<p>You are given a 2D matrix <code>grid</code> consisting of positive integers.</p>

<p>You have to select <em>one or more</em> cells from the matrix such that the following conditions are satisfied:</p>

<ul>
	<li>No two selected cells are in the <strong>same</strong> row of the matrix.</li>
	<li>The values in the set of selected cells are <strong>unique</strong>.</li>
</ul>

<p>Your score will be the <strong>sum</strong> of the values of the selected cells.</p>

<p>Return the <strong>maximum</strong> score you can achieve.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[1,2,3],[4,3,2],[1,1,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">8</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/07/29/grid1drawio.png" /></p>

<p>We can select the cells with values 1, 3, and 4 that are colored above.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[8,7,6],[8,3,2]]</span></p>

<p><strong>Output:</strong> <span class="example-io">15</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/07/29/grid8_8drawio.png" style="width: 170px; height: 114px;" /></p>

<p>We can select the cells with values 7 and 8 that are colored above.</p>
</div>

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

<ul>
	<li><code>1 &lt;= grid.length, grid[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 100</code></li>
</ul>

class Solution:
    def maxScore(self, gridI: List[List[int]]) -> int:
        for x in gridI:
            x.sort(reverse=True)
        memo = {}
        def auxi(grid):
            clave = ''
            for x in grid:
                for z in x:
                    clave += str(z) + ':'
            if clave in memo:
                return memo[clave]

            if len(grid) == 1:
                if len(grid[0]) == 0:
                    return 0
                return max(grid[0])

            ret = 0
            for c in range(len(grid[0])):
                valor = grid[0][c]
                m1 = []
                m2 = []
                for fi in range(1,len(grid)):
                    mifila1 = []
                    for ci in range(len(grid[0])):
                        if grid[fi][ci] == valor:
                            mifila1.append(0)
                        else:
                            mifila1.append(grid[fi][ci])
                    m1.append(mifila1)
                    m2.append(list(grid[fi]))

                a = valor + auxi(m1)
                b = auxi(m2)
                ret = max(ret, a, b)
            memo[clave] = ret
            return ret

        return auxi(gridI)
34800