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.io.BufferedReader;
import java.io.InputStreamReader;

public class Main{

	public static Node root = null;
	private static class Node {
		Node() {
			this.value = -1;
			this.leftNode = null;
			this.rightNode = null;
		}
		public int value;
		public Node leftNode;
		public Node rightNode;
	}

	public static void main(String[] args) throws Exception{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
//		Scanner s = new Scanner(System.in);
		int cnt = new Integer(br.readLine()).intValue();
		for(int i=0 ; i<cnt ; i++) {
			String[] tmp = br.readLine().split(" ");
			if("insert".equals(tmp[0])) {
				Node n = new Node();
				n.value = new Integer(tmp[1]).intValue();
				insert(n);
			}else if("find".equals(tmp[0])) {
				Node n = new Node();
				n.value = Integer.parseInt(tmp[1]);
				boolean result = find(n);
				if(result)
					System.out.println("yes");
				else
					System.out.println("no");
			}
			else {
				inorder(root);
				System.out.println();
				preorder(root);
				System.out.println();
			}
		}
		if(br!=null) {
			br.close();
			br = null;
		}
	}

	public static void insert(Node node) {
		if(root==null){
			root = node;
			return;
		}
		Node targetNode = root;
		Node parent = null;
		while(targetNode != null) {
			parent = targetNode;
			if(targetNode.value > node.value)
				targetNode = targetNode.leftNode;
			else
				targetNode = targetNode.rightNode;
		}
		if(parent.value > node.value)
			parent.leftNode = node;
		else
			parent.rightNode = node;
	}

	public static boolean find(Node node) {
		if(root==null)
			return false;
		Node target = root;
		while(target!=null) {
			if(target.value==node.value)
				return true;
			else{
				if(target.value>node.value) {
					target = target.leftNode;
				}else{
					target = target.rightNode;
				}
			}
		}
		return false;
	}

	public static void preorder(Node root) {
		System.out.print(" " + root.value);
		if(root.leftNode != null)
			preorder(root.leftNode);
		if(root.rightNode != null)
			preorder(root.rightNode);
	}

	public static void inorder(Node root) {
		if(root.leftNode != null)
			inorder(root.leftNode);
		System.out.print(" " + root.value);
		if(root.rightNode != null)
			inorder(root.rightNode);
	}
}