<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 defaultdict, Counter
from functools import lru_cache

class Solution:
    def maximumTotalDamage(self, power):
        @lru_cache(maxsize=0)
        def solve(ind):
            nonlocal arr, dp
            if ind >= len(arr):
                return 0
            if dp[ind] != -1:
                return dp[ind]

            not_pick = solve(ind + 1)

            s = {arr[ind][0] + 1, arr[ind][0] + 2}
            next_ind = ind + 1
            while next_ind < len(arr) and arr[next_ind][0] in s:
                next_ind += 1

            pick = arr[ind][0] * arr[ind][1] + solve(next_ind)

            dp[ind] = max(pick, not_pick)
            return dp[ind]

        arr = []
        mp = Counter(power)

        dp = [-1] * (len(power) + 1)

        for key, value in mp.items():
            arr.append((key, value))

        arr.sort()

        return solve(0)

199006