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 Python (judge verdict: Accepted)

import sys
import time

class Node:
    def __init__(self, key):
        self.key = key
        self.parent = None
        self.left = None
        self.right = None

def insert(z):
    global root
    y = None
    x = root
    while x is not None:
        y = x
        if z.key < x.key:
            x = x.left
        else:
            x = x.right
    z.parent = y
    if y is None:
        root = z
    elif z.key < y.key:
        y.left = z
    else:
        y.right = z

def find(node, key):
    if node is None:
        return False
    elif node.key == key:
        return True
    elif node.key > key:
        return find(node.left, key)
    else:
        return find(node.right, key)

def inorderTreeWalk(node):
    global In
    if node:
        inorderTreeWalk(node.left)
        In.append(str(node.key))
        inorderTreeWalk(node.right)

def preorderTreeWalk(node):
    global Pre
    if node:
        Pre.append(str(node.key))
        preorderTreeWalk(node.left)
        preorderTreeWalk(node.right)

if __name__ == "__main__":
    lines = sys.stdin.readlines()
    del lines[0]

    root = None
    for line in lines:
        if line[0] == "p":
            In = []
            Pre = []
            inorderTreeWalk(root)
            print " " + " ".join(map(str, In))
            preorderTreeWalk(root)
            print " " + " ".join(map(str, Pre))
        else:
            com = line.split()
            if com[0][0] == "i":
                insert(Node(int(com[1])))
            else:
                if find(root, int(com[1])):
                    print "yes"
                else:
                    print "no"