#include <bits/stdc++.h>
using namespace std;

class node;
node *root, *NIL;

class node{
public:
  node *p = NIL, *l = NIL, *r = NIL;
  int key = 0;

  node(int x) : key(x){}
};


void insert(int key){
  node *x = root, *y = NIL;
  while(x != NIL){
      y = x;
      if(key >= x->key) x = x->r;
      else x = x->l;
  }

  if(y == NIL) root = new node(key);
  else if(key >= y->key) y->r = new node(key);
  else y->l = new node(key);
}

node* find(int key){
  node* x = root;

  while(x != NIL && x->key != key){
    if(key >= x->key) x = x->r;
    else x = x->l;
  }

  return x;
}

void preorder(node* n){
  if(n == NIL) return;
  cout << " " << n->key;
  preorder(n->l);
  preorder(n->r);
}

void inorder(node* n){
  if(n == NIL) return;
  inorder(n->l);
  cout << " " << n->key;
  inorder(n->r);
}

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

int main(){
  root = NIL;

  int n; cin >> n;
  while(n--){
    string s; cin >> s;

    if(s == "insert"){
      int x; cin >> x;
      insert(x);
    }else if(s == "find"){
      int x; cin >> x;
      if(find(x) != NIL) cout << "yes" << endl;
      else cout << "no" << endl;
    }else{
      print();
    }
  }
}


### Prompt

Please provide a Cpp coded solution 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 <bits/stdc++.h>
using namespace std;

class node;
node *root, *NIL;

class node{
public:
  node *p = NIL, *l = NIL, *r = NIL;
  int key = 0;

  node(int x) : key(x){}
};


void insert(int key){
  node *x = root, *y = NIL;
  while(x != NIL){
      y = x;
      if(key >= x->key) x = x->r;
      else x = x->l;
  }

  if(y == NIL) root = new node(key);
  else if(key >= y->key) y->r = new node(key);
  else y->l = new node(key);
}

node* find(int key){
  node* x = root;

  while(x != NIL && x->key != key){
    if(key >= x->key) x = x->r;
    else x = x->l;
  }

  return x;
}

void preorder(node* n){
  if(n == NIL) return;
  cout << " " << n->key;
  preorder(n->l);
  preorder(n->r);
}

void inorder(node* n){
  if(n == NIL) return;
  inorder(n->l);
  cout << " " << n->key;
  inorder(n->r);
}

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

int main(){
  root = NIL;

  int n; cin >> n;
  while(n--){
    string s; cin >> s;

    if(s == "insert"){
      int x; cin >> x;
      insert(x);
    }else if(s == "find"){
      int x; cin >> x;
      if(find(x) != NIL) cout << "yes" << endl;
      else cout << "no" << endl;
    }else{
      print();
    }
  }
}


```