<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:
        values_map = defaultdict(set)
        m,n = len(grid), len(grid[0])
        for i in range(m):
            for j in range(n):
                values_map[grid[i][j]].add(i)
        
        uniq_vals = sorted(values_map.keys())
        uniq_vals.reverse()
        max_ind = len(uniq_vals)
        row_set = 0


        @cache
        def get_max_score(uniq_val_ind, row_set):
            
            if uniq_val_ind == max_ind:
                return 0
            # print(row_set, uniq_vals[uniq_val_ind])
            
            score = 0
            for row in values_map[uniq_vals[uniq_val_ind]]:
                if not (1<<row  & row_set):
                    row_set |= 1<<row
                    score = max(uniq_vals[uniq_val_ind] + get_max_score(uniq_val_ind+1, row_set), score)
                    row_set ^= 1<<row
            else:
                score = max(get_max_score(uniq_val_ind+1, row_set), score)
            return score
        
        return max(uniq_vals[0]+ get_max_score(1, 0 | 1<<row) for row in values_map[uniq_vals[0]])





        
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