Set Intersection Size At Least Two

You are given a 2D integer array intervals where intervals[i] = [starti, endi] represents all the integers from starti to endi inclusively.

A containing set is an array nums where each interval from intervals has at least two integers in nums.

Return the minimum possible size of a containing set.

Example 1

1---3
    3-------7
              8-9

Inputintervals = [[1,3],[3,7],[8,9]]

Output5

Using nums = [2, 3, 4, 8, 9] works, and it can be shown that no containing array of size 4 exists.

Example 2

1---3
1-----4
  2-----5
    3---5

Inputintervals = [[1,3],[1,4],[2,5],[3,5]]

Output3

Using nums = [2, 3, 4] works, and it can be shown that no containing array of size 2 exists.

Constraints