#include<iostream>
#include<string>
using namespace std;

struct NODE { int key; NODE *pa, *ri, *le; };
NODE *NIL, *root;

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

	z = new NODE;
	z->key = k;
	z->le = NIL;
	z->ri = NIL;

	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;
	}
}

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

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

void find(int k)
{
	NODE *s = root;
	while (s != NIL)
	{
		if (s->key == k)
		{
			cout << "yes" << endl; return;
		}
		else if (s->key > k)
			s = s->le;
		else
			s = s->ri;
	}
	cout << "no" << endl;
}

int main()
{
	string str;
	int i, n, k;
	cin >> n;
	
	for (i = 0; i < n; i++)
	{
		cin >> str;
		if (str[0] == 'i')
		{
			cin >> k;
			insert(k);
		}
		else if (str[0] == 'f')
		{
			cin >> k;
			find(k);
		}
		else  if (str[0] == 'p')
		{
			inorder(root);
			cout << endl;
			preorder(root);
			cout << endl;
		}
		
	}
	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<iostream>
#include<string>
using namespace std;

struct NODE { int key; NODE *pa, *ri, *le; };
NODE *NIL, *root;

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

	z = new NODE;
	z->key = k;
	z->le = NIL;
	z->ri = NIL;

	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;
	}
}

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

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

void find(int k)
{
	NODE *s = root;
	while (s != NIL)
	{
		if (s->key == k)
		{
			cout << "yes" << endl; return;
		}
		else if (s->key > k)
			s = s->le;
		else
			s = s->ri;
	}
	cout << "no" << endl;
}

int main()
{
	string str;
	int i, n, k;
	cin >> n;
	
	for (i = 0; i < n; i++)
	{
		cin >> str;
		if (str[0] == 'i')
		{
			cin >> k;
			insert(k);
		}
		else if (str[0] == 'f')
		{
			cin >> k;
			find(k);
		}
		else  if (str[0] == 'p')
		{
			inorder(root);
			cout << endl;
			preorder(root);
			cout << endl;
		}
		
	}
	return 0;
}

```