<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 dfs(self, cur: int, k: int, target: int, mask: int) -> int:
        if cur == len(self.val_list):
            return 0 if k<=target else self.inf
        elif k>target:
            return self.inf
        elif (cur, mask) in self.cache:
            return self.cache[(cur, mask)]
        else:
            # 1. skip current score
            res = self.dfs(cur+1, k, target, mask)
            # 2. select current score
            for row in self.vals[self.val_list[cur]]:
                if (mask & (1<<row) != 0):
                    continue
                next_mask = (mask | (1<<row))
                score = self.val_list[cur] + self.dfs(cur+1, k+1, target, next_mask)
                res = max(res, score)
            self.cache[(cur, mask)] = res
            return res
    
    def maxScore(self, grid: List[List[int]]) -> int:
        self.vals = {}
        self.cache = {}
        self.inf = -10**10
        m = len(grid)
        n = len(grid[0])
        for i in range(m):
            for j in range(n):
                if grid[i][j] not in self.vals:
                    self.vals[grid[i][j]] = set()
                self.vals[grid[i][j]].add(i)
        self.val_list = list(self.vals.keys())
        res = self.dfs(0, 0, m, 0)
        
        return res
25920