Problem:
Binary Search Tree II

Write a program which performs the following operations to a binary search tree $T$ by adding the find operation to A: Binary Search Tree I.

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

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

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

Input

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

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

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)

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

root = None

def find(target):
    result = root
    while result and target != result.key:
        result = result.left if target < result.key else result.right
    if result is None:
        return False
    else:
        return True

def insert(key):
    global root
    y = None  # xの親
    x = root
    while x:
        y = x
        x = x.left if key < x.key else x.right
    if y is None:  # Tが空の場合
        root = Node(key)
    elif key < y.key:
        y.left = Node(key)
    else:
        y.right = Node(key)

def in_order(node):
    if node is None:
        return ''
    return in_order(node.left) + f' {node.key}' + in_order(node.right)
def pre_order(node):
    if node is None:
        return ''
    return f' {node.key}' + pre_order(node.left) + pre_order(node.right)
input()
for e in sys.stdin:
    if e[0] == 'i':
        insert(int(e[7:]))
    elif e[0] == 'f':
        print('yes' if find(int(e[5:])) else 'no')
    else:
        print(in_order(root))
        print(pre_order(root))