Given an array nums of distinct integers representing a sequence inserted sequentially into an initially empty Binary Search Tree (BST), determine the number of different permutations of nums that will produce the identical BST.

A Binary Search Tree is constructed by inserting the first element as the root, and each subsequent element is recursively inserted into the left subtree if it is strictly smaller than the current node’s value, or into the right subtree if it is strictly greater.

Return the total number of alternative orderings of nums that result in the exact same BST structure and node values. Since the answer can be very large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ nums.length $\leq 1000$

• $1 \leq$ nums[i] $\leq$ nums.length

• All integers in nums are distinct.

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