Tree

One of the well-known data structures to represent sets is a binary search tree. Each node $v$ of this tree contains a single element of the set. All elements in the left subtree of $v$ must be less than the element in $v$, and all elements in the right subtree of $v$ must be greater than the element in $v$. An example of a binary search tree is shown in the figure. A node is called the root if it has no parent (node $5$ in the figure). A node is called a leaf if it has no children (nodes $2$, $4$, and $8$ in the figure). A path in the tree is a sequence of nodes such that each next node is a direct child of the previous one.

You are given a sequence of distinct integers. Determine whether there exists a binary search tree in which this sequence is a path from the root to some leaf. For example, a search tree path $5\text{-}1\text{-}3\text{-}2$ exists, while a path $5\text{-}2\text{-}3\text{-}1$ does not.