<p>Given an array of integers, return the maximum sum for a <strong>non-empty</strong>&nbsp;subarray (contiguous elements) with at most one element deletion.&nbsp;In other words, you want to choose a subarray and optionally delete one element from it so that there is still at least one element left and the&nbsp;sum of the remaining elements is maximum possible.</p>

<p>Note that the subarray needs to be <strong>non-empty</strong> after deleting one element.</p>

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

<pre>
<strong>Input:</strong> arr = [1,-2,0,3]
<strong>Output:</strong> 4
<strong>Explanation: </strong>Because we can choose [1, -2, 0, 3] and drop -2, thus the subarray [1, 0, 3] becomes the maximum value.</pre>

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

<pre>
<strong>Input:</strong> arr = [1,-2,-2,3]
<strong>Output:</strong> 3
<strong>Explanation: </strong>We just choose [3] and it&#39;s the maximum sum.
</pre>

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

<pre>
<strong>Input:</strong> arr = [-1,-1,-1,-1]
<strong>Output:</strong> -1
<strong>Explanation:</strong>&nbsp;The final subarray needs to be non-empty. You can&#39;t choose [-1] and delete -1 from it, then get an empty subarray to make the sum equals to 0.
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= arr[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def maximumSum(self, arr: List[int]) -> int:
        #do regu max subarray sum prefix
        #do it starting from end to beginning
        #then do another iteration combining the result of the prefix and suffix not including each index
        if len(arr) == 1:
            return arr[0]
        elif len(arr) == 2:
            return max(arr[0], arr[1], arr[0]+arr[1])
        prefix = [arr[0]]
        suffix = [-math.inf] * len(arr)
        suffix[-1] = arr[-1]

        currSum = arr[0]
        for i in range(1, len(arr)):
            i = arr[i]
            prefix.append(max(currSum+i, i))
            currSum = max(currSum+i, i)
        currSum = arr[-1]
        for i in range(len(arr)-2, -1, -1):
            num = arr[i]
            suffix[i] = max(num, currSum+num)
            currSum = max(num, currSum+num)
        res = -math.inf
        print(prefix)
        print(suffix)
        for i in range(len(arr)):
            if i == 0:
                res = max(res, suffix[i+1])
            elif i == len(arr)-1:
                res = max(res, prefix[i-1])
            else:
                res = max(res, prefix[i-1]+suffix[i+1])
        return max(max(prefix), res)

30800