<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>

from collections import defaultdict
from sortedcontainers import SortedDict

class Solution:
    def maxScore(self, matrix: List[List[int]]) -> int:
        m, n = len(matrix), len(matrix[0])
        dp = SortedDict()
        dp[0] = 0
        ans = 0
        
        for row in matrix:
            new_dp = SortedDict(dp)
            for state, score in dp.items():
                for value in row:
                    bitmask = 1 << value
                    if not state & bitmask:
                        new_state = state | bitmask
                        new_dp[new_state] = max(new_dp.get(new_state, 0), score + value)
                        ans = max(ans, new_dp[new_state])
            if len(new_dp) > 20000:
                new_dp = SortedDict({k: new_dp[k] for k in sorted(new_dp.keys(), key=lambda k: -new_dp[k])[:1000]})
            
            dp = new_dp
        
        return ans


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