The cows are summering near the Front Range of the Rocky Mountains, not so far from Coach Rob's house. Visible on the horizon are N mountains (N <= 100,000), for example (here, N=5):
/\ / \ /\
/ \/\ /\/ \/ \
/ \ \ / \ / \
Each mountain is an isosceles triangle whose height is exactly twice the length of its base. A mountain is described by specifying the x-coordinate of each of the two endpoints of its base; these coordinates will be positive integers that fit nicely in a 16-bit signed entity. Your task is to compute the total area of the union of these mountains.
* Line 1: A single integer, N
* Lines 2..N+1: Each line describes a single mountain with two sorted space-separated integers.
A single integer, giving the area of the union of the mountains. This area will always be an integer and will always fit into 32 signed bits.