<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:
        m, n = len(grid), len(grid[0])

        flatten = []
        for i in range(m):
            for j in range(n):
                flatten.append((i, j, grid[i][j]))

        flatten.sort(key=lambda x: x[2])

        # bottom ups
        # i in range [0, m * n]
        # visited in range [0, (1 << m)]
        # init value is 0
        dp = [[0 for _ in range(1 << (m + 1))] for _ in range(m * n + 1)]

        ans = 0
        for i in range(m * n):
            r, _, v = flatten[i]
            for visited in range(1 << (m + 1)):
                dp[i][visited] = max(dp[i][visited], dp[i - 1][visited])
                # Chech if value v in row r is selected or not
                if (1 << r) & visited == 0:
                    # Chose v in this row,
                    # Skip duplicate value on prev row
                    j = i
                    while j >= 0 and flatten[j][2] == v:
                        j -= 1
                    dp[i][visited] = max(dp[i][visited], dp[j][(1 << r) | visited] + v)
                ans = max(ans, dp[i][visited])

        return ans

20000