# City Horizon

Time Limit: 2000MS

Memory Limit: 65536K

## Description

Farmer John has taken his cows on a trip to the city! As the sun sets, the cows gaze at the city horizon and observe the beautiful silhouettes formed by the rectangular buildings.The entire horizon is represented by a number line with N (1 ≤ N ≤ 40,000) buildings. Building i's silhouette has a base that spans locations Ai through Bi along the horizon (1 ≤ Ai < Bi ≤ 1,000,000,000) and has height Hi (1 ≤ Hi ≤ 1,000,000,000). Determine the area, in square units, of the aggregate silhouette formed by all N buildings.

## Input

Line 1: A single integer: N Lines 2..N+1: Input line i+1 describes building i with three space-separated integers: Ai, Bi, and Hi

## Output

Line 1: The total area, in square units, of the silhouettes formed by all N buildings

## Sample Input

4
2 5 1
9 10 4
6 8 2
4 6 3

## Sample Output

16

## Hint

The first building overlaps with the fourth building for an area of 1 square unit, so the total area is just 3*1 + 1*4 + 2*2 + 2*3 - 1 = 16.

## Source

USACO 2007 Open Silver