A14409 · Telepanting

题目描述

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 $998\,244\,353$ .

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 $s_i$ ( $1\le y_i < x_i\le 10^9$ , $s_i\in\{0,1\}$ ) — 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 $x_1<x_2<\cdots<x_n$ . It is guaranteed that the $2n$ integers $x_1, \, x_2, \, \dots, \, x_n, \, y_1, \, y_2, \, \dots, \, y_n$ are all distinct.

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 $998\,244\,353$ .

输入 #1

输出 #1

输入 #2

1
454971987 406874902 1

输出 #2

503069073

输入 #3

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

输出 #3

899754847

输入 #4

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

输出 #4