<p>There is a pizza with <code>3n</code> slices of varying size, you and your friends will take slices of pizza as follows:</p>

<ul>
	<li>You will pick <strong>any</strong> pizza slice.</li>
	<li>Your friend Alice will pick the next slice in the anti-clockwise direction of your pick.</li>
	<li>Your friend Bob will pick the next slice in the clockwise direction of your pick.</li>
	<li>Repeat until there are no more slices of pizzas.</li>
</ul>

<p>Given an integer array <code>slices</code> that represent the sizes of the pizza slices in a clockwise direction, return <em>the maximum possible sum of slice sizes that you can pick</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/18/sample_3_1723.png" style="width: 500px; height: 266px;" />
<pre>
<strong>Input:</strong> slices = [1,2,3,4,5,6]
<strong>Output:</strong> 10
<strong>Explanation:</strong> Pick pizza slice of size 4, Alice and Bob will pick slices with size 3 and 5 respectively. Then Pick slices with size 6, finally Alice and Bob will pick slice of size 2 and 1 respectively. Total = 4 + 6.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/02/18/sample_4_1723.png" style="width: 500px; height: 299px;" />
<pre>
<strong>Input:</strong> slices = [8,9,8,6,1,1]
<strong>Output:</strong> 16
<strong>Explanation:</strong> Pick pizza slice of size 8 in each turn. If you pick slice with size 9 your partners will pick slices of size 8.
</pre>

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

<ul>
	<li><code>3 * n == slices.length</code></li>
	<li><code>1 &lt;= slices.length &lt;= 500</code></li>
	<li><code>1 &lt;= slices[i] &lt;= 1000</code></li>
</ul>

class Solution {
public:
    int maxSizeSlices(vector<int>& slices) {
        int N = slices.size();
        if (N == 3)
            return max(slices[0], max(slices[1], slices[2]));

        vector<vector<vector<int>>> dp(3, vector(N / 3 + 1, vector<int>(N, -1e9)));
        dp[0][0][0] = 0, dp[0][1][0] = slices[0];
        dp[0][0][1] = 0, dp[0][1][1] = slices[0];
        dp[0][0][2] = 0, dp[0][1][2] = max(slices[0], slices[2]), dp[0][2][2] = slices[0] + slices[2];
        for (int i = 3; i < N - 1; i++)
            for (int j = 1; j <= N / 3; j++)
                dp[0][j][i] = max(dp[0][j][i - 1], max(dp[0][j - 1][i - 2], dp[0][j - 1][i - 3]) + slices[i]);
        dp[1][0][0] = 0;
        dp[1][0][1] = 0, dp[1][1][1] = slices[1];
        dp[1][0][2] = 0, dp[1][1][2] = max(slices[1], slices[2]);
        for (int i = 3; i < N; i++)
            for (int j = 1; j <= N / 3; j++)
                dp[1][j][i] = max(dp[1][j][i - 1], max(dp[1][j - 1][i - 2], dp[1][j - 1][i - 3]) + slices[i]);
        
        int ans = 0;
        for (int i = 0; i < N; i++)
            ans = max(ans, max(dp[0][N / 3][i], dp[1][N / 3][i]));
        return ans;
    }
};
20700