<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:
        freq={}
        for i in range (len(grid)):
            grid[i]= list(set(grid[i]))
            for j in range(len(grid[i])):
                if grid[i][j] in freq:
                    freq[grid[i][j]].append(i)
                else:
                    freq[grid[i][j]]=[i]

        newlst = list(sorted(freq.items(),key= lambda x:x[0] ,reverse= True))
        print(newlst)
        dp= {}
        def fun(indx,string):
            if indx == len(newlst):
                return 0
            a = 0 
            if (indx,string) in dp:
                return dp[(indx,string)]
            for row in newlst[indx][1]:
                # print(string,row)
                if string[row] == "0":
                    a= max(a, newlst[indx][0]+ fun(indx+1,string[:row]+"1"+string[row+1:]))
            a= max(a,fun(indx+1,string))
            dp[(indx,string)]=a
            return a
        return fun(0,"0"*len(grid))

            
79200