<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):
        rowNumByVal = {}
        m = len(grid)
        for i in range(m):
            for val in grid[i]:
                if val not in rowNumByVal:
                    rowNumByVal[val] = set()
                rowNumByVal[val].add(i)
        numSet = list(rowNumByVal.keys())
        numSet.sort(reverse = True)

        n = len(numSet)
        memo = [{} for _ in range(n)]
        def dfs(i,j):
            if i == n: return 0
            if j in memo[i]: return memo[i][j]
            res = dfs(i+1, j)
            for row in rowNumByVal[numSet[i]]:
                if j & (1 << row) ==0:
                    res = max(res, numSet[i] + dfs(i+1, j | (1<< row)))

            memo[i][j] = res
            return res
        return dfs(0,0)
    

# Example usage:
# grid = [[1, 2], [3, 4]]
# solution = Solution()
# print(solution.maxScore(grid))
        
33320