<p>Given an array of integers called <code>nums</code>, you can perform <strong>any</strong> of the following operation while <code>nums</code> contains <strong>at least</strong> <code>2</code> elements:</p>

<ul>
	<li>Choose the first two elements of <code>nums</code> and delete them.</li>
	<li>Choose the last two elements of <code>nums</code> and delete them.</li>
	<li>Choose the first and the last elements of <code>nums</code> and delete them.</li>
</ul>

<p>The<strong> score</strong> of the operation is the sum of the deleted elements.</p>

<p>Your task is to find the <strong>maximum</strong> number of operations that can be performed, such that <strong>all operations have the same score</strong>.</p>

<p>Return <em>the <strong>maximum</strong> number of operations possible that satisfy the condition mentioned above</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [3,2,1,2,3,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We perform the following operations:
- Delete the first two elements, with score 3 + 2 = 5, nums = [1,2,3,4].
- Delete the first and the last elements, with score 1 + 4 = 5, nums = [2,3].
- Delete the first and the last elements, with score 2 + 3 = 5, nums = [].
We are unable to perform any more operations as nums is empty.
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,2,6,1,4]
<strong>Output:</strong> 2
<strong>Explanation:</strong> We perform the following operations:
- Delete the first two elements, with score 3 + 2 = 5, nums = [6,1,4].
- Delete the last two elements, with score 1 + 4 = 5, nums = [6].
It can be proven that we can perform at most 2 operations.
</pre>

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

<ul>
	<li><code>2 &lt;= nums.length &lt;= 2000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
</ul>

class Solution:
    def maxOperations(self, nums: List[int]) -> int:
        start=0
        length=len(nums)
        end=length-1
        dp=[[0]* length for _ in range(length)]
        maxResult=0
        maxResult=max(maxResult,1+self.solve(start+2,end,nums[start]+nums[start+1],dp,nums))
        maxResult=max(maxResult,1+self.solve(start+1,end-1,nums[start]+nums[end],dp,nums))
        maxResult=max(maxResult,1+self.solve(start,end-2,nums[end]+nums[end-1],dp,nums))
        return maxResult


    def solve(self,left,right,target,dp,nums):
        if left>=right:
            return 0
        if dp[left][right]!=0:
            return dp[left][right]
        maxVal=0
        if(nums[left]+nums[left+1] == target):
            maxVal=max(maxVal,1+self.solve(left+2,right,target,dp,nums))        
        if(nums[left]+nums[right] == target):
            maxVal=max(maxVal,1+self.solve(left+1,right-1,target,dp,nums))  
        if(nums[right]+nums[right-1] == target):
            maxVal=max(maxVal,1+self.solve(left,right-2,target,dp,nums))  

        dp[left][right]=maxVal
        return maxVal    
64733