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: Time Limit Exceeded)

import sys

class Node:
    def __init__(self, x):
        self.data = x
        self.left = None
        self.right = None
    
    def insert(node, x):
        if node == None:
            return Node(x)
        elif x == node.data:
            return node
        elif x < node.data:
            node.left = Node.insert(node.left, x)
        else:
            node.right = Node.insert(node.right, x)
        return node
    
    def find(node, x):
        if node.data == x:
            return True
        elif node.left != None and node.data > x:
            return Node.find(node.left, x)
        elif node.right != None and node.data < x:
            return Node.find(node.right, x)
        else:
            return False
        
    def print1(node):
        if node.left != None:
            Node.print1(node.left)
        print("",node.data,  end="")
        if node.right != None:
            Node.print1(node.right)
    def print2(node):
        print("",node.data,  end="")
        if node.left != None:
            Node.print2(node.left)
        if node.right != None:
            Node.print2(node.right)
        
class BinaryTree:
    def __init__(self):
        self.root = None
    
    def insert(self, x):
        self.root = Node.insert(self.root, x)

    def find(self, x):
        if Node.find(self.root, x):
            print("yes")
        else:
            print("no")

    def print_tree(self):
        Node.print1(self.root)
        print()
        Node.print2(self.root)
        print()

def main():
    T = BinaryTree()
    m = int(sys.stdin.readline())
    for i in range(m):
        s = sys.stdin.readline().strip()
        if(s == "print"):
            T.print_tree()
        elif s.split()[0] == "find":
            T.find(int(s.split()[1]))
        else:
            z = int(s.split()[1])
            T.insert(z)

if __name__ == "__main__":
    main()