human
PYTHON3 solution for "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...":



Can you provide a Python program to compute it modulo 998 244 353?
assistant
#Here is Python program to compute it modulo 998 244 353.
 def find(i):
    left = 0
    right = n - 1
    if portal[0][0] >= i:
        return 0
    while left + 1 < right:
        m = (left + right) // 2
        if portal[m][0] < i:
            left = m
        else:
            right = m
    return right

N = 998244353
n = int(input())
portal = []
for _ in range(n):
    portal.append(list(map(int, input().split())))
M = portal[-1][0] + 1
for i in range(n):
    portal[i].append(find(portal[i][1]))
time = [0] * n
sum_time = [0] * (n + 1)
for j in range(n):
    time[j] = portal[j][0] - portal[j][1]
    time[j] += sum_time[j] - sum_time[portal[j][3]]
    time[j] %= N
    sum_time[j + 1] = time[j] + sum_time[j]
    sum_time[j + 1] %= N
t = portal[-1][0] + 1
for i in range(n):
    if portal[i][2]:
        t += time[i]
print(t % N)