#include"bits/stdc++.h"
using namespace std;

struct node {
	int key;
	node *p, *l, *r;
};

node *root, *NIL;

void insert(int k)
{
	node* y = NIL;
	node* x = root;
	node* z;

	z = (node*)malloc(sizeof(node));
	z->key = k;
	z->l = NIL;
	z->r = NIL;

	while (x != NIL)
	{
		y = x;
		if (z->key < x->key) x = x->l;
		else x = x->r;
	}

	z->p = y;
	if (y == NIL) {
		root = z;
	}
	else {
		if (z->key < y->key) y->l = z;
		else y->r = z;
	}
}

void find_t(node* n, int k)
{
	node* x = n;
	while (x != NIL && k != x->key)
	{
		if (k < x->key) x = x->l;
		else x = x->r;
	}
	if (x != NIL) cout << "yes" << endl;
	else cout << "no" << endl;

	return;
}

void inorder(node *n)
{
	if (n == NIL) return;

	inorder(n->l);
	cout << " " <<  n->key;
	inorder(n->r);

	return;
}

void preorder(node *n)
{
	if (n == NIL) return;

	cout << " " << n->key;
	preorder(n->l);
	preorder(n->r);

	return;
}

int main(void)
{
	int N, k;
	string s;
	list<node> t;
	cin >> N;
	for (int i = 0; i < N; i++)
	{
		cin >> s;
		if (s == "insert"){
			cin >> k;
			insert(k);
		}
		else if (s == "print") {
			inorder(root);
			cout << endl;
			preorder(root);
			cout << endl;
		}
		else if (s == "find") {
			cin >> k;
			find_t(root, k);
		}
	}
	

	return 0;
}

### Prompt

Generate 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"bits/stdc++.h"
using namespace std;

struct node {
	int key;
	node *p, *l, *r;
};

node *root, *NIL;

void insert(int k)
{
	node* y = NIL;
	node* x = root;
	node* z;

	z = (node*)malloc(sizeof(node));
	z->key = k;
	z->l = NIL;
	z->r = NIL;

	while (x != NIL)
	{
		y = x;
		if (z->key < x->key) x = x->l;
		else x = x->r;
	}

	z->p = y;
	if (y == NIL) {
		root = z;
	}
	else {
		if (z->key < y->key) y->l = z;
		else y->r = z;
	}
}

void find_t(node* n, int k)
{
	node* x = n;
	while (x != NIL && k != x->key)
	{
		if (k < x->key) x = x->l;
		else x = x->r;
	}
	if (x != NIL) cout << "yes" << endl;
	else cout << "no" << endl;

	return;
}

void inorder(node *n)
{
	if (n == NIL) return;

	inorder(n->l);
	cout << " " <<  n->key;
	inorder(n->r);

	return;
}

void preorder(node *n)
{
	if (n == NIL) return;

	cout << " " << n->key;
	preorder(n->l);
	preorder(n->r);

	return;
}

int main(void)
{
	int N, k;
	string s;
	list<node> t;
	cin >> N;
	for (int i = 0; i < N; i++)
	{
		cin >> s;
		if (s == "insert"){
			cin >> k;
			insert(k);
		}
		else if (s == "print") {
			inorder(root);
			cout << endl;
			preorder(root);
			cout << endl;
		}
		else if (s == "find") {
			cin >> k;
			find_t(root, k);
		}
	}
	

	return 0;
}

```