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
readline = sys.stdin.readline
class Node:
    __slots__ = ['value', 'left', 'right']
    def __init__(self, value = None, left = None, right = None):
        self.value = value
        self.left = left
        self.right = right
class BinTree:
    __slots__ = ['_tree', 'result']
    def __init__(self):
        self._tree = None
    def insert(self, value):
        p = None
        c = self._tree
        while c is not None:
            p = c
            if value < c.value:
                c = c.left
            else:
                c = c.right
        if p is None:
            self._tree = Node(value)
        elif value < p.value:
            p.left = Node(value)
        else:
            p.right = Node(value)
    def find(self, value):
        c = self._tree
        while c is not None:
            if value == c.value:
                return True
            elif value < c.value:
                c = c.left
            else:
                c = c.right
        return False
    def preoder_walk(self):
        self.result = []
        def preoder(node):
            if node is not None:
                self.result.append(node.value)
                preoder(node.left)
                preoder(node.right)
        preoder(self._tree)
        print(" " + " ".join(map(str, self.result)))
    def inorder_walk(self):
        self.result = []
        def inorder(node):
            if node is not None:
                inorder(node.left)
                self.result.append(node.value)
                inorder(node.right)
        inorder(self._tree)
        print(" " + " ".join(map(str, self.result)))
n = int(input())
tree = BinTree()
for _ in range(n):
    com = readline().split()
    if com[0] == "insert":
        tree.insert(int(com[1]))
    elif com[0] == "find":
        print("yes" if tree.find(int(com[1])) else "no")
    else:
        tree.inorder_walk()
        tree.preoder_walk()