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

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

typedef Node* Nodepointer;

Nodepointer T;

void insert(int z){
  Nodepointer t=(Node*)malloc(sizeof(Node));
  t->l=NULL;
  t->r=NULL;
  t->key=z;
  if(!f){
    T->key=z;
    f=1;
    return;
  }
  Nodepointer y=NULL,x=T;
  while(x!=NULL){
    y=x;
    if(t->key<x->key)x=x->l;
    else x=x->r;
  }
  t->p=y;
  if(y==NULL)T=t;
  else if(t->key<y->key)y->l=t;
  else y->r=t;
}

bool find(int key){
  Nodepointer x=T;
  while(x!=NULL){
    if(x->key==key)return true;
    if(key<x->key)x=x->l;
    else x=x->r;
  }
  return false;
}

void print(Nodepointer x,int y){
  if(y)cout<<' '<<x->key;
  if(x->l!=NULL)print(x->l,y);
  if(!y)cout<<' '<<x->key;
  if(x->r!=NULL)print(x->r,y);
}

int main(){
  string s;
  int n,z;
  cin>>n;
  T=(Node*)malloc(sizeof(Node));
  T->p=NULL;
  T->l=NULL;
  T->r=NULL;
  while(n--){
    cin>>s;
    if(s=="insert")cin>>z,insert(z);
    else if(f&&s=="find"){
      cin>>z;
      if(find(z))cout<<"yes"<<endl;
      else cout<<"no"<<endl;
    }
    else if(f){
      print(T,0);
      cout<<endl;
      print(T,1);
      cout<<endl;
    }
  }
  return 0;
}
### Prompt

Generate a CPP solution to the following problem:

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;
int f;

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

typedef Node* Nodepointer;

Nodepointer T;

void insert(int z){
  Nodepointer t=(Node*)malloc(sizeof(Node));
  t->l=NULL;
  t->r=NULL;
  t->key=z;
  if(!f){
    T->key=z;
    f=1;
    return;
  }
  Nodepointer y=NULL,x=T;
  while(x!=NULL){
    y=x;
    if(t->key<x->key)x=x->l;
    else x=x->r;
  }
  t->p=y;
  if(y==NULL)T=t;
  else if(t->key<y->key)y->l=t;
  else y->r=t;
}

bool find(int key){
  Nodepointer x=T;
  while(x!=NULL){
    if(x->key==key)return true;
    if(key<x->key)x=x->l;
    else x=x->r;
  }
  return false;
}

void print(Nodepointer x,int y){
  if(y)cout<<' '<<x->key;
  if(x->l!=NULL)print(x->l,y);
  if(!y)cout<<' '<<x->key;
  if(x->r!=NULL)print(x->r,y);
}

int main(){
  string s;
  int n,z;
  cin>>n;
  T=(Node*)malloc(sizeof(Node));
  T->p=NULL;
  T->l=NULL;
  T->r=NULL;
  while(n--){
    cin>>s;
    if(s=="insert")cin>>z,insert(z);
    else if(f&&s=="find"){
      cin>>z;
      if(find(z))cout<<"yes"<<endl;
      else cout<<"no"<<endl;
    }
    else if(f){
      print(T,0);
      cout<<endl;
      print(T,1);
      cout<<endl;
    }
  }
  return 0;
}
```