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Maximize the Total Height of Unique Towers

You are given an array maximumHeight, where maximumHeight[i] denotes the maximum height the ith tower can be assigned.

You are given an array maximumHeight, where maximumHeight[i] denotes the maximum height the ith tower can be assigned.

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

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

Maximize the Total Height of Unique Towers diagram

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

  • 1 <= maximumHeight.length <= 10^5
  • 1 <= maximumHeight[i] <= 10^9

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