<p>You are given an array <code>points</code> containing the coordinates of points on a 2D plane, sorted by the x-values, where <code>points[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> such that <code>x<sub>i</sub> &lt; x<sub>j</sub></code> for all <code>1 &lt;= i &lt; j &lt;= points.length</code>. You are also given an integer <code>k</code>.</p>

<p>Return <em>the maximum value of the equation </em><code>y<sub>i</sub> + y<sub>j</sub> + |x<sub>i</sub> - x<sub>j</sub>|</code> where <code>|x<sub>i</sub> - x<sub>j</sub>| &lt;= k</code> and <code>1 &lt;= i &lt; j &lt;= points.length</code>.</p>

<p>It is guaranteed that there exists at least one pair of points that satisfy the constraint <code>|x<sub>i</sub> - x<sub>j</sub>| &lt;= k</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> points = [[1,3],[2,0],[5,10],[6,-10]], k = 1
<strong>Output:</strong> 4
<strong>Explanation:</strong> The first two points satisfy the condition |x<sub>i</sub> - x<sub>j</sub>| &lt;= 1 and if we calculate the equation we get 3 + 0 + |1 - 2| = 4. Third and fourth points also satisfy the condition and give a value of 10 + -10 + |5 - 6| = 1.
No other pairs satisfy the condition, so we return the max of 4 and 1.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> points = [[0,0],[3,0],[9,2]], k = 3
<strong>Output:</strong> 3
<strong>Explanation: </strong>Only the first two points have an absolute difference of 3 or less in the x-values, and give the value of 0 + 0 + |0 - 3| = 3.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= points.length &lt;= 10<sup>5</sup></code></li>
	<li><code>points[i].length == 2</code></li>
	<li><code>-10<sup>8</sup> &lt;= x<sub>i</sub>, y<sub>i</sub> &lt;= 10<sup>8</sup></code></li>
	<li><code>0 &lt;= k &lt;= 2 * 10<sup>8</sup></code></li>
	<li><code>x<sub>i</sub> &lt; x<sub>j</sub></code> for all <code>1 &lt;= i &lt; j &lt;= points.length</code></li>
	<li><code>x<sub>i</sub></code> form a strictly increasing sequence.</li>
</ul>

import heapq

class Solution:
    def findMaxValueOfEquation(self, points: List[List[int]], k: int) -> int:
        # Initialize the priority queue (max heap)
        heap = []
        max_value = float('-inf')
        
        for xj, yj in points:
            # Remove points that are out of range from the heap
            while heap and xj - heap[0][1] > k:
                heapq.heappop(heap)
            
            # If the heap is not empty, calculate the maximum value
            if heap:
                max_value = max(max_value, -heap[0][0] + yj + xj)
            
            # Add the current point to the heap
            heapq.heappush(heap, (xj - yj, xj))
        
        return max_value

# Example usage:
solution = Solution()
points = [[1,3],[2,0],[5,10],[6,-10]]
k = 1
print(solution.findMaxValueOfEquation(points, k))  # Output: 4

points = [[0,0],[3,0],[9,2]]
k = 3
print(solution.findMaxValueOfEquation(points, k))  # Output: 3
965