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)

// Binary Search Tree II
#include <stdio.h>
#include <stdlib.h>

struct node{
  struct node *right;
  struct node *left;
  struct node *parent;
  int key;
};
typedef struct node * Node;

Node root, nil;

// 木から key の値を持つノードを探す //
Node treeSearch(Node x, int k){
  if(x == nil || k == x->key) return x;
  if(k < x->key) treeSearch(x->left, k);
  else treeSearch(x->right, k);
}

// ノード x から最小の key を探す //
Node treeMinimum(Node x){
  while(x->left != nil)x = x->left;
  return x;
}

// ノード x から最大の key を探す //
Node treeMaximum(Node x){
  while(x->right != nil)x = x->right;
  return x;
}

//  二分探索木へkを挿入 //
void insert(int k){
  Node y = nil; // x の親
  Node x = root; // T の根
  Node z;
  
  //z->parent = y;
  z = (Node)malloc(sizeof(struct node));
  z->key = k;
  z->left = nil;
  z->right = nil;

  while(x != nil){
    y = x;   // 親を設定
    if(z->key < x->key)x = x->left; // 左の子へ移動
    else x = x->right;            // 右の子へ移動
  }
  z->parent = y;

  if(y == nil)root = z; // T が空の場合
  else if(z->key < y->key)y->left = z; // z を y の左の子にする
  else y->right = z; // z を y の右の子にする
}

// 再帰を使って中間順巡回(Inorder)で表示
void printInorder(Node u){
  if(u == nil)return;
  printInorder(u->left);
  printf(" %d", u->key);
  printInorder(u->right);
}

// 再帰を使って先行順巡回(Preorder)で表示
void printPreorder(Node u){
  if(u == nil)return;
  printf(" %d", u->key);
  printPreorder(u->left);
  printPreorder(u->right);
}

int main(){
  int n, i, x;
  char com[20];
  Node t;
  scanf("%d", &n);

  for ( i = 0; i < n; i++ ){
    scanf("%s", com);
    if ( com[0] == 'f' ){
      scanf("%d", &x);
      Node t = treeSearch(root, x);
      if ( t != nil ) printf("yes\n");
      else printf("no\n");
    } else if ( com[0] == 'i' ){
      scanf("%d", &x);
      insert(x);
    } else if ( com[0] == 'p' ){
      printInorder(root);
      printf("\n");
      printPreorder(root);
      printf("\n");
    }
  }

  return 0;
}