<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:

    @cache
    def solve(self,i,n,t,mask):
        if i == n:
            return 0
        
        ans = 0
        for j in self.mp[t[i]]:
            if (mask & 1 << j) == 0:
                ans = max( ans , t[i] + self.solve(i+1,n,t,mask | 1 << j ))

        ans = max(ans , self.solve(i+1,n,t, mask))

        return ans
        
    def maxScore(self, grid: List[List[int]]) -> int:
        m = len(grid)
        n = len(grid[0])
        s = set()

        for i in range(m):
            for j in range(n):
                s.add(grid[i][j])

        t = sorted(s,reverse=True)
        self.mp = defaultdict(list)

        for i in range(m):
            for j in range(n):
                self.mp[grid[i][j]].append(i)
        
        #self.dp = [[ -1 for _ in range(101)] for _ in range(2001)]

        return self.solve(0,len(t),tuple(t),0)
89560