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We all know that we can insert values one by one to construct a new binary search tree. However, if we are given a binary search tree, how many insertion sequences are possible to construct this binary search tree?

For example, if the binary search tree is 2, 1, 3. There are two possible sequences to construct this tree, which are 2, 1, 3, and 2, 3, 1.

To simplify the question, you are only required to count the number of all possible sequences given the structure of a binary search tree.

See the basic structure of the binary search tree in BSTsequence.h, and finish the function in BSTsequence.cpp. To submit your code, zip the two source code and submit it on JOJ.