You are given a 2D array of integers coordinates of length n and an integer k, where 0 <= k < n.
coordinates[i] = [xi, yi] indicates the point (xi, yi) in a 2D plane.
An increasing path of length m is defined as a list of points (x1, y1), (x2, y2), (x3, y3), ..., (xm, ym) such that:
xi < xi + 1 and yi < yi + 1 for all i where 1 <= i < m.(xi, yi) is in the given coordinates for all i where 1 <= i <= m.Return the maximum length of an increasing path that contains coordinates[k].
Example 1:
Input: coordinates = [[3,1],[2,2],[4,1],[0,0],[5,3]], k = 1
Output: 3
Explanation:
(0, 0), (2, 2), (5, 3) is the longest increasing path that contains (2, 2).
Example 2:
Input: coordinates = [[2,1],[7,0],[5,6]], k = 2
Output: 2
Explanation:
(2, 1), (5, 6) is the longest increasing path that contains (5, 6).
Constraints:
1 <= n == coordinates.length <= 105coordinates[i].length == 20 <= coordinates[i][0], coordinates[i][1] <= 109coordinates are distinct.0 <= k <= n - 1