<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:
        # l = []
        # rows, cols = len(grid), len(grid[0])
        # for i in range(rows):
        #     for j in range(cols):
        #         l.append((grid[i][j], i))
        # l.sort()
        # print(l)

        # @cache
        # def dp(n, mask):
        #     if n < 0:
        #         return 0
        #     pos = bisect_left(l, (l[n][0], 0))
        #     print(f'curr = {l[n]} n = {n} pos = {pos}')
        #     ans = dp(pos-1, mask)
        #     for j in range(n, -1, -1):
        #         if l[j][0] < l[n][0]: break
        #         if mask ^ (1 << l[j][1]):
        #             print(f'using val = {l[j][0]}')
        #             ans = max(ans, l[j][0] + dp(pos-1, mask | (1 << l[j][1])))
        #     print(f'ans = {ans} n = {n} mask = {mask}')
        #     return ans

        l = [[] for _ in range(101)]
        rows, cols = len(grid), len(grid[0])
        for i in range(rows):
            for j in range(cols):
                l[grid[i][j]].append(i)
        
        print(l)
        @cache
        def dp(i, mask):
            if i == -1:
                return 0
            ans = dp(i-1, mask)
            for r in l[i]:
                if ((mask >> r) & 1) == 0:
                    ans = max(ans, i + dp(i-1, mask | (1 << r)))
            # print(f' i = {i} mask = {mask} ans = {ans} ')
            return ans
        
        return dp(100, 0)
        
125080