的 $n$ 行中，第 $i$ 行包含三个整数 $x_i$、$y_i$ 和 $s_i$（$1\le y_i \lt x_i\le 10^9$，$s_i\in\{0,1\}$）—— 分别表示第 $i$ 个传送门的位置、蚂蚁穿过该传送门（当其处于激活状态时）后被传送到的位置，以及该传送门的初始状态。

传送门的位置严格递增，即 $x_1 \lt x_2 \lt \cdots \lt x_n$。保证 $2n$ 个整数 $x_1,\,x_2,\,\dots,\,x_n,\,y_1,\,y_2,\,\dots,\,y_n$ 两两互不相同。

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 $998\,244\,353$.

输出蚂蚁从开始移动到到达位置 $x_n+1$ 所经过的时间（单位：秒）。由于答案可能非常大，请对 $998\,244\,353$ 取模后输出。

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 $x_n+1=899754846+1=899754847$.

第一个样例的解释：蚂蚁的移动过程如下（弯曲箭头表示传送，直线箭头表示以速度 $1$ 的正常移动，箭头上方的数字表示该次移动所花费的时间）：

$$0 \\stackrel{6}{\\longrightarrow} 6 \\leadsto 5 \\stackrel{3}{\\longrightarrow} 8 \\leadsto 1 \\stackrel{2}{\\longrightarrow} 3 \\leadsto 2 \\stackrel{4}{\\longrightarrow} 6 \\leadsto 5 \\stackrel{2}{\\longrightarrow} 7 \\leadsto 4 \\stackrel{2}{\\longrightarrow} 6 \\leadsto 5 \\stackrel{4}{\\longrightarrow} 9$$

注意，总时间为 $6+3+2+4+2+2+4=23$。

第二个样例的解释：蚂蚁的移动过程如下（弯曲箭头表示传送，直线箭头表示以速度 $1$ 的正常移动，箭头上方的数字表示该次移动所花费的时间）：

$$0 \\stackrel{454971987}{\\longrightarrow} 454971987 \\leadsto 406874902 \\stackrel{48097086}{\\longrightarrow} 454971988$$

注意，总时间为 $454971987+48097086=503069073$。

第三个样例的解释：由于所有传送门初始均处于关闭状态，蚂蚁不会被传送，而是直接从 $0$ 走到 $x_n+1=899754846+1=899754847$。