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

struct Node{
  int key;
  Node *right,*left,*parent;
};

Node *root,*NIL;

Node * find(Node *p, int a){
  while(p!=NIL && a!=p->key){
    if(a < p->key) p=p->left;
    else p=p->right;
  }
  return p;
}

void insert(int a){
  Node *y=NIL, *x=root, *z;
  z = (Node *)malloc(sizeof(Node));
  z->key=a;
  z->left=NIL;
  z->right=NIL;

  while(x!=NIL){
    y=x;
    if(z->key<x->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 inorder(Node *p){
  if(p==NIL) return;
  inorder(p->left);
  cout << " " << p->key;
  inorder(p->right);
}

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

int main(){
  int n,x;
  string str;

  cin >> n;

  for(int i=0;i<n;i++){
    cin >> str;
    if(str=="find"){
      cin >> x;
      Node *p=find(root,x);
      if(p!=NIL) cout << "yes" << endl;
      else cout << "no" << endl;
    }
    else if(str=="insert"){
      cin >> x;
      insert(x);
    }
    else if(str=="print"){
      inorder(root);
      cout << endl;
      preorder(root);
      cout << endl;
    }
  }
  return 0;
}

### 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;

struct Node{
  int key;
  Node *right,*left,*parent;
};

Node *root,*NIL;

Node * find(Node *p, int a){
  while(p!=NIL && a!=p->key){
    if(a < p->key) p=p->left;
    else p=p->right;
  }
  return p;
}

void insert(int a){
  Node *y=NIL, *x=root, *z;
  z = (Node *)malloc(sizeof(Node));
  z->key=a;
  z->left=NIL;
  z->right=NIL;

  while(x!=NIL){
    y=x;
    if(z->key<x->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 inorder(Node *p){
  if(p==NIL) return;
  inorder(p->left);
  cout << " " << p->key;
  inorder(p->right);
}

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

int main(){
  int n,x;
  string str;

  cin >> n;

  for(int i=0;i<n;i++){
    cin >> str;
    if(str=="find"){
      cin >> x;
      Node *p=find(root,x);
      if(p!=NIL) cout << "yes" << endl;
      else cout << "no" << endl;
    }
    else if(str=="insert"){
      cin >> x;
      insert(x);
    }
    else if(str=="print"){
      inorder(root);
      cout << endl;
      preorder(root);
      cout << endl;
    }
  }
  return 0;
}

```