#include <iostream>
#include <string>
#include <cstdlib>
using namespace std;

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

Node *root,*NIL;

Node * find(Node *u,int k){
	while(u!=NIL&&k!=u->key) u=(k<u->key?u->left:u->right); 
	return u;
}

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

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

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

int main(){
	int n,x;
	string com;
	
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>com;
		if(com=="find"){
			cin>>x;
			Node *t=find(root,x);
			if(t!=NIL) cout<<"yes\n";
			else cout<<"no\n";
		}else if(com=="insert"){
			cin>>x;
			insert(x);
		}else{
			inParse(root);
			cout<<endl;
			preParse(root);
			cout<<endl;
		}
	}
	
	return 0;
}



### Prompt

In Cpp, your task is to solve 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 <string>
#include <cstdlib>
using namespace std;

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

Node *root,*NIL;

Node * find(Node *u,int k){
	while(u!=NIL&&k!=u->key) u=(k<u->key?u->left:u->right); 
	return u;
}

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

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

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

int main(){
	int n,x;
	string com;
	
	cin>>n;
	for(int i=0;i<n;i++){
		cin>>com;
		if(com=="find"){
			cin>>x;
			Node *t=find(root,x);
			if(t!=NIL) cout<<"yes\n";
			else cout<<"no\n";
		}else if(com=="insert"){
			cin>>x;
			insert(x);
		}else{
			inParse(root);
			cout<<endl;
			preParse(root);
			cout<<endl;
		}
	}
	
	return 0;
}



```