class BST:

    def __init__(self):
        self._left = None   ## is the left subtree
        self._value = None
        self._right = None  ## is the right subtree

    def empty(self):
        return self._value == None
            
    def minBST(self):
        if self.empty():  #BASE Case if not found
            return None
        elif self._left == None:
            return self._value
        else:
            return self._left.minBST()
   
    def maxBST(self): 
        if self.empty():  #BASE Case if not found
            return None
        elif self._right == None:
            return self._value
        else:
            return self._right.maxBST()
        
    def member(self,x):
        if self.empty():  #BASE Case if not found
            return False
        elif x < self._value:
            return self._left.member(x)
        elif x > self._value:
            return self._right.member(x)
        else:  # BASE Case if found
            return True
  
    def height(self):
        if self.empty():
            return 0
        else:
            return 1 + max(self._left.height(),self._right.height())
  
    def size(self):
        if self.empty():  #BASE Case
            return 0
        else:
            return 1 + self._left.size() + self._right.size()
  
    def insert(self,x):  # return a boolean; True if successful and False otherwise
        if self.empty(): # BASE CASE
            self._value = x
            self._left = BST()  ## MOST CRITICAL PART OF CODE; should not be None; This is where
                               ## a future insert will happen
            self._right = BST() ## MOST CRITICAL PART OF CODE; should not be None
        elif x < self._value:
            return self._left.insert(x)
        elif x > self._value:
            return self._right.insert(x)
        else: # item found BASE CASE
            return False

    def delete(self,x):
        return self.delete_helper(x) != None
    
    def delete_helper(self,x):
        if self.empty():
            return None
        elif x == self._value:
            if self._right.empty():
                return self._left
            elif self._left.empty():
                return self._right
            else:
                rmin = self._right.min()
                self._value = rmin
                self._right = self._right.delete_helper(rmin)
                return self
        elif x < self._value:
            t = self._left.delete_helper(x)
            if t == None:
                return None
            else:
                self._left = t
                return self
        else:
            t = self._right.delete_helper(x)
            if t == None:
                return None
            else:
                self._right = t
                return self

    def __str__(self):
        return "{ " + self.str_helper().strip(', ') + " }"

    def str_helper(self):
        if self.empty():
            return ""
        else:
            return self._left.str_helper()+str(self._value)+", "+self._right.str_helper() 

def main():
    #t1 = BST(BST(BST(),10,BST()), 20, BST(BST(),30,BST()))
    #t2 = BST(BST(BST(BST(),10,BST()),20,BST(BST(),30,BST())), \
    #       40, \
    #       BST(BST(BST(),50,BST()),600,BST(BST(),70,BST())))

    nums = [47,34,97,88,41,20,16,105,100,83,99,97]
    
    t3 = BST()
    for x in nums:
        t3.insert(x) 

    t4 = BST()
    for x in nums[::-1]:
        t4.insert(x) 

    print("************************")
    print("BST t3")
    print(t3)
    print("************************")
    print("BST t4")
    print(t4)
    print("************************")

main()

************************
BST t3
{ 16, 20, 34, 41, 47, 83, 88, 97, 99, 100, 105 }
************************
BST t4
{ 16, 20, 34, 41, 47, 83, 88, 97, 99, 100, 105 }
************************

[1,2,3][::-1]

[3, 2, 1]