Given an array of integers nums, in each move, you can select any element and reduce its value by $1$.

An array nums is a zigzag array if either of the following conditions is satisfied:

• Every even indexed element is strictly greater than its adjacent elements (that is, for every even index $i$, nums[i] > nums[i - 1] and nums[i] > nums[i + 1], whenever the adjacent elements exist).

• Every odd indexed element is strictly greater than its adjacent elements (that is, for every odd index $i$, nums[i] > nums[i - 1] and nums[i] > nums[i + 1], whenever the adjacent elements exist).

Return the minimum number of moves needed to transform nums into a zigzag array.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq 1000$

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.