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Length of the Longest Increasing Path

You are given a 2D array of integers coordinates of length n and an integer k, where 0 <= k < n.

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:

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 <= 10^5
  • coordinates[i].length == 2
  • 0 <= coordinates[i][0], coordinates[i][1] <= 10^9
  • All elements in coordinates are distinct.
  • 0 <= k <= n - 1

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