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# 3225. Maximum Score From Grid Operations

## Description

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 `j`

column starting from the top row down to the ^{th}`i`

row.^{th}

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`

`0 <= grid[i][j] <= 10`

^{9}