#include<iostream>
#include<cstdlib>
#include<string>

using namespace std;

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

Node *root,*NIL;//????????????NULL??§????????????????????????

void insert(int k);
void inorder(Node *u);
void preorder(Node *u);
Node* find(Node *x,int key);

int main(){
	int m; cin>>m;
	int key;
	string command;
	for(int i=0;i<m;i++){
		cin>>command;
		if(command=="insert"){
			cin>>key;
			insert(key);
		}else if(command=="print"){
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<endl;
		}else if(command=="find"){
			Node *x;
			cin>>key;
			x = find(root,key);
			if(x==NULL){
				cout<<"no"<<endl;
			}else if(x->key==key){
				cout<<"yes"<<endl;
			}
		}
	}
}

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

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

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

void preorder(Node *u){
	if(u==NIL) return ;
	cout<<" "<<u->key;
	preorder(u->left);
	preorder(u->right);
}
### 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>
#include<cstdlib>
#include<string>

using namespace std;

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

Node *root,*NIL;//????????????NULL??§????????????????????????

void insert(int k);
void inorder(Node *u);
void preorder(Node *u);
Node* find(Node *x,int key);

int main(){
	int m; cin>>m;
	int key;
	string command;
	for(int i=0;i<m;i++){
		cin>>command;
		if(command=="insert"){
			cin>>key;
			insert(key);
		}else if(command=="print"){
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<endl;
		}else if(command=="find"){
			Node *x;
			cin>>key;
			x = find(root,key);
			if(x==NULL){
				cout<<"no"<<endl;
			}else if(x->key==key){
				cout<<"yes"<<endl;
			}
		}
	}
}

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

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

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

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