<p>You are given an <code>m x n</code> integer matrix <code>points</code> (<strong>0-indexed</strong>). Starting with <code>0</code> points, you want to <strong>maximize</strong> the number of points you can get from the matrix.</p>

<p>To gain points, you must pick one cell in <strong>each row</strong>. Picking the cell at coordinates <code>(r, c)</code> will <strong>add</strong> <code>points[r][c]</code> to your score.</p>

<p>However, you will lose points if you pick a cell too far from the cell that you picked in the previous row. For every two adjacent rows <code>r</code> and <code>r + 1</code> (where <code>0 &lt;= r &lt; m - 1</code>), picking cells at coordinates <code>(r, c<sub>1</sub>)</code> and <code>(r + 1, c<sub>2</sub>)</code> will <strong>subtract</strong> <code>abs(c<sub>1</sub> - c<sub>2</sub>)</code> from your score.</p>

<p>Return <em>the <strong>maximum</strong> number of points you can achieve</em>.</p>

<p><code>abs(x)</code> is defined as:</p>

<ul>
	<li><code>x</code> for <code>x &gt;= 0</code>.</li>
	<li><code>-x</code> for <code>x &lt; 0</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong><strong> </strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/12/screenshot-2021-07-12-at-13-40-26-diagram-drawio-diagrams-net.png" style="width: 300px; height: 300px;" />
<pre>
<strong>Input:</strong> points = [[1,2,3],[1,5,1],[3,1,1]]
<strong>Output:</strong> 9
<strong>Explanation:</strong>
The blue cells denote the optimal cells to pick, which have coordinates (0, 2), (1, 1), and (2, 0).
You add 3 + 5 + 3 = 11 to your score.
However, you must subtract abs(2 - 1) + abs(1 - 0) = 2 from your score.
Your final score is 11 - 2 = 9.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/07/12/screenshot-2021-07-12-at-13-42-14-diagram-drawio-diagrams-net.png" style="width: 200px; height: 299px;" />
<pre>
<strong>Input:</strong> points = [[1,5],[2,3],[4,2]]
<strong>Output:</strong> 11
<strong>Explanation:</strong>
The blue cells denote the optimal cells to pick, which have coordinates (0, 1), (1, 1), and (2, 0).
You add 5 + 3 + 4 = 12 to your score.
However, you must subtract abs(1 - 1) + abs(1 - 0) = 1 from your score.
Your final score is 12 - 1 = 11.
</pre>

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

<ul>
	<li><code>m == points.length</code></li>
	<li><code>n == points[r].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= points[r][c] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
  long long maxPoints(vector<vector<int>>& points) {
    int row = points.size(), col = points[0].size();
 
    if (row == 1) return *std::max_element(points[0].begin(), points[0].end());

    std::vector<long long> cur(col, 0), prev(col, 0);
    
    for (int i = 0; i < row; ++i) {
      long long max = 0;
      
      for (int k = 0; k < col; ++k) {
        max = std::max(max-1, prev[k]);
        cur[k] = max;
      }
      max = 0;
      for (int k = col-1; k >= 0; --k) {
        max = std::max(max-1, prev[k]);
        cur[k] = std::max(cur[k], max) + points[i][k];
      }
      prev = cur;
    }
    return *std::max_element(prev.begin(), prev.end());
  }
};
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