#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>

using namespace std;

struct node{
	int key;
	node *pa,*le,*ri;
};

node *root,*NIL;

void Insert(int k)
{
	node *y=NIL;
	node *x=root;
	node *z;
	z=(node *)malloc(sizeof(node));
	z->le=NIL;
	z->ri=NIL;
	z->key=k;
	while(x!=NIL){
		y=x;
		if(z->key < x->key){
			x=x->le;
		}else{
			x=x->ri;
		}
	} 
	z->pa=y;
	if(y==NIL){
		root=z;
	}else{
		if(z->key < y->key){
			y->le=z;
		}else{
			y->ri=z;
		}
	}
}

node* Find(node *x,int k)
{
	while(x!=NIL&&k!=x->key){
		if(k< x->key){
			x=x->le;
		}else{
			x=x->ri;
		}
	}
	return x;
}

void inorder(node *u)
{
	if(u==NIL)return;
	inorder(u->le);
	cout<<' '<<u->key;
	inorder(u->ri);
}

void preorder(node *u)
{
	if(u==NIL)return;
	cout<<' '<<u->key;
	preorder(u->le);
	preorder(u->ri);
}

int main()
{
	int n;
	cin>>n;
	string str;
	int k;
	while(n--){
		cin>>str;
		if(str[0]=='i'){
			cin>>k;
			Insert(k);
		}else if(str[0]=='f'){
			cin>>k;
			node *t=Find(root,k);
			if(t!=NIL){
				cout<<"yes"<<endl;
			}else{
				cout<<"no"<<endl;
			}
		}else if(str[0]=='p'){
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<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>
#include<cstdio>
#include<cstdlib>
#include<cstring>

using namespace std;

struct node{
	int key;
	node *pa,*le,*ri;
};

node *root,*NIL;

void Insert(int k)
{
	node *y=NIL;
	node *x=root;
	node *z;
	z=(node *)malloc(sizeof(node));
	z->le=NIL;
	z->ri=NIL;
	z->key=k;
	while(x!=NIL){
		y=x;
		if(z->key < x->key){
			x=x->le;
		}else{
			x=x->ri;
		}
	} 
	z->pa=y;
	if(y==NIL){
		root=z;
	}else{
		if(z->key < y->key){
			y->le=z;
		}else{
			y->ri=z;
		}
	}
}

node* Find(node *x,int k)
{
	while(x!=NIL&&k!=x->key){
		if(k< x->key){
			x=x->le;
		}else{
			x=x->ri;
		}
	}
	return x;
}

void inorder(node *u)
{
	if(u==NIL)return;
	inorder(u->le);
	cout<<' '<<u->key;
	inorder(u->ri);
}

void preorder(node *u)
{
	if(u==NIL)return;
	cout<<' '<<u->key;
	preorder(u->le);
	preorder(u->ri);
}

int main()
{
	int n;
	cin>>n;
	string str;
	int k;
	while(n--){
		cin>>str;
		if(str[0]=='i'){
			cin>>k;
			Insert(k);
		}else if(str[0]=='f'){
			cin>>k;
			node *t=Find(root,k);
			if(t!=NIL){
				cout<<"yes"<<endl;
			}else{
				cout<<"no"<<endl;
			}
		}else if(str[0]=='p'){
			inorder(root);
			cout<<endl;
			preorder(root);
			cout<<endl;
		}
	}
	return 0;	
}

```