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: Time Limit Exceeded)

using System;
using System.Text;
using System.Collections.Generic;
 
public class node
{
    public node parent;
    public node rightChild;
    public node leftChild;
    public int key;
}
 
public class Test
{
    public static int[] preorderKey, inorderKey;
    public static int precount, incount;
     
    public static void Main()
    {
 
        int n = int.Parse(Console.ReadLine());
        List<node> tree = new List<node>();
         
        for(int i = 0; i < n ; i++) {
            string[] atom = Console.ReadLine().Split(" ".ToCharArray());
             
            switch(atom[0][0]){
                case 'i':
                    Insert(int.Parse(atom[1]), tree);
                    break;
				
				case 'f':
					if(tree.Count == 0) {
						Console.WriteLine("no");
					} else {
						Console.WriteLine( Find( int.Parse(atom[1]), tree[0], tree.ToArray() )? "yes" : "no" );
					}
					break;
                 
                case 'p':
                    Print(tree.ToArray());
                    break;
            }
        }
    }
     
    public static void Insert(int v ,List<node> T)
    {
        node y = null;
        
        node z = new node();
		z.key = v;
		T.Add(z);
        
        if(T.Count == 1) return;
        node x = T[0];
 
        while(x != null) {
            y = x;
            if(v < x.key) x = x.leftChild;
            else x = x.rightChild;
        }
        z.parent = y;
         
        if(y == null) {
            
        } else if (v < y.key) {
            y.leftChild = T[T.Count - 1];
        } else {
            y.rightChild = T[T.Count - 1];
        }
    }
	
	public static bool Find(int v, node x, node[] T)
	{
		while(x != null) {
			if(x.key == v) return true;
			else if(v < x.key) x = x.leftChild;
			else x = x.rightChild;
		}
		
		return false;
	}
 
    public static void Print(node[] T)
    {
        preorderKey = new int[T.Length];
        inorderKey = new int[T.Length];
        precount = 0;
        incount = 0;
         
        node root = T[0];
        Inorder(root, T);
        Preorder(root, T);
        
        StringBuilder sb = new StringBuilder();
        for(int i = 0; i < T.Length; i++) {
            sb.Append(" " + inorderKey[i]);
        }
        Console.WriteLine(sb.ToString());
        sb = new StringBuilder();
        for(int i = 0; i < T.Length; i++) {
            sb.Append(" " + preorderKey[i]);
        }
        Console.WriteLine(sb.ToString());
         
    }
     
    public static void Preorder(node t, node[] tree)
    {
        preorderKey[precount++] = t.key;
        if(t.leftChild != null) Preorder(t.leftChild, tree);
        if(t.rightChild != null) Preorder(t.rightChild, tree);
    }
     
    public static void Inorder(node t, node[] tree)
    {
        if(t.leftChild != null) Inorder(t.leftChild, tree);
        inorderKey[incount++] = t.key;
        if(t.rightChild != null) Inorder(t.rightChild, tree);
    }
     
    public static node GetRoot(node[] T)
    {
        if ( T ==  null ) return null;
        if ( T.Length == 0) return null;
         
        node u = T[0];
        while(u.parent != null) {
            u = u.parent;
        }
         
        return u;
    }
}