Maximize Sum from Array

Given an integer array ARR of size N, your objective is to perform a series of operations to maximize the sum of selected elements from the array. During each operation, you should:

1. Select an element at index i (i.e., ARR[i]).
2. Remove one occurrence of the selected element from the array.
3. Remove all occurrences of ARR[i]-1 and ARR[i]+1 from the array, if present.

Continue doing this until the array is empty. Your task is to determine the maximum possible sum of the selected elements.

Example:

Input:

ARR = [2, 3, 3, 3, 4, 5]

Output:

14

Explanation:

Select one of the '3's, removing one '3', '2', and '4'. The array becomes [3, 3, 5]. Then select the '3' two more times. The array becomes [5]. Finally, select '5'. The sum of selected elements is 3+3+3+5 = 14.

Input:

First line contains an integer 'T', the number of test cases.
For each test case:
 First line contains an integer N, the size of the array.
Second line contains N space-separated integers, the elements of the array.

Output:

For each test case, output a single integer representing the maximum sum in a new line.

Constraints:

• 1 ≤ T ≤ 10
• 1 ≤ N ≤ 105
• 1 ≤ ARR[i] ≤ 105
• Execution time limit is 1 second.

Note:

Implementation should focus on maximizing the sum. Printing results is handled separately.