A magician has various spells.
\n\nYou are given an array power, where each element represents the damage of a spell. Multiple spells can have the same damage value.
It is a known fact that if a magician decides to cast a spell with a damage of power[i], they cannot cast any spell with a damage of power[i] - 2, power[i] - 1, power[i] + 1, or power[i] + 2.
Each spell can be cast only once.
\n\nReturn the maximum possible total damage that a magician can cast.
\n\n\n
Example 1:
\n\nInput: power = [1,1,3,4]
\n\nOutput: 6
\n\nExplanation:
\n\nThe maximum possible damage of 6 is produced by casting spells 0, 1, 3 with damage 1, 1, 4.
\nExample 2:
\n\nInput: power = [7,1,6,6]
\n\nOutput: 13
\n\nExplanation:
\n\nThe maximum possible damage of 13 is produced by casting spells 1, 2, 3 with damage 1, 6, 6.
\n\n
Constraints:
\n\n1 <= power.length <= 1051 <= power[i] <= 109x, then we will use all spells with power x.",
"Think of dynamic programming.",
"dp[i][j] represents the maximum damage considering up to the i-th unique spell and j represents the number of spells skipped (up to 3 as per constraints)."
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