<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:
        d = defaultdict(list)

        for i in range(len(grid)):
            grid[i] = list(set(grid[i]))
        
        allnums = []
        for i in range(len(grid)):
            for j in range(len(grid[i])):
                allnums.append(grid[i][j])
        
        allnums = list(set(allnums))
        allnums.sort(reverse=True)
        
        #print(allnums)
        
        #print(grid)

        for i in range(len(grid)):
            for j in range(len(grid[i])):
                d[grid[i][j]].append(i)
        
        visited = set()

        dp = dict()
        
        def backtrack(idx):
            if len(visited) == len(grid):
                return 0

            if idx >= len(allnums):
                return 0

            tuplevisit = tuple(sorted(visited))
            if (idx, tuplevisit) in dp:
                return dp[(idx, tuplevisit)]
            
            currnum = allnums[idx]
            
            best = backtrack(idx+1) # skip case
            
            for row in d[currnum]:
                if row in visited:
                    continue
                visited.add(row)
                best = max(best, currnum + backtrack(idx+1))
                visited.remove(row)
            
            dp[(idx, tuplevisit)] = best
            return best
        
        ans = backtrack(0)
        return ans
36280