<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>

import heapq
class Solution:
    def maxScore(self, grid: List[List[int]]) -> int:
        value_to_rows = defaultdict(list)
        for i in range(len(grid)):
            for n in set(grid[i]):
                value_to_rows[n].append(i)
        value_to_rows = [[k, v] for k, v in value_to_rows.items()]
        @cache
        def dfs(row_index, used_rows):
            if row_index == len(value_to_rows):
                return 0
            res = dfs(row_index + 1, used_rows)
            n, rows = value_to_rows[row_index]
            for r in rows:
                if (used_rows >> r) & 1 != 0:
                    continue
                cur = n + dfs(row_index + 1, used_rows | 1 << r)
                res = max(res, cur)
            # for r in rows:
            #     if (used_rows >> r) & 1 != 0:
            #         continue
            #     cur = n + dfs(row_index + 1, used_rows | 1 << r)
            #     if cur == res:
            #         print('row_index', row_index, 'used_rows', bin(used_rows), 'res', res, 'with', n)
            return res
        return dfs(0, 0)

77720