Disjoint Intervals

Given a set of N intervals denoted by 2D array A of size N x 2, the task is to find the length of maximal set of mutually disjoint intervals.

Two intervals [x, y] & [p, q] are said to be disjoint if they do not have any point in common.

Return a integer denoting the length of maximal set of mutually disjoint intervals.

1 <= N <= 10⁵

1 <= A[i][0] <= A[i][1] <= 10⁹

First and only argument is a 2D array A of size N x 2 denoting the N intervals.

Return a integer denoting the length of maximal set of mutually disjoint intervals.

Input 1:

 A = [
       [1, 4]
       [2, 3]
       [4, 6]
       [8, 9]
     ]

Input 2:

 A = [
       [1, 9]
       [2, 3]
       [5, 7]
     ]

Output 1:

 3

Output 2:

 2

Explanation 1:

 Intervals: [ [1, 4], [2, 3], [4, 6], [8, 9] ]
 Intervals [2, 3] and [1, 4] overlap.
 We must include [2, 3] because if [1, 4] is included thenwe cannot include [4, 6].
 We can include at max three disjoint intervals: [[2, 3], [4, 6], [8, 9]]

Explanation 2:

 Intervals: [ [1, 9], [2, 3], [5, 7] ]
 We can include at max two disjoint intervals: [[2, 3], [5, 7]]