<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, grid: List[List[int]]) -> int:
        
        def dp(idx: int, mask_row: int) -> int:

            n = len(values)
            if idx == n: return 0
            
            if (idx, mask_row) in d: return d[(idx, mask_row)]
            
            ans, row = 0, values[idx][1]
            
            if (1 << row) & mask_row:
                ans+= dp(idx + 1, mask_row)
            else:
                j = idx
                while j < n and values[idx][0] == values[j][0]:
                    j += 1
                
                ans1 = values[idx][0] + dp(j, mask_row | (1 << row))
                ans2 = dp(idx + 1, mask_row)
                
                ans = max(ans1, ans2)
            
            d[(idx, mask_row)] = ans
            return ans
    


        values, d = [], defaultdict(tuple)
        
        for i, j in product(range(len(grid)), range(len(grid[0]))):
            values.append([grid[i][j], i, j])
        
        values.sort(key = lambda x: -x[0])
        
        return dp(0, 0)
129520