<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:
    vector<vector<int>> dp;
    int f(vector<int> &arr,int i,int num){
        int n=arr.size();
        if(i==n)return 0;
        if(dp[i][num]!=-1)return dp[i][num];
        int ans=INT_MIN;
        ans=max(ans,arr[i]+f(arr,i+1,num));
        if(arr[i]<0){
            if(num==0){
                ans=max(ans,f(arr,i+1,1));
                
            }
        }
        ans=max(ans,arr[i]);
        return dp[i][num]= ans;
    }
    int maximumSum(vector<int>& arr) {
        int n=arr.size();
        int res=INT_MIN;
        int cnt=0;
        int mini=INT_MIN;
        dp.resize(n,vector<int>(2,-1));
        for(int i=0;i<n;i++){
            res=max(res,f(arr,i,0));
            if(arr[i]>=0)cnt++;
            if(arr[i]<0){
                mini=max(mini,arr[i]);
            }
        }
        if(res==0){
            if(cnt>0)return res;
            else{
                return mini;
            }
        }
        return res;
    }
};
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