<p>You are installing a billboard and want it to have the largest height. The billboard will have two steel supports, one on each side. Each steel support must be an equal height.</p>

<p>You are given a collection of <code>rods</code> that can be welded together. For example, if you have rods of lengths <code>1</code>, <code>2</code>, and <code>3</code>, you can weld them together to make a support of length <code>6</code>.</p>

<p>Return <em>the largest possible height of your billboard installation</em>. If you cannot support the billboard, return <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> rods = [1,2,3,6]
<strong>Output:</strong> 6
<strong>Explanation:</strong> We have two disjoint subsets {1,2,3} and {6}, which have the same sum = 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> rods = [1,2,3,4,5,6]
<strong>Output:</strong> 10
<strong>Explanation:</strong> We have two disjoint subsets {2,3,5} and {4,6}, which have the same sum = 10.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> rods = [1,2]
<strong>Output:</strong> 0
<strong>Explanation:</strong> The billboard cannot be supported, so we return 0.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= rods.length &lt;= 20</code></li>
	<li><code>1 &lt;= rods[i] &lt;= 1000</code></li>
	<li><code>sum(rods[i]) &lt;= 5000</code></li>
</ul>

class Solution {
public:
    int tallestBillboard(vector<int>& rods) {
        unordered_map<int, int> left;
        unordered_map<int, int> right;

        auto enumerate = [](int idx, const vector<int>& vec, unordered_map<int, int>& hash, int left, int diff, auto Dfs) -> void {
            if (idx == vec.size()) {
                hash[diff] = max(hash[diff], left);
                return;
            }

            int right = left - diff;
            int element = vec[idx];
            Dfs(idx + 1, vec, hash, left + element, diff + element, Dfs);
            Dfs(idx + 1, vec, hash, left, diff - element, Dfs);
            Dfs(idx + 1, vec, hash, left, diff, Dfs);
        };

        vector<int> left_rods;
        for (int i = 0; i < rods.size() / 2; i++) {
            left_rods.push_back(rods[i]);
        }
        vector<int> right_rods;
        for (int i = rods.size() / 2; i < rods.size(); i++) {
            right_rods.push_back(rods[i]);
        }

        enumerate(0, left_rods, left, 0, 0, enumerate);
        enumerate(0, right_rods, right, 0, 0, enumerate);

        int answer = 0;
        for (auto [diff, left] : left) {
            if (right.find(-diff) != right.end()) {
                answer = max(answer, left + right[-diff]);
            }
        }
        return answer;
    }
};
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