<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 functools import lru_cache

class Solution(object):
    def maxScore(self, grid):
        """
        :type grid: List[List[int]]
        :rtype: int
        """
        rows = len(grid)
        columns = len(grid[0])
        arr = defaultdict(set)

        for i in range(rows):
            for j in range(columns):
                arr[grid[i][j]].add(i)
        
        list_values = list(arr.items())
        list_values = [(x[0], list(x[1])) for x in list_values]

        @lru_cache(None)
        def find_ans(idx, dp_mask):
            if idx == len(list_values): return 0
            elem = list_values[idx][0]
            list_idx = list_values[idx][1]
            ans = 0
            for i in range(len(list_idx)):
                row_idx = list_idx[i]
                if dp_mask&1<<row_idx == 0:
                    ans = max(ans, elem + find_ans(idx+1, dp_mask^1<<row_idx))

            ans = max(ans, find_ans(idx+1, dp_mask))
            
            return ans
        
        return find_ans(0, 0)
74760