3225 - Maximum Score From Grid Operations.

Hard

You are given a 2D matrix grid of size n x n. Initially, all cells of the grid are colored white. In one operation, you can select any cell of indices (i, j), and color black all the cells of the <code>j^th</code> column starting from the top row down to the <code>i^th</code> row.

The grid score is the sum of all grid[i][j] such that cell (i, j) is white and it has a horizontally adjacent black cell.

Return the maximum score that can be achieved after some number of operations.

Example 1:

Input: grid = \[\[0,0,0,0,0],0,0,3,0,0,0,1,0,0,0,5,0,0,3,0,0,0,0,0,2]

Output: 11

Explanation:

In the first operation, we color all cells in column 1 down to row 3, and in the second operation, we color all cells in column 4 down to the last row. The score of the resulting grid is grid[3][0] + grid[1][2] + grid[3][3] which is equal to 11.

Example 2:

Input: grid = \[\[10,9,0,0,15],7,1,0,8,0,5,20,0,11,0,0,0,0,1,2,8,12,1,10,3]

Output: 94

Explanation:

We perform operations on 1, 2, and 3 down to rows 1, 4, and 0, respectively. The score of the resulting grid is grid[0][0] + grid[1][0] + grid[2][1] + grid[4][1] + grid[1][3] + grid[2][3] + grid[3][3] + grid[4][3] + grid[0][4] which is equal to 94.

Constraints:

• 1 <= n == grid.length <= 100

• n == grid[i].length

• <code>0 <= gridj<= 10⁹</code>