<p>You are given an integer array <code>nums</code>. You want to maximize the number of points you get by performing the following operation any number of times:</p>

<ul>
	<li>Pick any <code>nums[i]</code> and delete it to earn <code>nums[i]</code> points. Afterwards, you must delete <b>every</b> element equal to <code>nums[i] - 1</code> and <strong>every</strong> element equal to <code>nums[i] + 1</code>.</li>
</ul>

<p>Return <em>the <strong>maximum number of points</strong> you can earn by applying the above operation some number of times</em>.</p>

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

<pre>
<strong>Input:</strong> nums = [3,4,2]
<strong>Output:</strong> 6
<strong>Explanation:</strong> You can perform the following operations:
- Delete 4 to earn 4 points. Consequently, 3 is also deleted. nums = [2].
- Delete 2 to earn 2 points. nums = [].
You earn a total of 6 points.
</pre>

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

<pre>
<strong>Input:</strong> nums = [2,2,3,3,3,4]
<strong>Output:</strong> 9
<strong>Explanation:</strong> You can perform the following operations:
- Delete a 3 to earn 3 points. All 2&#39;s and 4&#39;s are also deleted. nums = [3,3].
- Delete a 3 again to earn 3 points. nums = [3].
- Delete a 3 once more to earn 3 points. nums = [].
You earn a total of 9 points.</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def deleteAndEarn(self, nums: List[int]) -> int:
        num_to_cnt: defaultdict[int, int] = defaultdict(int)
        for n in nums:
            num_to_cnt[n] += 1
        counts = []
        nums = list(num_to_cnt.keys())
        N = len(nums)
        nums.sort()
        for n in nums:
            counts.append(num_to_cnt[n])

        @cache
        def dfs(i: int, select: bool):
            if i < 0:
                return 0
            if i == 0:
                return nums[0] * counts[0]
            res = 0
            if select:
                if nums[i] == nums[i - 1] + 1:
                    res = counts[i] * nums[i] + max(dfs(i - 2, False), dfs(i - 2, True))
                else:
                    res = counts[i] * nums[i] + max(dfs(i - 1, False), dfs(i - 1, True))
            else:
                res = max(dfs(i - 1, True), dfs(i - 1, False))
            return res

        return max(dfs(N - 1, True), dfs(N - 1, False))
24858