<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])
        ans = 0
        valList = []
        for r in range(m):
            for c in range(n):
                valList.append((grid[r][c],r))
        total = 2**m
        #dp[mask][k]: (score,set), max score with mask and k is the last num in
        dp = [[[float('-inf'),set()] for i in range(101)] for mask in range(total)]
        for i in range(101):
            dp[0][i][0] = 0
        
        for mask in range(total):
            for i in range(101):
                if(dp[mask][i][0] == float('-inf')):
                    continue

                for v,r in valList:
                    if(mask>>r&1):
                        continue
                    if(v in dp[mask][i][1]):
                        continue
                    
                    nextMask = mask|(1<<r)

                    if(dp[nextMask][v][0]<dp[mask][i][0]+v):
                        dp[nextMask][v][0] = dp[mask][i][0]+v
                        dp[nextMask][v][1] = set(dp[mask][i][1])
                        dp[nextMask][v][1].add(v)
                        ans = max(ans,dp[nextMask][v][0])
                #print(dp)                        
        return ans
61440