#include<cstdio>
#define MAXN 500000
struct node{
	int key;
	node *ch[2],*fa;
};
node tree[MAXN+5];
node *Root,*NIL,*ncnt;
void Init(){
	NIL=&tree[0];
	NIL->fa=NIL->ch[0]=NIL->ch[1]=NIL;
	ncnt=&tree[1];
	Root=NIL;
}
inline node * NewNode(int val){
	node *p=++ncnt;
	p->key=val;
	p->fa=p->ch[0]=p->ch[1]=NIL;
	return p;
}
void Insert(node *&rt,node *fa,int val){
	if(rt==NIL){
		rt=NewNode(val);
		rt->fa=fa;
		return ;
	}
	int d=(val>=rt->key);
	Insert(rt->ch[d],rt,val);
}
void InOrder(node *rt){
	if(rt==NIL)return ;
	InOrder(rt->ch[0]);
	printf(" %d",rt->key);
	InOrder(rt->ch[1]);
}
void PreOrder(node *rt){
	if(rt==NIL)return ;
	printf(" %d",rt->key);
	PreOrder(rt->ch[0]);
	PreOrder(rt->ch[1]);
}
node *Find(node *rt,int val){
	if(rt==NIL)return NIL;
	if(rt->key==val)return rt;
	int d=(val>=rt->key);
	return Find(rt->ch[d],val);
}
int main(){
	int n,x;
	char op[100];
	Init();
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%s",op);
		if(op[0]=='p')
		{
			InOrder(Root);puts("");
			PreOrder(Root);puts("");
		}
		if(op[0]=='i')
		{
			scanf("%d",&x);
			Insert(Root,NIL,x);
		}
		if(op[0]=='f')
		{
			scanf("%d",&x);
			node *p=Find(Root,x);
			if(p==NIL)puts("no");
			else puts("yes");
		}
		if(op[0]=='d')
		{
			
		}
	}
	return 0;
}
### Prompt

Construct a Cpp code solution to the problem outlined:

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<cstdio>
#define MAXN 500000
struct node{
	int key;
	node *ch[2],*fa;
};
node tree[MAXN+5];
node *Root,*NIL,*ncnt;
void Init(){
	NIL=&tree[0];
	NIL->fa=NIL->ch[0]=NIL->ch[1]=NIL;
	ncnt=&tree[1];
	Root=NIL;
}
inline node * NewNode(int val){
	node *p=++ncnt;
	p->key=val;
	p->fa=p->ch[0]=p->ch[1]=NIL;
	return p;
}
void Insert(node *&rt,node *fa,int val){
	if(rt==NIL){
		rt=NewNode(val);
		rt->fa=fa;
		return ;
	}
	int d=(val>=rt->key);
	Insert(rt->ch[d],rt,val);
}
void InOrder(node *rt){
	if(rt==NIL)return ;
	InOrder(rt->ch[0]);
	printf(" %d",rt->key);
	InOrder(rt->ch[1]);
}
void PreOrder(node *rt){
	if(rt==NIL)return ;
	printf(" %d",rt->key);
	PreOrder(rt->ch[0]);
	PreOrder(rt->ch[1]);
}
node *Find(node *rt,int val){
	if(rt==NIL)return NIL;
	if(rt->key==val)return rt;
	int d=(val>=rt->key);
	return Find(rt->ch[d],val);
}
int main(){
	int n,x;
	char op[100];
	Init();
	scanf("%d",&n);
	for(int i=0;i<n;i++)
	{
		scanf("%s",op);
		if(op[0]=='p')
		{
			InOrder(Root);puts("");
			PreOrder(Root);puts("");
		}
		if(op[0]=='i')
		{
			scanf("%d",&x);
			Insert(Root,NIL,x);
		}
		if(op[0]=='f')
		{
			scanf("%d",&x);
			node *p=Find(Root,x);
			if(p==NIL)puts("no");
			else puts("yes");
		}
		if(op[0]=='d')
		{
			
		}
	}
	return 0;
}
```