<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 {
public:
    int maximumSum(vector<int>& arr) {
        int n = arr.size();
        if(n==1)return arr[0];
        long long possi = 0;
        vector<long long>lmax(n),rmax(n),lsum(n,-1e6),rsum(n,-1e5);
        long long sum = 0,maxsum =-1e6,ans=-1e9;
        for(int i=0;i<n;i++){
            possi+=arr[i];
            lmax[i] = maxsum;
            sum+=arr[i];
            if(maxsum<sum){
                maxsum = sum;
            }
            if(sum<0){
                sum = arr[i];
            }
            ans = max(ans,lmax[i]);
        }
        long long tempsum=0;
        bool flag = true;
        for(int i=0;i<n;i++){
            if(flag)
            lsum[i] = tempsum;
            cout<<lsum[i]<<" ";
            tempsum+=arr[i];
            flag=true;
            if(tempsum<0){
                tempsum=0;
                flag=false;
            }
        }
        cout<<endl;
        sum = 0,maxsum =-1e6;
        for(int i=n-1;i>=0;i--){
            rmax[i] = maxsum;
            sum+=arr[i];
            if(maxsum<sum){
                maxsum = sum;
            }
            if(sum<0){
                sum = arr[i];
            }
            ans = max(ans,rmax[i]);
        }
        tempsum=0;
        flag = true;
        for(int i=n-1;i>=0;i--){
            if(flag)
            rsum[i] = tempsum;
            tempsum+=arr[i];
            flag=true;
            if(tempsum<0){
                flag=false;
                tempsum=0;
            }
        }
        for(int i=0;i<n;i++)cout<<rsum[i]<<" ";
        for(int i=0;i<n;i++){
            ans = max(ans,lsum[i]+rsum[i]);
        }
        return max(possi,ans);
    }
};
31600