757 - Set Intersection Size At Least Two.

Hard

You are given a 2D integer array intervals where <code>intervalsi = start_i, end_i</code> represents all the integers from <code>start_i</code> to <code>end_i</code> inclusively.

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

• For example, if intervals = [[1,3], [3,7], [8,9]], then [1,2,4,7,8,9] and [2,3,4,8,9] are containing sets.

Return the minimum possible size of a containing set.

Example 1:

Input: intervals = [1,3,3,7,8,9]

Output: 5

Explanation: let nums = 2, 3, 4, 8, 9. It can be shown that there cannot be any containing array of size 4.

Example 2:

Input: intervals = [1,3,1,4,2,5,3,5]

Output: 3

Explanation: let nums = 2, 3, 4. It can be shown that there cannot be any containing array of size 2.

Example 3:

Input: intervals = [1,2,2,3,2,4,4,5]

Output: 5

Explanation: let nums = 1, 2, 3, 4, 5. It can be shown that there cannot be any containing array of size 4.

Constraints:

• 1 <= intervals.length <= 3000

• intervals[i].length == 2

• <code>0 <= start_i< end_i<= 10⁸</code>