<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>

from collections import Counter
class Solution:
    def maximumTotalDamage(self, power: List[int]) -> int:
        h = Counter(power)
        power = list(set(power))
        power.sort(reverse=True)
        print(power)
        d = {}
        if len(power) == 1:
            return power[0] * h[power[0]]
        def pow(pos, num):
            if pos == len(power):
                return num * h[num]
            if (pos,num) in d.keys():
                return d[(pos,num)] 
            if num - power[pos] > 2:
                d[(pos, num)] = (num * h[num]) + pow(pos+1, power[pos])
                return d[(pos, num)]
            elif num - power[pos] <= 2:
                d[(pos, num)] = max(pow(pos+1, num), pow(pos+1, power[pos]))
                return d[(pos, num)]
        return pow(1, power[0])
            


            
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