#include <cstdio>
#include <cstdlib>
using namespace std;
char s[10];
struct node {
	int key;
	node *p,*left,*right;
};
node *NIL,*root=NIL;
void ins (int key) {
	node *p=NIL,*cur=root,*n=(node *)malloc(sizeof(node));
	n->key=key;
	n->left=NIL;
	n->right=NIL;
	while (cur!=NIL) {
		p=cur;
		if (key<cur->key) cur=cur->left;
		else cur=cur->right;
	}
	n->p=p;
	if (p==NIL) root=n;
	else if (key<p->key) p->left=n;
	else p->right=n;
}
node* find (int key,node *cur) {
	while (cur!=NIL&&cur->key!=key) {
		if (key<cur->key) cur=cur->left;
		else cur=cur->right;
	}
	return cur;
}
void preOrder (node *u) {
	if (u==NIL) return;
	printf (" %d",u->key);
	preOrder (u->left);
	preOrder (u->right);
}
void inOrder (node *u) {
	if (u==NIL) return;
	inOrder (u->left);
	printf (" %d",u->key);
	inOrder (u->right);
}
int main () {
	int m;
	scanf ("%d",&m);
	for (int i=0;i<m;i++) {
		scanf ("%s",s);
		if (s[0]=='i') {
			int key;
			scanf ("%d",&key);
			ins (key);
		} else if (s[0]=='f') {
			int key;
			scanf ("%d",&key);
			if (find (key,root)!=NIL) printf ("yes\n");
			else printf ("no\n");
		} else {
			inOrder (root);
			printf ("\n");
			preOrder (root);
			printf ("\n");
		}
	}
    return 0;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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>
#include <cstdlib>
using namespace std;
char s[10];
struct node {
	int key;
	node *p,*left,*right;
};
node *NIL,*root=NIL;
void ins (int key) {
	node *p=NIL,*cur=root,*n=(node *)malloc(sizeof(node));
	n->key=key;
	n->left=NIL;
	n->right=NIL;
	while (cur!=NIL) {
		p=cur;
		if (key<cur->key) cur=cur->left;
		else cur=cur->right;
	}
	n->p=p;
	if (p==NIL) root=n;
	else if (key<p->key) p->left=n;
	else p->right=n;
}
node* find (int key,node *cur) {
	while (cur!=NIL&&cur->key!=key) {
		if (key<cur->key) cur=cur->left;
		else cur=cur->right;
	}
	return cur;
}
void preOrder (node *u) {
	if (u==NIL) return;
	printf (" %d",u->key);
	preOrder (u->left);
	preOrder (u->right);
}
void inOrder (node *u) {
	if (u==NIL) return;
	inOrder (u->left);
	printf (" %d",u->key);
	inOrder (u->right);
}
int main () {
	int m;
	scanf ("%d",&m);
	for (int i=0;i<m;i++) {
		scanf ("%s",s);
		if (s[0]=='i') {
			int key;
			scanf ("%d",&key);
			ins (key);
		} else if (s[0]=='f') {
			int key;
			scanf ("%d",&key);
			if (find (key,root)!=NIL) printf ("yes\n");
			else printf ("no\n");
		} else {
			inOrder (root);
			printf ("\n");
			preOrder (root);
			printf ("\n");
		}
	}
    return 0;
}

```