You are given an integer array nums of length n.

A positive integer k is a divisor of n ($n \pmod k = 0$). Dividing nums into contiguous subarrays of length k, the integer k is called sortable if each subarray can be independently cyclically rotated such that the entire array becomes sorted in nondecreasing order.

Return the sum of all sortable integers k.

Constraints:

• $1 \leq$ n $==$ nums.length $\leq 10^5$

• $1 \leq$ nums[i] $\leq 10^5$

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.