human
Give me a Python code to compute it modulo 998 244 353 given the following:
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...
assistant
#Here is Python code to compute it modulo 998 244 353.

from bisect import bisect_left
from sys import stdin, gettrace

if gettrace():
    def inputi():
        return input()
else:
    def input():
        return next(stdin)[:-1]

    def inputi():
        return stdin.buffer.readline()

MOD = 998244353

def solve():
    n = int(input())
    xys = [[int(a) for a in input().split()] for _ in range(n)]
    vs = [0]
    xx,_,_ = list(zip(*xys))
    res = (xx[-1]+1)%MOD
    for x,y,s in xys:
        si = bisect_left(xx, y)
        v = ((x-y) + vs[-1] - vs[si])%MOD
        vs.append((vs[-1] + v)%MOD)
        if s == 1:
            res = (v+res)%MOD
    print(res)



def main():
    solve()

if __name__ == "__main__":
    main()