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.Collections.Generic;
using System.Linq;
using System.Text;

namespace Practice
{
    class Program
    {
        public class Node
        {
            public int key;
            public Node parent;
            public Node left;
            public Node right;
        }
        static void Main(string[] args)
        {
            SolveA(args);
            //SolveB(args);
            //SolveC(args);
            //SolveD(args);


        }
        static void SolveA(string[] args)
        {
            int n = int.Parse(Console.ReadLine());
            Node rootNode = null;
            for(int i=0;i<n;++i)
            {
                string[] szarr = Console.ReadLine().Split(' ');
                if (szarr[0] == "print")
                {
                    InOrder(rootNode);
                    Console.WriteLine();
                    PreOrder(rootNode);
                    Console.WriteLine();
                }
                else if( szarr[0] == "find")
                {
                    int key = int.Parse(szarr[1]);
                    Node fount = Find(rootNode, key);
                    if( fount != null)
                    {
                        Console.WriteLine("yes");
                    }else
                    {
                        Console.WriteLine("no");
                    }
                }
                else
                {
                    int key = int.Parse(szarr[1]);
                    var z = new Node();
                    z.key = key;
                    Insert(ref rootNode, z);
                }
            }

        }
        static Node Find (Node p, int k)
        {
            while( p != null && k != p.key)
            {
                if( k < p.key)
                {
                    p = p.left;
                }else
                {
                    p = p.right;
                }
            }
            return p;
        }
        static void Insert(ref Node rootNode, Node z)
        {
            Node y = null;

            Node x = rootNode;
            while(x != null)
            {
                y = x;
                if( z.key < x.key)
                {
                    x = x.left;
                }else
                {
                    x = x.right;
                }
            }
            z.parent = y;
            if(y == null)
            {
                rootNode = z;
            }else if( z.key < y.key)
            {
                y.left = z;
            }else
            {
                y.right = z;
            }
        }

        static void PreOrder(Node p)
        {
            if( p == null) { return; }
            Console.Write(" " + p.key);
            PreOrder(p.left);
            PreOrder(p.right);
        }
        static void InOrder(Node p)
        {
            if( p == null) { return; }
            InOrder(p.left);
            Console.Write(" " + p.key);
            InOrder(p.right);
        }
    }

}