Cell Fusion

You are given a list of integers cells, representing sizes of different cells. In each iteration, the two largest cells a and b interact according to these rules:

• If a = b, they both die.
• Otherwise, the two cells merge and their size becomes floor((a + b) / 3).

Return the size of the last cell or return -1 if there’s no cell is remaining.

Constraints

• n ≤ 100,000 where n is the length of cells

https://binarysearch.com/problems/Cell-Fusion

Examples

Example 1

Input

• cells = [10, 30, 30, 20]

Output

• answer = 10

Explanation

In the first iteration, the two largest cells both have the size of 30 so they both die. In the second iteration, cells 10, and 20 merge to become 10.

Solution