You are given an array of positive integers arr. You can perform two types of operations any number of times:

1. Decrease the value of any element in arr to any smaller positive integer.

2. Rearrange the elements of arr in any order.

Return the maximum possible value of an element in arr after applying the operations such that arr satisfies the following conditions:

1. The first element of arr must be equal to $1$.

2. The absolute difference between any two adjacent elements must be at most $1$. That is, $|$arr$[i] -$ arr$[i - 1]| \leq 1$ for all $1 \leq i <$ arr.length (using $0$ based indexing).

Constraints:

• $1 \leq$ arr.length $\leq 10^5$

• $1 \leq$ arr[i] $\leq 10^9$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.