You are given an integer array nums of length n which represents a permutation of all integers in the range $[0, n - 1]$.

The number of global inversions is the total number of pairs $(i, j)$ satisfying:

• $0 \leq i < j < n$

• nums[i] $>$ nums[j]

The number of local inversions is the total number of indices i satisfying:

• $0 \leq i < n - 1$

• nums[i] $>$ nums[i + 1]

Return true if the number of global inversions equals the number of local inversions, or false otherwise.

Constraints:

• n $==$ nums.length

• $1 \leq n \leq 10^5$

• $0 \leq$ nums[i] $< n$

• All integers in nums are unique.

• nums is a permutation of all integers in the range $[0, n - 1]$.

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.