Problem:
Binary Search Tree III

Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

insert $k$: Insert a node containing $k$ as key into $T$.

find $k$: Report whether $T$ has a node containing $k$.

delete $k$: Delete a node containing $k$.

print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.

The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).

If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.

If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s key.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ or print are given.

Output

For each find $k$ operation, print "yes" if $T$ has a node containing $k$, "no" if not.

In addition, for each print operation, print a list of keys obtained by inorder tree walk and preorder tree walk in a line respectively. Put a space character before each key

Constraints

The number of operations $\leq 500,000$

The number of print operations $\leq 10$.

$-2,000,000,000 \leq key \leq 2,000,000,000$

The height of the binary tree does not exceed 100 if you employ the above pseudo code.

The keys in the binary search tree are all different.

Sample Input 1

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print

Sample Output 1

yes
yes
yes
no
no
no
yes
yes
1 2 3 7 8 22
8 2 1 3 7 22
1 2 8 22
8 2 1 22

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in Python3 (judge verdict: Accepted)

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None
        self.parent = None
    
    def delete_connect(self, parent, child):
        if parent:
            if parent.val > self.val:
                parent.left = child
            else:
                parent.right = child
        if child:
            child.parent = parent
    
    def delete(self):
        left, right = self.left, self.right
        if not left and not right:
            self.delete_connect(self.parent, None)
        elif not left and right:
            self.delete_connect(self.parent, right)
        elif left and not right:
            self.delete_connect(self.parent, left)
        else:
            next_node = right.get_leftmost()
            self.val = next_node.val
            next_node.delete()
    
    def get_leftmost(self):
        if self.left:
            return self.left.get_leftmost()
        return self


class BinarySearchTree:
    def __init__(self):
        self.root = None
    
    def insert(self, node: Node):
        if not self.root:
            self.root = node
            return

        cur = self.root
        while cur:
            if node.val > cur.val:
                if cur.right:
                    cur = cur.right
                    continue
                else:
                    cur.right,node.parent = node,cur
                    return
            else:
                if cur.left:
                    cur = cur.left
                    continue
                else:
                    cur.left,node.parent = node,cur
                    return

    def find(self, val):
        cur = self.root
        while cur:
            if cur.val == val:
                return "yes"
            elif cur.val > val:
                cur = cur.left
            else:
                cur = cur.right
        return "no"
    
    def find_node(self, val):
        cur = self.root
        while cur:
            if cur.val == val:
                return cur
            elif cur.val > val:
                cur = cur.left
            else:
                cur = cur.right
        return None

    def delete(self, val):
        node = self.find_node(val)
        if node:
            node.delete()

def main():

    ## preorder tree walk
    preorder = []

    def preorder_walk(node):
        preorder.append(str(node.val))
        if node.left:
            preorder_walk(node.left)
        if node.right:
            preorder_walk(node.right)

    ## inorder tree walk

    inorder = []

    def inorder_walk(node):
        if node.left:
            inorder_walk(node.left)
        inorder.append(str(node.val))
        if node.right:
            inorder_walk(node.right)


    n = int(input())
    
    bst = BinarySearchTree()
    
    for _ in range(n):
        op = input().strip().split()
        if op[0] == "insert":
            bst.insert(Node(int(op[1])))
        elif op[0] == "print":
            preorder,inorder = [],[]
            preorder_walk(bst.root)
            inorder_walk(bst.root)
            print(""," ".join(inorder))
            print("", " ".join(preorder))
        elif op[0] == "find":
            print(bst.find(int(op[1])))
        elif op[0] == "delete":
            bst.delete(int(op[1]))

if __name__ == "__main__":
    main()