<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 typing import List

class Solution:
    def maximumTotalDamage(self, power: List[int]) -> int:
        n = len(power)
        power.sort()
        
        # Create spell list with (power, damage) tuples
        spells = [(power[0], power[0])]
        for i in range(1, n):
            if power[i] != power[i-1]:
                spells.append((power[i], power[i]))
            else:
                spells[-1] = (spells[-1][0], spells[-1][1] + power[i])
        
        memo = [-1] * len(spells)
        
        def dfs(index: int) -> int:
            if index >= len(spells):
                return 0
            
            if memo[index] != -1:
                return memo[index]
            
            # Use current spell
            current_power, current_damage = spells[index]
            next_index = index + 1
            while next_index < len(spells) and spells[next_index][0] <= current_power + 2:
                next_index += 1
            use_current = current_damage + dfs(next_index)
            
            # Skip current spell
            skip_current = dfs(index + 1)
            
            memo[index] = max(use_current, skip_current)
            return memo[index]
        
        return dfs(0)
138916