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(object):
    def __init__(self):
        self.left = None
        self.right = None
        self.value = None
        self.parent = None

class Tree(object):
    def __init__(self):
        self.root = None
        self.value_dic = {}
    
    def is_find(self,value):
        if value in self.value_dic:
            return True
        else:
            return False
    
    def find(self,value):
        node = T.root

        while node :
            if value == node.value:
                break
            elif value > node.value:
                node = node.right
            else :
                node = node.left
        return node

def insert(T,z):
    y = None
    x = T.root
    while x != None:
        y = x
        if z.value < x.value:
            x = x.left
        else:
            x = x.right
    
    z.parent = y
    if y == None:
        T.root = z
    elif z.value < y.value:
        y.left = z
    else :
        y.right = z

    T.value_dic[z.value] = 1

def getMinimum(z):
    while z.left != None:
        z = z.left
    return z

def getSuccessor(z):
    if z.right != None:
        return getMinimum(z.right)

    y = z.parent
    while y != None and z == y.right:
        z = y
        y = y.parent
    return y

def delete(T,z):
    # 削除する対象をyとする
    if z.left is None or z.right is None:
        y = z
    else:
        y = getSuccessor(z)

    # 子をxとする
    if y.left != None:
        x = y.left
    else:
        x = y.right
    

    # 子がいる場合
    if x != None:
        x.parent = y.parent
    
    if y.parent is None:
        T.root = x
    elif y.parent.left == y:
        y.parent.left = x
    else:
        y.parent.right = x
    
    if y != z:
        z.value = y.value



# 先行順巡回
def preorder(node):
    if node is None:
        return 
    print(" "+str(node.value),end="")    
    preorder(node.left)
    preorder(node.right)
    
# 中間順巡回 
def inorder(node):
    if node is None:
        return 
    inorder(node.left)
    print(" "+str(node.value),end="")
    inorder(node.right)
    
def print_all_node(root):
    stack = [root]
    while stack:
        node = stack.pop()
        print("p: ",node.parent,"r:",node.right,"l:",node.left)
        if node.left:
            stack.append(node.left)
        if node.right:
            stack.append(node.right)

if __name__ == "__main__":
    n = int(input())
    T = Tree()
    queries = [input().split() for _ in range(n)]
    for query in queries:
        if query[0] == "print":
            #print_all_node(T.root)
            inorder(T.root)
            print("")
            preorder(T.root)
            print("")

        else:
            command,value = query
            if command == "insert":
                node_z = Node()
                node_z.value = int(value)
                insert(T,node_z)
            elif command == "find":
                if T.is_find(int(value)):
                    print("yes")
                else:
                    print("no")
            elif command == "delete":
                node = T.find(int(value))
                if node:
                    T.value_dic.pop(int(value))
                delete(T,node)