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 C# (judge verdict: Accepted)

using System;
using System.IO;

namespace Binary_search_trees
{
    class Binary_Search_Tree_II
    {
        class BinaryTree
        {
            public class Node
            {
                internal int val;
                internal Node left, right, parent;

                internal Node() : this(0, null) { }

                internal Node(int val, Node parent)
                {
                    this.val = val;
                    this.parent = parent;
                    left = right = null;
                }
            }

            Node root;

            public BinaryTree()
            {
                root = null;
            }

            public void Insert(int elem)
            {
                if (root == null)
                {
                    root = new Node(elem, null);
                    return;
                }

                Node n = root;
                Node p = null;
                while (n != null)
                {
                    p = n;
                    if (n.val > elem) n = n.left;
                    else n = n.right;
                }

                n = new Node(elem, p);
                if (p.val > elem) p.left = n;
                else p.right = n;
            }
            public Node Find(int elem)
            {
                Node n = root;
                while (n != null)
                {
                    if (n.val > elem) n = n.left;
                    else if (n.val < elem) n = n.right;
                    else break;
                }
                return n;
            }

            public bool Contains(int elem)
            {
                return Find(elem) != null;
            }

            public void PrintPreorder(Node n)
            {
                if (n == null) return;
                Console.Write(" " + n.val);
                PrintPreorder(n.left);
                PrintPreorder(n.right);
            }

            public void PrintPreorder()
            {
                PrintPreorder(root);
                Console.WriteLine();
            }

            public void PrintInorder(Node n)
            {
                if (n == null) return;
                PrintInorder(n.left);
                Console.Write(" " + n.val);
                PrintInorder(n.right);
            }

            public void PrintInorder()
            {
                PrintInorder(root);
                Console.WriteLine();
            }
        }

        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var bt = new BinaryTree();
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            for (int i = 0; i < n; i++)
            {
                var line = Console.ReadLine();
                switch (line[0])
                {
                    case 'i':
                        bt.Insert(int.Parse(line.Substring(7)));
                        break;
                    case 'f':
                        if (bt.Contains(int.Parse(line.Substring(5)))) Console.WriteLine("yes");
                        else Console.WriteLine("no");
                        break;
                    case 'p':
                        bt.PrintInorder();
                        bt.PrintPreorder();
                        break;
                }
            }
            Console.Out.Flush();
        }
    }
}