<p>You are given several <code>boxes</code> with different colors represented by different positive numbers.</p>

<p>You may experience several rounds to remove boxes until there is no box left. Each time you can choose some continuous boxes with the same color (i.e., composed of <code>k</code> boxes, <code>k &gt;= 1</code>), remove them and get <code>k * k</code> points.</p>

<p>Return <em>the maximum points you can get</em>.</p>

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

<pre>
<strong>Input:</strong> boxes = [1,3,2,2,2,3,4,3,1]
<strong>Output:</strong> 23
<strong>Explanation:</strong>
[1, 3, 2, 2, 2, 3, 4, 3, 1] 
----&gt; [1, 3, 3, 4, 3, 1] (3*3=9 points) 
----&gt; [1, 3, 3, 3, 1] (1*1=1 points) 
----&gt; [1, 1] (3*3=9 points) 
----&gt; [] (2*2=4 points)
</pre>

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

<pre>
<strong>Input:</strong> boxes = [1,1,1]
<strong>Output:</strong> 9
</pre>

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

<pre>
<strong>Input:</strong> boxes = [1]
<strong>Output:</strong> 1
</pre>

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

<ul>
	<li><code>1 &lt;= boxes.length &lt;= 100</code></li>
	<li><code>1 &lt;= boxes[i]&nbsp;&lt;= 100</code></li>
</ul>

class Solution {
public:
    using V = vector<int>;
    using VV = vector<vector<vector<int>>>;

    int solve(int i, int j, int s, V& a, VV& dp) {
        if (i > j) return 0;
        if (dp[i][j][s] != -1) return dp[i][j][s];
        int i1=i, s1=s;
        while (i+1 <= j && a[i] == a[i+1]) {
            s++;
            i++;
        }
        int ans = solve(i+1,j,0,a,dp)+(s+1)*(s+1);
        for (int k = i+1; k <= j; k++) if (a[i] == a[k]) {
            ans = max(ans, solve(i+1,k-1,0,a,dp) + solve(k,j,s+1,a,dp));
        }
        dp[i1][j][s1] = ans;
        return ans;
    }

    int removeBoxes(vector<int>& boxes) {
        int n = boxes.size();
        VV dp(n, vector<vector<int>>(n, V(n+1, -1)));
        return solve(0,n-1,0,boxes,dp);
    }
};
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