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;

namespace A
{
    public class Node
    {
        public int left;
        public int right;
        public int value;
        public Tree tree;
    }

    public class Tree
    {
        List<Node> nodes;

        public Tree()
        {
            nodes = new List<Node>();
        }

        public void Insert(int x)
        {
            if (nodes.Count == 0) Insert(x, -1);
            else Insert(x, 0);
        }
        public bool Find(int x)
        {
            if (nodes.Count == 0) return false;
            else return Find(x, 0);
        }

        public void Preorder(int node)
        {
            Console.Write(" " + nodes[node].value);
            if (nodes[node].left != -1) Preorder(nodes[node].left);
            if (nodes[node].right != -1) Preorder(nodes[node].right);
        }
        public void Inorder(int node)
        {
            if (nodes[node].left != -1) Inorder(nodes[node].left);
            Console.Write(" " + nodes[node].value);
            if (nodes[node].right != -1) Inorder(nodes[node].right);
        }
        private void Insert(int x, int parent)
        {
            if (parent == -1) nodes.Add(NewNode(x));
            else
            {
                if (nodes[parent].value > x)
                {
                    if (nodes[parent].left == -1)
                    {
                        nodes.Add(NewNode(x));
                        nodes[parent].left = nodes.Count - 1;
                    }
                    else Insert(x, nodes[parent].left);
                }
                else
                {
                    if (nodes[parent].right == -1)
                    {
                        nodes.Add(NewNode(x));
                        nodes[parent].right = nodes.Count - 1;
                    }
                    else Insert(x, nodes[parent].right);
                }
            }
        }
        private bool Find(int x, int node)
        {
            if (node == -1) return false;
            if (nodes[node].value == x) return true;
            else
            {
                if (nodes[node].value > x) return Find(x, nodes[node].left);
                else return Find(x, nodes[node].right);
            }
        }
        private Node NewNode(int value)
        {
            return new Node() { value = value, left = -1, right = -1, tree = this };
        }
    }
    class Program
    {
        static void Main(string[] args)
        {
            var n = int.Parse(Console.ReadLine());
            var tree = new Tree();
            for (int i = 0; i < n; i++)
            {
                var strs = Console.ReadLine().Split(' ');
                if (strs[0][0] == 'i') tree.Insert(int.Parse(strs[1]));
                else if (strs[0][0] == 'p')
                {
                    tree.Inorder(0); Console.WriteLine();
                    tree.Preorder(0); Console.WriteLine();
                }
                else Console.WriteLine(tree.Find(int.Parse(strs[1])) ? "yes" : "no");
            }
        }
    }
}