For each subset of unique values, try to assign each value to a row where it appears (no two values in the same row).
For each subset, if assignment is possible, sum the values and update the answer.
Use bitmask DP: dp[row][mask] = max sum for first 'row' rows, using values in 'mask'.
Code

[{"language":"C++","code":"#include <vector>\n#include <unordered_map>\n#include <algorithm>\nusing namespace std;\nclass Solution {\npublic:\n    int maxScore(vector<vector<int>>& grid) {\n        int m = grid.size(), n = grid[0].size();\n        vector<int> vals;\n        unordered_map<int, vector<int>> valRows;\n        for (int i = 0; i < m; ++i)\n            for (int j = 0; j < n; ++j) {\n                int v = grid[i][j];\n                if (valRows.count(v) == 0) vals.push_back(v);\n                valRows[v].push_back(i);\n            }\n        int U = vals.size(), res = 0;\n        for (int mask = 1; mask < (1<<U); ++mask) {\n            vector<int> used(m, 0);\n            int sum = 0, ok = 1;\n            for (int i = 0; i < U; ++i) if (mask & (1<<i)) {\n                int found = 0;\n                for (int r : valRows[vals[i]]) if (!used[r]) {\n                    used[r] = 1; sum += vals[i]; found = 1; break;\n                }\n                if (!found) { ok = 0; break; }\n            }\n            if (ok) res = max(res, sum);\n        }\n        return res;\n    }\n};","lang":"cpp","html":"<pre class=\"shiki shiki-themes github-light github-dark\" style=\"background-color:#fff;--shiki-dark-bg:#24292e;color:#24292e;--shiki-dark:#e1e4e8\" tabindex=\"0\"><code><span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">#include</span><span style=\"color:#032F62;--shiki-dark:#9ECBFF\"> &#x3C;vector></span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">#include</span><span style=\"color:#032F62;--shiki-dark:#9ECBFF\"> &#x3C;unordered_map></span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">#include</span><span style=\"color:#032F62;--shiki-dark:#9ECBFF\"> &#x3C;algorithm></span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">using</span><span style=\"color:#D73A49;--shiki-dark:#F97583\"> namespace</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> std</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">;</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">class</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> Solution</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\"> {</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">public:</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;--shiki-dark:#F97583\">    int</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\"> maxScore</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">(</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\">vector</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">&#x3C;</span><span style=\"color:#6F42C1;--shiki-dark:#B392F0\">vector</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">&#x3C;</span><span style=\"color:#D73A49;--shiki-dark:#F97583\">int</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">>></span><span style=\"color:#D73A49;--shiki-dark:#F97583\">&#x26;</span><span style=\"color:#E36209;--shiki-dark:#FFAB70\"> grid</span><span style=\"color:#24292E;--shiki-dark:#E1E4E8\">) {</span></span>\n<span class=\"line\"><span style=\"color:#D73A49;-
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