#include<cstdio>
const int MAXN = 500000;
struct node{
	int key;
	node *ch[2];
};
node tree[MAXN + 5];
node *Root,*NIL,*ncnt;
void Init() {
	NIL = &tree[0];
	Root = NIL -> ch[0] = NIL -> ch[1] = NIL;
	ncnt  = &tree[1];
}
inline node * NewNode(int val) {
	node *p = (++ncnt);
	p->key = val;
	p->ch[0] = p->ch[1] = NIL;
	return p;
};
void Insert(node *&rt,int val) {
	if( rt == NIL ) {
		rt = NewNode(val);
		return ;
	}
	int d = (val > rt->key);
	Insert(rt->ch[d],val);
}
node * Find(node *rt,int val){
	if( rt == NIL ) return NIL;
	if( rt->key == val ) return rt;
	return Find(rt->ch[val>rt->key],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]);
}
char s1[10];
int main()
{
	int n,x;
	Init();
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%s",s1);
		if( s1[0] == 'p' )
		{
			InOrder(Root);
			puts("");
			PreOrder(Root);
			puts("");
		}
		else if( s1[0] == 'i' )
		{
			scanf("%d",&x);
			Insert(Root,x);
		}
		else
		{
			scanf("%d",&x);
			printf("%s\n",Find(Root,x) != NIL ?"yes":"no");
		}
	}
}
### 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>
const int MAXN = 500000;
struct node{
	int key;
	node *ch[2];
};
node tree[MAXN + 5];
node *Root,*NIL,*ncnt;
void Init() {
	NIL = &tree[0];
	Root = NIL -> ch[0] = NIL -> ch[1] = NIL;
	ncnt  = &tree[1];
}
inline node * NewNode(int val) {
	node *p = (++ncnt);
	p->key = val;
	p->ch[0] = p->ch[1] = NIL;
	return p;
};
void Insert(node *&rt,int val) {
	if( rt == NIL ) {
		rt = NewNode(val);
		return ;
	}
	int d = (val > rt->key);
	Insert(rt->ch[d],val);
}
node * Find(node *rt,int val){
	if( rt == NIL ) return NIL;
	if( rt->key == val ) return rt;
	return Find(rt->ch[val>rt->key],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]);
}
char s1[10];
int main()
{
	int n,x;
	Init();
	scanf("%d",&n);
	for(int i=1;i<=n;i++)
	{
		scanf("%s",s1);
		if( s1[0] == 'p' )
		{
			InOrder(Root);
			puts("");
			PreOrder(Root);
			puts("");
		}
		else if( s1[0] == 'i' )
		{
			scanf("%d",&x);
			Insert(Root,x);
		}
		else
		{
			scanf("%d",&x);
			printf("%s\n",Find(Root,x) != NIL ?"yes":"no");
		}
	}
}
```