<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:
    def maxSizeSlices(self, slices: List[int]) -> int:
        
        REM = len(slices)//3
        oute = 0

        prevtook = [{0: 0, 1: 0} for i in range(REM+1)]
        prevnot = [{0: 0, 1: 0} for i in range(REM+1)]
        curtook = [{0: 0, 1: 0} for i in range(REM+1)]
        curnot = [{0: 0, 1: 0} for i in range(REM+1)]
        newcurtook = [{0: 0, 1: 0} for i in range(REM+1)]
        newcurnot = [{0: 0, 1: 0} for i in range(REM+1)]

        curtook[1][1] = slices[0]


        for i in range(1, len(slices)):
            for j in range(1, REM+1):
                for key in (0, 1):
                    if key == 0 or i < len(slices)-1:
                        newcurtook[j][key] = slices[i]+curnot[j-1][key]
                    newcurnot[j][key] = max(curnot[j][key], curtook[j][key])
            oute = max(oute, newcurtook[-1][0], newcurtook[-1][1], newcurnot[-1][0], newcurnot[-1][1])
            curtook, curnot, newcurtook, newcurnot = newcurtook, newcurnot, [{0: 0, 1: 0} for i in range(REM+1)], [{0: 0, 1: 0} for i in range(REM+1)]
            
        return oute
16900