Given a sorted array of N numbers, we need to maximize the sum of selected numbers. At each step, you need to select a number A_i, delete one occurrence of A_i-1 (if exists), and A_i each from the array. Repeat these steps until the array gets empty. The problem is to maximize the sum of the selected numbers.

Example 1:

​Input : arr[ ] = {1, 2, 2, 2, 3, 4}
Output : 10
Explanation:
We select 4, so 4 and 3 are deleted leaving us with {1,2,2,2}.
Then we select 2, so 2 & 1 are deleted. We are left with{2,2}.
We select 2 in next two steps, thus the sum is 4+2+2+2=10.

​Example 2:

Input : arr[ ] = {1, 2, 3} 
Output :  4

Your Task:
This is a function problem. The input is already taken care of by the driver code. You only need to complete the function maximizeSum() that takes an array (arr), sizeOfArray (n), and return the maximum sum of the selected numbers. The driver code takes care of the printing.

Expected Time Complexity: O(N).
Expected Auxiliary Space: O(N).

Constraints:
1 ≤ N ≤ 10⁵
1 ≤ A[i] ≤ 10⁵
Note: Numbers need to be selected from maximum to minimum.