<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 __init__(self) -> None:
        self.nums = []

    @cache
    def my_sol(self, left: int, right: int, score: int) -> int:
        sol1, sol2, sol3 = 0, 0, 0
        if 0 <= left < right < len(self.nums):
            if self.nums[left] + self.nums[right] == score:
                sol1 = self.my_sol(left + 1, right - 1, score) + 1
            
            if self.nums[left] + self.nums[left + 1] == score:
                sol2 = self.my_sol(left + 2, right, score) + 1

            if self.nums[right] + self.nums[right - 1] == score:
                sol3 = self.my_sol(left, right - 2, score) + 1
        # print(f"left={left}, right={right}, self.nums[left: right + 1]={self.nums[left: right + 1]}, max(sol1, sol2, sol3)={max(sol1, sol2, sol3)}, score={score}")
        return max(sol1, sol2, sol3)

    def maxOperations(self, nums: List[int]) -> int:
        self.nums = nums
        sol1 = self.my_sol(1, len(nums) - 2, nums[0] + nums[-1]) + 1
        sol2 = self.my_sol(2, len(nums) - 1, nums[0] + nums[1]) + 1
        sol3 = self.my_sol(0, len(nums) - 3, nums[-1] + nums[-2]) + 1
        return max(sol1, sol2, sol3)
234138