Please use Julia Programming Language to answer this question.

Write each of the following functions on a binary tree with a given root of the type BTree.

$-$ Return the in$-$order traversal of a tree as a list.

$-$ Test if a binary tree is symmetric $($a binary tree is symmetric if rotating it about the vertical bar through the root for $180$ degrees gives the same tree$).$

$-$ Return the maximum path sum $($the sum of the path from the root to a leaf is the sum of values in the nodes on the path$).$

$-$ Test if a binary tree is a search tree.

$-$ Test if a given value occurs in a binary search tree.

$-$ Insert a value into a binary search tree such that the resulting tree remains a search tree.