<p>A magician has various spells.</p>

<p>You are given an array <code>power</code>, where each element represents the damage of a spell. Multiple spells can have the same damage value.</p>

<p>It is a known fact that if a magician decides to cast a spell with a damage of <code>power[i]</code>, they <strong>cannot</strong> cast any spell with a damage of <code>power[i] - 2</code>, <code>power[i] - 1</code>, <code>power[i] + 1</code>, or <code>power[i] + 2</code>.</p>

<p>Each spell can be cast <strong>only once</strong>.</p>

<p>Return the <strong>maximum</strong> possible <em>total damage</em> that a magician can cast.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">power = [1,1,3,4]</span></p>

<p><strong>Output:</strong> <span class="example-io">6</span></p>

<p><strong>Explanation:</strong></p>

<p>The maximum possible damage of 6 is produced by casting spells 0, 1, 3 with damage 1, 1, 4.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">power = [7,1,6,6]</span></p>

<p><strong>Output:</strong> <span class="example-io">13</span></p>

<p><strong>Explanation:</strong></p>

<p>The maximum possible damage of 13 is produced by casting spells 1, 2, 3 with damage 1, 6, 6.</p>
</div>

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

<ul>
	<li><code>1 &lt;= power.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= power[i] &lt;= 10<sup>9</sup></code></li>
</ul>

import heapq

class Solution:
    def maximumTotalDamage(self, power: List[int]) -> int:
        count = sorted(Counter(power).items())
        dp = [0] * len(count)
        dp[0] = count[0][0] * count[0][1]
        def aux(i):
            if i <0:
                return 0
            if dp[i] != 0:
                return dp[i]
            if i == len(count):
                return
            dp[i] = count[i][0] * count[i][1]
            if count[i-1][0] < count[i][0]-2:
                dp[i] += aux(i-1)
                return dp[i]
            if count[i-1][0] == count[i][0]-1:
                if i > 1 and count[i-2][0] == count[i][0]-2:
                    dp[i] = max(aux(i-3) + count[i][0] * count[i][1], aux(i-1), aux(i-2))
                else:
                    dp[i] = max(aux(i-2) + count[i][0] * count[i][1], aux(i-1))
            else:
                dp[i] = max(aux(i-2) + count[i][0] * count[i][1], aux(i-1))
            return dp[i]
        
        return aux(len(count)-1)


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