#include <iostream>
struct node{int k,p,l,r;};
node t[500010];
using namespace std;
void find(int now,int k,int ori){
  if(k<t[now].k){
    if(t[now].l) find(t[now].l,k,ori);
    else {
      t[ori].k=k;
      t[ori].p=now;
      t[now].l=ori;
      return;
    } 
  } else {
    if(t[now].r) find(t[now].r,k,ori);
    else {
      t[ori].k=k;
      t[ori].p=now;
      t[now].r=ori;      
      return;
    }
  }
}
string fi(int now,int k){
  if(t[now].k==k) return "yes";
  else if(k<t[now].k){
    if(t[now].l) return fi(t[now].l,k);
    else return "no";
  } else {
    if(t[now].r) return fi(t[now].r,k);
    else return "no";
  } 
}
void pr(int now){
  cout<<" "<<t[now].k;
  if(t[now].l) pr(t[now].l);
  if(t[now].r) pr(t[now].r);
}
void in(int now){
  if(t[now].l) in(t[now].l);
  cout<<" "<<t[now].k;
  if(t[now].r) in(t[now].r);
}
int main(){
  int tmp,n;
  string s;
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>s;
    if(s=="insert"){
      cin>>tmp;
      if(i) find(0,tmp,i);
      else t[i].k=tmp;
    } else if(s=="print"){
      in(0);
      cout<<endl;
      pr(0);
      cout<<endl;
    } else {
      cin>>tmp;
      cout<<fi(0,tmp)<<endl;
    }
  }
  return 0;
}
### Prompt

Your challenge is to write 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 <iostream>
struct node{int k,p,l,r;};
node t[500010];
using namespace std;
void find(int now,int k,int ori){
  if(k<t[now].k){
    if(t[now].l) find(t[now].l,k,ori);
    else {
      t[ori].k=k;
      t[ori].p=now;
      t[now].l=ori;
      return;
    } 
  } else {
    if(t[now].r) find(t[now].r,k,ori);
    else {
      t[ori].k=k;
      t[ori].p=now;
      t[now].r=ori;      
      return;
    }
  }
}
string fi(int now,int k){
  if(t[now].k==k) return "yes";
  else if(k<t[now].k){
    if(t[now].l) return fi(t[now].l,k);
    else return "no";
  } else {
    if(t[now].r) return fi(t[now].r,k);
    else return "no";
  } 
}
void pr(int now){
  cout<<" "<<t[now].k;
  if(t[now].l) pr(t[now].l);
  if(t[now].r) pr(t[now].r);
}
void in(int now){
  if(t[now].l) in(t[now].l);
  cout<<" "<<t[now].k;
  if(t[now].r) in(t[now].r);
}
int main(){
  int tmp,n;
  string s;
  cin>>n;
  for(int i=0;i<n;i++){
    cin>>s;
    if(s=="insert"){
      cin>>tmp;
      if(i) find(0,tmp,i);
      else t[i].k=tmp;
    } else if(s=="print"){
      in(0);
      cout<<endl;
      pr(0);
      cout<<endl;
    } else {
      cin>>tmp;
      cout<<fi(0,tmp)<<endl;
    }
  }
  return 0;
}
```