#include<iostream>
#include<string>
using namespace std;

class Node {
public:    
  int key;
  Node *parent, *left, *right;
};

Node *root, *NIL;

void insert(int key) {
  Node *x, *y, *z;

  z = new Node;
  z->key = key;
  z->left = z->right = NIL;
  y = NIL;
  x = root;

  while (x != NIL) {
    y = x;
    if (z->key < y->key) x = x->left;
    else x = x->right;
  }

  z->parent = y;
  if (y == NIL) root = z;
  else if (z->key < y->key) y->left = z;
  else y->right = z;
}

void preorder(Node *node) {
  if (node == NIL) return;
  cout << " " << node->key;
  preorder(node->left);
  preorder(node->right);
}

void inorder(Node *node) {
  if (node == NIL) return;
  inorder(node->left);
  cout << " " << node->key;
  inorder(node->right);
}

void print() {
  inorder(root);
  cout << endl;
  preorder(root);
  cout << endl;
};

bool find(int key) {
  Node *x = root;

  while (x != NIL) {
    if (key < x->key) x = x->left;
    else if (key > x->key)  x = x->right;
    else return true;
  }
  
  return false;
}

int main() {
  int i, m, key;
  string command;

  cin >> m;
  for (i = 0; i < m; i++) {
    cin >> command;
    if (command[0] == 'i') {
      cin >> key;
      insert(key);
    } else if (command[0] == 'f') {
      cin >> key;
      if (find(key)) cout << "yes" << endl;
      else cout << "no" << endl;
    } else {
      print();
    }
  }
    
  return 0;
}


### Prompt

Develop a solution in CPP to the problem described below:

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.

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.

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.

Example

Input

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print


Output

yes
no
 1 12 17 20 25 30 88
 30 12 1 20 17 25 88

### Response

```cpp
#include<iostream>
#include<string>
using namespace std;

class Node {
public:    
  int key;
  Node *parent, *left, *right;
};

Node *root, *NIL;

void insert(int key) {
  Node *x, *y, *z;

  z = new Node;
  z->key = key;
  z->left = z->right = NIL;
  y = NIL;
  x = root;

  while (x != NIL) {
    y = x;
    if (z->key < y->key) x = x->left;
    else x = x->right;
  }

  z->parent = y;
  if (y == NIL) root = z;
  else if (z->key < y->key) y->left = z;
  else y->right = z;
}

void preorder(Node *node) {
  if (node == NIL) return;
  cout << " " << node->key;
  preorder(node->left);
  preorder(node->right);
}

void inorder(Node *node) {
  if (node == NIL) return;
  inorder(node->left);
  cout << " " << node->key;
  inorder(node->right);
}

void print() {
  inorder(root);
  cout << endl;
  preorder(root);
  cout << endl;
};

bool find(int key) {
  Node *x = root;

  while (x != NIL) {
    if (key < x->key) x = x->left;
    else if (key > x->key)  x = x->right;
    else return true;
  }
  
  return false;
}

int main() {
  int i, m, key;
  string command;

  cin >> m;
  for (i = 0; i < m; i++) {
    cin >> command;
    if (command[0] == 'i') {
      cin >> key;
      insert(key);
    } else if (command[0] == 'f') {
      cin >> key;
      if (find(key)) cout << "yes" << endl;
      else cout << "no" << endl;
    } else {
      print();
    }
  }
    
  return 0;
}


```