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.Linq;

public class Tree{
  public int value;
  public Tree parent;
  public Tree left;
  public Tree right;
}

class A8{
   static Tree root = new Tree();
  public static void Main(){
    int n = int.Parse(Console.ReadLine());
    int i = 0,k = 0,count = 0;
    string[] str = new string[n];
    for(i = 0;i < n;i++){
      var command = Console.ReadLine().Split(' ');
      if(command[0].Equals("insert")) Insert(root,int.Parse(command[1]));
      else if(command[0].Equals("find")){
       if(Find(int.Parse(command[1])) == null)  str[k++] = "no";
       else str[k++] = "yes";
     }
     if(command[0].Equals("print")){
       for(int j = count;j < k;j++){
         Console.WriteLine(str[j]);
         count++;
       }
     Print(root);
      }else if(i == n - 1){
        for(int j = count;j < k;j++){
          Console.WriteLine(str[j]);
          count++;
        }
      }
    }
  }
  public static Tree Find(int key){
    Tree n = root;
    while(n != null){
      if(n.value > key) n = n.left;
      else if(n.value < key) n = n.right;
      else break;
    }
    return n;
  }
  public static void Insert(Tree tree,int value){
    Tree x = tree;
    Tree y = null;
    while(x != null && x.value != 0){
      y = x;
      if(value < x.value) x = x.left;
      else x = x.right;
    }
    Tree tmp = new Tree();
    tmp.value = value;
    tmp.parent = y;

    if(y == null){
      tree.value = value;
    }else if(value < y.value){
      y.left = tmp;
    }else{
      y.right = tmp;
    }
  }
  public static void Print(Tree tree){
    Inorder(tree);
    Console.WriteLine();
    Preorder(tree);
    Console.WriteLine();
  }

  public static void Inorder(Tree tree){
    if(tree == null) return;
    Inorder(tree.left);
    Console.Write(" " + tree.value);
    Inorder(tree.right);
  }
  public static void Preorder(Tree tree){
    if(tree == null) return;
    Console.Write(" " + tree.value);
    Preorder(tree.left);
    Preorder(tree.right);
  }
}