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)

from collections import deque
import sys
readline = sys.stdin.readline
write = sys.stdout.write

class Node:
    __slots__ = ['key', 'left', 'right']
    def __init__(self, key):
        self.key = key
        self.left = self.right = None


root = None

def insert(key):
    global root
    x = root #Tの根
    y = None #親を設定
    while x is not None:
        y = x
        if key < x.key:
            x = x.left #左の子へ移動
        else:
            x = x.right  #右の子へ移動

    if y is None: #Tが空の場合
        root = Node(key)
    elif key < y.key:
        y.left = Node(key) #keyをyの左の子にする
    else:
        y.right = Node(key) #keyをyの右の子にする

def delete(target):
    def remove_node(p,c,a):
        if p.left == c: p.left = a
        else: p.right = a
    p,c = None,root
    while c.key != target: p,c = c,c.left if target < c.key else c.right
    if c.left is None:
        remove_node(p, c, c.right)
    elif c.right is None:
        remove_node(p, c, c.left)
    elif c.right.left is None:
        c.right.left = c.left
        remove_node(p, c, c.right)
    else:
        g = c.right
        while g.left.left: g = g.left
        c.key = g.left.key
        g.left = g.left.right

# def find(key):
#     x = root
#     while x and key != x.key:
#         x = x.left if key < x.key else x.right
#     return x is None

def find(target):
    result = root
    while result and target != result.key:
        result = result.left if target < result.key else result.right
    return result is None # result が None ⇒ false

def inorder(node):
    return   inorder(node.left) + " "+ str(node.key) + inorder(node.right) if node else ''
def preorder(node):
    return   " " + str(node.key) + preorder(node.left) + preorder(node.right) if node else ''
input()
for e in sys.stdin:
    if e[0] == "i":
        insert(int(e[7:]))
    elif e[0] == 'f':
        if find(int(e[5:])):
            print("no")
        else:
            print("yes")
        # print(['yes','no'][find(int(e[5:]))])

    elif e[0] == 'd':
        delete(int(e[7:]))

    else:
        print(inorder(root))
        print(preorder(root))