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 ConsoleApplication1
{
    class Node
    {
        internal int key;
        internal Node left, right;

        public Node(int key)
        {
            this.key = key;
        }
    }

    class Program
    {
        static StringBuilder sb = new StringBuilder();
        static Node root;

        static void Main(string[] args)
        {
            int n = int.Parse(Console.ReadLine());

            for(int i = 0; i < n; i++)
            {
                string[] input = Console.ReadLine().Split(' ');

                switch (input[0][0])
                {
                    case 'i':
                        Insert(int.Parse(input[1]));
                        break;
                    case 'f':
                        sb.AppendLine(find(root, int.Parse(input[1])) ? "yes" : "no");
                        break;
                    default:
                        Inorder(root);
                        sb.AppendLine();
                        Preorder(root);
                        sb.AppendLine();
                        break;
                }
            }
            Console.Write(sb);
        }

        static bool find(Node u,int k)
        {
            while (u != null)
            {
                if (k == u.key) return true;
                u = k < u.key ? u.left : u.right;
            }
            return false;
        }
        
        static void Insert(int k)
        {
            Node x = root;
            Node y = null;
            Node z = new Node(k);

            while (x != null)
            {
                y = x;
                x = z.key < x.key ? x.left : x.right;
            }

            if (y != null)
            {
                if (z.key < y.key) y.left = z;
                else y.right = z;
            }
            else root = z;
        }

        static void Inorder(Node u)
        {
            if (u == null) return;

            Inorder(u.left);
            sb.Append(" " + u.key);
            Inorder(u.right);
        }

        static void Preorder(Node u)
        {
            if (u == null) return;

            sb.Append(" " + u.key);
            Preorder(u.left);
            Preorder(u.right);
        }
    }
}