<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:
        mem = dict()
        nums = []
        rowLen = len(grid)
        for i in range(rowLen):
            for num in set(grid[i]):
                nums.append((num, i))
        # (1,0), (2,0), (3,0), (4,1), (3,1), (2,1), (1,2), (1,2), (1,2)
        # (1,0), (1,2), (1,2), (1,2), (2,0), (2,1), (3,0), (3,1), (4,1)
        # (1,0), (1,2), (2,0), (2,1), (3,0), (3,1), (4,1)
        nums.sort()
        numsLen = len(nums)
        def rec(ind, mask):
            if ind >= numsLen:
                return 0
            if (ind, mask) in mem:
                return mem[(ind, mask)]
            num, row = nums[ind]
            ans = 0
            if (1 << row) & mask == 0:
                nextInd = ind + 1
                while nextInd < numsLen and nums[nextInd][0] == num:
                    nextInd += 1
                ans = num + rec(nextInd, mask | 1 << row)
            ans = max(ans, rec(ind+1, mask))
            mem[(ind, mask)] = ans
            return ans
        return rec(0, 0)


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