Longest Interval

You are given a two-dimensional list of integers intervals where each list represents an inclusive [start, end] interval. Return the longest interval that you can make by merging any number of intersecting intervals.

Constraints

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

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

Examples

Example 1

Input

• intervals =

[[ 1, 5],
 [ 3, 8],
 [ 4, 5],
 [10,13],
 [15,17]]

Output

• answer = 8

Explanation

After merging, we have the interval [1, 8] which has a length of 8

Solution