Create a Java program that implements a Binary Search Tree $($BST$)$and provides a range of operations to test understanding of data structures, recursion, and traversal techniques. Requirements $1.$Class Definition $(20$pts$)$Define a class $`$BST$`$to represent the binary search tree. Include an inner class $`$Node$`$to store the value, left child, and right child. $2.$Core BST Operations $(20$pts$)$Implement the following methods: $-$void insert$($int value$)$: Adds a value to the BST$.$Ensure that duplicates are not allowed. $-$boolean search$($int value$)$: Returns $`$true$`$if the value exists in the tree, $`$false$`$otherwise$.-$void delete$($int value$)$: Removes a node from the BST while preserving the tree structure. $3.$Traversal Methods $(20$pts$)$Implement methods for di$]$erent tree traversals: $-$void inorderTraversal$()$: Prints nodes in ascending order. $-$void preorderTraversal$()$: Prints nodes in preorder. $-$void postorderTraversal$()$: Prints nodes in postorder. $-$List levelOrderTraversal$()$: Returns the level$-$order traversal $($BFS$)$as a list. $4.$Additional Operations $(20$pts$)$Implement the following methods to enhance the BST functionality: $-$int height$()$: Returns the height $($or depth$)$of the tree. $-$int minValue$()$: Returns the smallest value in the BST$.-$int maxValue$()$: Returns the largest value in the BST$.-$boolean isBalanced$()$: Checks if the BST is height$-$balanced $($di$]$erence in height between left and right subtrees of any node is at most $1).-$void printPaths$()$: Prints all root$-$to$-$leaf paths. $5.$Testing $(20$pts$)$Write a $`$main$`$method to test the BST$.$Perform the following: $-$Insert a series of values and print the BST in all traversal orders. $-$Search for a value that exists and one that does not. $-$Delete a few values, including a leaf node, a node with one child, and a node with two children. $-$Check the height, minimum, and maximum values. $-$Test if the tree is balanced and print all root$-$to$-$leaf paths