F. Telepantingtime limit per test2 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard outputAn 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.InputThe 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.OutputOutput 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.ExamplesInput
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
NoteExplanation 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.
4
3 2 0
6 5 1
7 4 0
8 1 1

23 
['binary search', 'data structures', 'dp', 'sortings', '*2200']