You are given an array of distinct integers nums.

A subarray nums[i...j] with a length of at least $3$ (where $j - i \ge 2$) is called a bowl if both of its boundary elements are strictly greater than every element situated between them. That is, $\min($ nums[i], nums[j] $) > \max($ nums[k] $)$ for all indices $k$ such that $i < k < j$.

Return the total number of bowl subarrays in nums.

Constraints:

• $3 \le$ nums.length $\le 10^5$

• $1 \le$ nums[i] $\le 10^9$

• nums consists of distinct elements.

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