Interval Duration

You are given a two-dimensional list of integers intervals where each list represents an inclusive [start, end] interval.

Return the total unique duration it covers.

Constraints

• n ≤ 100,000 where n is length of intervals.

https://binarysearch.com/problems/Interval-Duration

Examples

Example 1

Input

• intervals =

[[45,60],
 [ 1, 5],
 [ 5,15],
 [ 2, 3]]

Output

• answer = 31

Explanation

The total unique covered distance is [45, 60] (duration of 16) and [1 ,15] (duration of 15).

Solution