3301 - Maximize the Total Height of Unique Towers.

Medium

You are given an array maximumHeight, where maximumHeight[i] denotes the maximum height the <code>i^th</code> tower can be assigned.

Your task is to assign a height to each tower so that:

• The height of the <code>i^th</code> tower is a positive integer and does not exceed maximumHeight[i].

• No two towers have the same height.

Return the maximum possible total sum of the tower heights. If it's not possible to assign heights, return -1.

Example 1:

Input: maximumHeight = 2,3,4,3

Output: 10

Explanation:

We can assign heights in the following way: [1, 2, 4, 3].

Example 2:

Input: maximumHeight = 15,10

Output: 25

Explanation:

We can assign heights in the following way: [15, 10].

Example 3:

Input: maximumHeight = 2,2,1

Output: \-1

Explanation:

It's impossible to assign positive heights to each index so that no two towers have the same height.

Constraints:

• <code>1 <= maximumHeight.length <= 10⁵</code>

• <code>1 <= maximumHeighti<= 10⁹</code>