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: WA: Presentation Error)

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

class Node
{
    internal int key;
    internal Node left, right, parent;
    public Node(int key) {
        this.key = key;
    }
}

class B
{
    static Node root;
    public static void Main() {
        int n = int.Parse(Console.ReadLine());
        StringBuilder output = new StringBuilder();
        for (int i = 0; i < n; i++) {
            String[] input = Console.ReadLine().Split(' ');
            if (input[0] == "insert") {
                Insert(int.Parse(input[1]));
            }else if (input[0] == "find") {
                output.AppendLine(find(root, int.Parse(input[1]))? "yes":"no");
            } else {
                Inorder(root, output);
                output.AppendLine();
                Preorder(root, output);
                if (i != n - 1) {
                    output.AppendLine();
                }
            }

        }
        Console.WriteLine(output);


    }
    static bool find(Node x, int key) {
        while (x != null) {
            if (x.key == key) {
                return true;
            }
            x = key < x.key ? x.left : x.right;
        }
        return false;
    }
    static void Insert(int key) {
        Node x = root;
        Node y = null;
        Node z = new Node(key);
        while (x != null) {
            y = x;
            x = z.key < x.key ? x.left : x.right;
        }
        z.parent = y;
        if (y == null) {
            root = z;
        }else if (z.key < y.key) {
            y.left = z;
        } else {
            y.right = z;
        }
    }
    static void Preorder(Node nodes, StringBuilder output) {
        if (nodes == null) {
            return;
        }
        output.Append(" " + nodes.key);
        Preorder(nodes.left, output);
        Preorder(nodes.right, output);
    }

    static void Inorder(Node nodes, StringBuilder output) {
        if (nodes == null) {
            return;
        }
        Inorder(nodes.left, output);
        output.Append(" " + nodes.key);
        Inorder(nodes.right, output);
    }

    /*static void Postorder(Node[] nodes, int num, StringBuilder output) {
        if (num == -1) {
            return;
        }
        Postorder(nodes, nodes[num].left, output);
        Postorder(nodes, nodes[num].right, output);
        output.Append(" " + num);
    }*/
}