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문제

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 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

  • 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

 

출력

  • 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 3*1 + 1*4 + 2*2 + 2*3 - 1 = 16.