Given an integer array nums of length n, you can perform the following operation any number of times.

In one move, choose exactly $n - 1$ elements of nums and increment each chosen element by $1$.

Return the minimum number of moves required to make all elements in nums equal.

Note: The result is guaranteed to fit in a $32$ bit integer.

Constraints:

• n == nums.length

• $1 \leq$ nums.length $\leq 10^5$

• $-10^9 \leq$ nums[i] $\leq 10^9$

Input: nums = [1, 2, 3]-List[int]
Output: 3-int
Explanation: Each move increments n-1 elements, which is equivalent to decrementing the one element you don’t pick. To make all values equal, reduce everything down to the minimum value 1, so the moves needed are (1-1) + (2-1) + (3-1) = 0 + 1 + 2 = 3.

Input: nums = [5, 5, 5]-List[int]
Output: 0-int
Explanation: All elements are already equal, so no moves are required.

Input: nums = [1, 1, 100]-List[int]
Output: 99-int
Explanation: The minimum is 1, so the moves needed are (1-1) + (1-1) + (100-1) = 0 + 0 + 99 = 99.

Input: nums = [-1, 2, -3]-List[int]
Output: 7-int
Explanation: The minimum is -3, so the moves needed are (-1 - (-3)) + (2 - (-3)) + (-3 - (-3)) = 2 + 5 + 0 = 7.

Input: nums = [0]-List[int]
Output: 0-int
Explanation: With only one element, it is trivially equal to itself, so no moves are needed.

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.