<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>

class Solution:
    def TopDown(self , i , N , P , DP):
        if i == N:
            return 0
        if DP[i] != -1:
            return DP[i]
        c1 = self.TopDown(i + 1, N, P, DP)
        c2 = P[i][1]
        for j in range(i + 1 , min(N - 1 , i + 3) + 1):
            if P[j][0] - P[i][0] > 2:
                c2 += self.TopDown(j , N , P , DP)
                break
        DP[i] = max(c1 , c2)
        return DP[i]

    def maximumTotalDamage(self, power):
        hashmap = defaultdict(int)
        for num in power:
            hashmap[num] += num

        newPowers = [[P, D] for P, D in sorted(hashmap.items())]
        
        N = len(newPowers)
        DP = [-1] * (N + 1)
        return self.TopDown(0 , N , newPowers, DP)
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