#include <iostream>
using namespace std;

typedef struct node{
  struct node *p,*r,*l;
  int key;
}Node;

Node *insert(Node *p,int key){
  Node *x,*y,*n;
  x=p;
  y=NULL;
  while(x!=NULL){
    y=x;
    if(x->key<=key)x=x->r;
    else x=x->l;
  }
  
  n=new Node;
  n->p=y;
  n->r=NULL;
  n->l=NULL;
  n->key=key;

  if (p==NULL)return n;
  if (y->key<=key) y->r=n;
  else y->l=n;
  return p;
}

void printA(Node *p){
  if (p==NULL) return;
  printA(p->l);
  cout << " " << p->key;
  printA(p->r);
}

void printB(Node *p){
  if (p==NULL) return;
  cout << " " << p->key;
  printB(p->l);
  printB(p->r);
}

void print(Node *p){
  printA(p);
  cout << endl;
  printB(p);
  cout << endl;
}

void find(Node *p,int key){
  Node *x=p;
  while(x!=NULL){
    if (x->key<key) x=x->r;
    else if (x->key>key) x=x->l;
    else {
      cout << "yes" << endl;
      return;
    }
  }
  cout << "no"<<endl;
}

int main(){
  int n,k;
  Node *root=NULL;
  char cmd[16];

  cin >> n;
  for (int i=0;i<n;i++){
    cin >> cmd;
    if (cmd[0]=='i'){
      cin >> k;
      root=insert(root,k);
    }else if (cmd[0]=='p'){
      print(root);
    }else if (cmd[0]=='f'){
      cin >> k;
      find(root,k);
    }//else if (cmd[0]==''){
    //}
  }
  
  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>
using namespace std;

typedef struct node{
  struct node *p,*r,*l;
  int key;
}Node;

Node *insert(Node *p,int key){
  Node *x,*y,*n;
  x=p;
  y=NULL;
  while(x!=NULL){
    y=x;
    if(x->key<=key)x=x->r;
    else x=x->l;
  }
  
  n=new Node;
  n->p=y;
  n->r=NULL;
  n->l=NULL;
  n->key=key;

  if (p==NULL)return n;
  if (y->key<=key) y->r=n;
  else y->l=n;
  return p;
}

void printA(Node *p){
  if (p==NULL) return;
  printA(p->l);
  cout << " " << p->key;
  printA(p->r);
}

void printB(Node *p){
  if (p==NULL) return;
  cout << " " << p->key;
  printB(p->l);
  printB(p->r);
}

void print(Node *p){
  printA(p);
  cout << endl;
  printB(p);
  cout << endl;
}

void find(Node *p,int key){
  Node *x=p;
  while(x!=NULL){
    if (x->key<key) x=x->r;
    else if (x->key>key) x=x->l;
    else {
      cout << "yes" << endl;
      return;
    }
  }
  cout << "no"<<endl;
}

int main(){
  int n,k;
  Node *root=NULL;
  char cmd[16];

  cin >> n;
  for (int i=0;i<n;i++){
    cin >> cmd;
    if (cmd[0]=='i'){
      cin >> k;
      root=insert(root,k);
    }else if (cmd[0]=='p'){
      print(root);
    }else if (cmd[0]=='f'){
      cin >> k;
      find(root,k);
    }//else if (cmd[0]==''){
    //}
  }
  
  return 0;
}
```