Black Boxes

Problem Statement

You have a two-dimensional plane, initially the plane is white. On this two-dimensional plane you will perform $n$ queries on this plane:

• Each query is given $l$, $r$ and $h$
• Colour the rectangle $(l, 0)$ to $(r, h)$ At the end of all $n$ queries, determine the total area which is black.

Input Format

Your first line will contain a single integer $n$. Your next $n$ lines will contain three integers each, representing $l$, $r$ and $h$ respectively.

Output Format

Output the total number of area that is coloured black after performing all queries.

Constraints

• $1 \leq n \leq 10^5$
• $0 \leq l \leq r \leq 10^9$
• $1 \leq h \leq 10^9$

Sample Cases

3
0 1 1
0 3 3
2 4 2

11

2
0 100000 100000
1 99999 100001

10000099998

Template

n = int(input())
rectangles = [tuple(map(int, input().split())) for _ in range(n)]

# print your output