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.Text;

namespace ALDS1_8_B {
    class Node {
        public int Key { get; set; }
        public Node Parent { get; set; }
        public Node Left { get; set; }
        public Node Right { get; set; }

        public Node(int key = default(int), Node parent = null) {
            Key = key;
            Parent = parent;
        }
    }

    class Problem {
        private Node _root;
        private StringBuilder _sb;

        public void Run() {
            _sb = new StringBuilder();
            int n = int.Parse(Console.ReadLine());
            SetRoot();
            for (int i = 1; i < n; i++) {
                string[] input = Console.ReadLine().Split(' ');

                switch (input[0]) {
                    case "insert":
                        Insert(int.Parse(input[1]));
                        break;
                    case "print":
                        Inorder(_root);
                        _sb.AppendLine();
                        Preorder(_root);
                        _sb.AppendLine();
                        break;
                    case "find":
                        _sb.AppendLine(Find(int.Parse(input[1])) != null ? "yes" : "no");
                        break;
                }
            }
            Console.Write(_sb);
        }

        private Node Find(int key) {
            Node ret = _root;
            while (ret != null && key != ret.Key) {
                ret = key < ret.Key ? ret.Left : ret.Right;
            }
            return ret;
        }
        
        private void Insert(int key) {
            Node x = _root;
            Node y = null;
            while (x != null) {
                y = x;
                x = key < x.Key ? x.Left : x.Right;
            }

            if (key < y.Key)
                y.Left = new Node(key, parent: y);
            else
                y.Right = new Node(key, parent: y);
        }

        private void Inorder(Node node) {
            if (node == null)
                return;
            Inorder(node.Left);
            _sb.Append(" " + node.Key);
            Inorder(node.Right);
        }

        private void Preorder(Node node) {
            if (node == null)
                return;
            _sb.Append(" " + node.Key);
            Preorder(node.Left);
            Preorder(node.Right);
        }
        
        private void SetRoot() {
            string[] input = Console.ReadLine().Split(' ');
            _root = new Node(int.Parse(input[1]));
        }
    }

    class Program {
        static void Main(string[] args) {
            Problem p = new Problem();
            p.Run();
        }
    }
}