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.</p>

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 A_i through B_i along the horizon (1 <= A_i < B_i <= 1,000,000,000) and has height H_i (1 <= H_i <= 1,000,000,000). Determine the area, in square units, of the aggregate silhouette formed by all N buildings.

입력 형식

• Line 1: A single integer: N
• Lines 2..N+1: Input line i+1 describes building i with three space-separated integers: A_i, B_i, and H_i
</ul>

 

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

예제 입력

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

예제 출력

16

힌트

The first building overlaps with the fourth building for an area of 1 square unit, so the total area is just 31 + 14 + 22 + 23 - 1 = 16.