Exercise $1(35$ points$)$

$$ Suppose that we have numbers between $1$ and $1200$ in a binary search tree $($BST$),$ and we want to search for the number $400.$ Which of the following sequences could not be the sequence of nodes examined on a BST$?($Recall Grading Guidelines. I suggest to use tree drawing to justify your answer. Drawing is strongly advised to make explanations easier to follow for you and your grader. Justify only for the sequence$($s$)$that could not be the sequence of nodes examined.$)$

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A requirement of a binary search tree is that, for any given node in the tree, then all the nodes in the left subtree should have a value less than that of the parent node, and all nodes in the right subtree should have a value greater than that of the parent. In order to find which of the following sequences could not be the sequence of nodes examined on a binary search tree, we would need to find a sequence that would not adhere to this requirement.

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a$.102,499,489,321,368,484,483,405,501.$