You are given a $0$ indexed array nums consisting of positive integers.

You can perform two types of operations on the array any number of times:

• Choose $2$ elements with equal values and remove them from the array.

• Choose $3$ elements with equal values and remove them from the array.

Return the minimum number of operations required to make the array empty, or $-1$ if it is impossible to empty the array.

Constraints:

• $2 \leq$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^6$

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.