<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 = len(grid)
        n = len(grid[0])
        na = []
        for i in range(m):
            for j in range(n):
                na.append([grid[i][j], i])
        na.sort(reverse=True)
        # print(na)
        @cache
        def dp(i, state):
            if (1<<m)-1 == state:
                return 0
            if i == len(na):
                return 0
            ans2 = 0
            rows = []
            j = i
            while j < len(na) and na[i][0] == na[j][0]:
                    rows.append(j)
                    j +=1
            # print("initail ", rows)
            ans2= 0
            for cri in rows:
                cr = na[cri][1]
                if (state & (1<< cr) == 0):
                    tans = dp(rows[-1]+1, state| (1<< cr))
                    if( tans != -1):
                        ans2 = max(ans2, na[i][0] + tans)
            ans = max(dp(rows[-1]+1, state), ans2)
            # print(rows)
            # print(i, state, ans, ans2)
            return  ans
        return dp(0, 0)
62920