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# Set Intersection

Problem Description

An integer interval [X, Y] (for integers X < Y) is a set of all consecutive integers from X to Y, including X and Y.
You are given a 2D array A with dimensions N x 2, where each row denotes an interval.
Find the minimum size of a set S such that for every integer interval Z in A, the intersection of S with Z has a size of at least two.

Problem Constraints
1 <= N <= 105
1 <= A[i][0] < A[i][1] <= 109

Input Format
The first argument is a 2D integer array A.

Output Format
Return a single integer denoting the minimum size of S.

Example Input
Input 1:

``````A = [[1, 3], [1, 4], [2, 5], [3, 5]]
``````

Input 2:

``````A = [[1, 2], [2, 3], [2, 4], [4, 5]]
``````

Example Output
Output 1:

``````3
``````

Output 2:

``````5
``````

Example Explanation
Explanation 1:

``````Consider the set S = {2, 3, 4}.  For each interval, there are at least 2 elements from S in the interval.
Also, there isn't a smaller size set that fulfills the above condition.
Thus, we output the size of this set, which is 3.``````

Explanation 2:

``````An example of a minimum sized set is {1, 2, 3, 4, 5}.
``````

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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