An escape game requires that players solve various puzzles to obtain objects that will aid them in escaping. In one such puzzle, players are given an array of integers and a set of rules to follow in order. Here are the instructions given to the players: "Given an array of integer values, maximize the points earned using the following method:

$1.$ Choose a value v$.$ Delete all elements of that value and add their sum to the points.

$2.$ Delete all elements equal to v $+1$ or v $-1$ for no points.

$3.$ Repeat steps $1$ and $2$ until there are no more elements in the array.