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 JAVA (judge verdict: Accepted)

import java.util.Scanner;

public class Main {
	final boolean DEBUG = false;
	class Node {
		int key;
		Node p, l, r;
		Node(int key) {
			this.key = key;
		}
		void insert(Node z) {
			Node y = null;
			Node x = this;
			while (x != null) {
				y = x;
				if (z.key < x.key)
					x = x.l;
				else
					x = x.r;
			}
			z.p = y;
			
			if (z.key < y.key)
				y.l = z;
			else
				y.r = z;
		}
		boolean find(int key) {
			Node x = this;
			while (x != null) {
				if (key == x.key)
					return true;
				else if (key < x.key)
					x = x.l;
				else
					x = x.r;
			}
			return false;
		}
		void print() {
			this.inorder();
			System.out.println();
			this.preorder();
			System.out.println();
		}
		void preorder() {
			System.out.print(" " + this.key);
			if (this.l != null)
				this.l.preorder();
			if (this.r != null)
				this.r.preorder();
		}
		void inorder() {
			if (this.l != null)
				this.l.inorder();
			System.out.print(" " + this.key);
			if (this.r != null)
				this.r.inorder();
		}
	}
	void run() {
		Scanner scan = new Scanner(System.in);
		int n = scan.nextInt();
		Node t = null;
		for (int i = 0; i < n; i++) {
			String inst = scan.next();
			// set a root node
			if (i == 0) {
				int key = scan.nextInt();
				t = new Node(key);
				continue;
			}
			
			switch(inst) {
			case "insert":
				int key = scan.nextInt();
				if (DEBUG)
					System.out.println("insert: " + key);
				t.insert(new Node(key));
				break;
			case "find":
				int findKey = scan.nextInt();
				if (DEBUG)
					System.out.println("find: " + findKey);
				System.out.println(t.find(findKey) ? "yes" : "no");
				break;
			case "print":
				if (DEBUG)
					System.out.println("print");
				t.print();
				break;
			}
		}
	}
	public static void main(String[] args) {
		new Main().run();
	}
}