<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:
        import functools

        max_grid_val = 0
        for cells in grid:
            cells.sort(reverse=True)
            i = 0
            for j in range(len(cells)):
                if j + 1 == len(cells) or cells[j] != cells[j + 1]:
                    cells[i] = cells[j]
                    i += 1
            while i < len(cells):
                cells.pop()
            max_grid_val = max(cells[0], max_grid_val)

        full_mask = (1 << len(grid)) - 1

        @functools.cache
        def find_max_sum(mask: int, upper_bound: int) -> int:
            if mask == full_mask:
                return 0
            max_sum = 0
            for i in range(len(grid)):
                if (mask & (1 << i)) != 0:
                    continue
                new_mask = mask | (1 << i)
                for val in grid[i]:
                    if val >= upper_bound:
                        continue
                    sub = find_max_sum(new_mask, val)
                    if sub is None:
                        continue
                    if max_sum is None:
                        max_sum = val + sub
                    else:
                        max_sum = max(val + sub, max_sum)
            return max_sum

        return find_max_sum(0, 201) or -1

        

            
51080