#include<bits/stdc++.h>
using namespace std;
#define int long long
struct node{
  int key;
  node *left,*right,*p;
  node(){}
  node(int key):key(key){left=right=p=NULL;};
};
node *root;
void insert(node z){
  node *y=NULL;
  node *x=root;
  while(x!=NULL){
    y=x;
    if(z.key<x->key) x=x->left;
    else x=x->right;
  }
  z.p=y;
  if(y==NULL) root=new node(z);
  else if(z.key<y->key) y->left=new node(z);
  else y->right=new node(z);
}
bool find(int z){
  node *x=root;
  while(x!=NULL){
    if(z==x->key) return true;
    if(z<x->key) x=x->left;
    else x=x->right;
  }
  return false;
}
void inorderTreeWalk(node *v){
  if(v==NULL) return;
  inorderTreeWalk(v->left);
  cout<<" "<<v->key;
  inorderTreeWalk(v->right);
}
void preorderTreeWalk(node *v){
  if(v==NULL) return;
  cout<<" "<<v->key;
  preorderTreeWalk(v->left);
  preorderTreeWalk(v->right);
}
signed main(){
  int n;
  cin>>n;
  root=NULL;
  for(int i=0;i<n;i++){
    string s;
    cin>>s;
    //cout<<(root==NULL?-1:root->key)<<endl;
    if(s=="print"){
      inorderTreeWalk(root);
      cout<<endl;
      preorderTreeWalk(root);
      cout<<endl;
      continue;
    }
    int x;
    cin>>x;
    if(s=="insert"){
      insert(node(x));
    }
    if(s=="find"){
      cout<<(find(x)?"yes":"no")<<endl;
    }
  }
}

### 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;
#define int long long
struct node{
  int key;
  node *left,*right,*p;
  node(){}
  node(int key):key(key){left=right=p=NULL;};
};
node *root;
void insert(node z){
  node *y=NULL;
  node *x=root;
  while(x!=NULL){
    y=x;
    if(z.key<x->key) x=x->left;
    else x=x->right;
  }
  z.p=y;
  if(y==NULL) root=new node(z);
  else if(z.key<y->key) y->left=new node(z);
  else y->right=new node(z);
}
bool find(int z){
  node *x=root;
  while(x!=NULL){
    if(z==x->key) return true;
    if(z<x->key) x=x->left;
    else x=x->right;
  }
  return false;
}
void inorderTreeWalk(node *v){
  if(v==NULL) return;
  inorderTreeWalk(v->left);
  cout<<" "<<v->key;
  inorderTreeWalk(v->right);
}
void preorderTreeWalk(node *v){
  if(v==NULL) return;
  cout<<" "<<v->key;
  preorderTreeWalk(v->left);
  preorderTreeWalk(v->right);
}
signed main(){
  int n;
  cin>>n;
  root=NULL;
  for(int i=0;i<n;i++){
    string s;
    cin>>s;
    //cout<<(root==NULL?-1:root->key)<<endl;
    if(s=="print"){
      inorderTreeWalk(root);
      cout<<endl;
      preorderTreeWalk(root);
      cout<<endl;
      continue;
    }
    int x;
    cin>>x;
    if(s=="insert"){
      insert(node(x));
    }
    if(s=="find"){
      cout<<(find(x)?"yes":"no")<<endl;
    }
  }
}

```