There is a computer that can run an unlimited number of tasks at the same time. You are given a 2D integer array tasks where tasks[i] = [starti, endi, durationi] indicates that the ith task should run for a total of durationi seconds (not necessarily continuous) within the inclusive time range [starti, endi].

You may turn on the computer only when it needs to run a task. You can also turn it off if it is idle.

Return the minimum time during which the computer should be turned on to complete all tasks.

 

Example 1:

Input: tasks = [[2,3,1],[4,5,1],[1,5,2]]
Output: 2
Explanation: 
- The first task can be run in the inclusive time range [2, 2].
- The second task can be run in the inclusive time range [5, 5].
- The third task can be run in the two inclusive time ranges [2, 2] and [5, 5].
The computer will be on for a total of 2 seconds.

Example 2:

Input: tasks = [[1,3,2],[2,5,3],[5,6,2]]
Output: 4
Explanation: 
- The first task can be run in the inclusive time range [2, 3].
- The second task can be run in the inclusive time ranges [2, 3] and [5, 5].
- The third task can be run in the two inclusive time range [5, 6].
The computer will be on for a total of 4 seconds.

 

Constraints:

• 1 <= tasks.length <= 2000
• tasks[i].length == 3
• 1 <= starti, endi <= 2000
• 1 <= durationi <= endi - starti + 1