
#include <iostream>
#include <string>
#include <malloc.h>


using namespace std;

struct Node {
	int key;
	Node *pa, *le, *ri;
};

Node *root, *NIL;

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

	z = (Node*)malloc(sizeof(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 pre(Node *a) {
	if (a == NIL) {
		return;
	}

	int number = a->key;
	
	cout << " " << number;
	pre(a->le);
	pre(a->ri);
}

void ino(Node *a) {
	if (a == NIL) {
		return;
	}

	int number = a->key;

	ino(a->le);
	cout << " " << number;
	ino(a->ri);
}

void find(int k) {
	Node *x = root;

	while (x != NIL) {
		if (k == x->key) {
			cout << "yes" << endl;
			return;
		}

		if (k < x->key) {
			x = x->le;
			continue;
		}
		else if (k > x->key) {
			x = x->ri;
			continue;
		}
	}

	cout << "no" << endl;
	return;
}


int main()
{
	int n, num;
	string order;

	cin >> n;

	for (int i = 0; i < n; ++i) {
		cin >> order;
		if (order == "insert") {
			cin >> num;
			insert(num);
		}
		else if (order == "print") {
			ino(root);
			cout << endl;
			pre(root);
			cout << endl;
		}
		else if (order == "find") {
			cin >> num;
			find(num);
		}
	}

	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 <iostream>
#include <string>
#include <malloc.h>


using namespace std;

struct Node {
	int key;
	Node *pa, *le, *ri;
};

Node *root, *NIL;

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

	z = (Node*)malloc(sizeof(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 pre(Node *a) {
	if (a == NIL) {
		return;
	}

	int number = a->key;
	
	cout << " " << number;
	pre(a->le);
	pre(a->ri);
}

void ino(Node *a) {
	if (a == NIL) {
		return;
	}

	int number = a->key;

	ino(a->le);
	cout << " " << number;
	ino(a->ri);
}

void find(int k) {
	Node *x = root;

	while (x != NIL) {
		if (k == x->key) {
			cout << "yes" << endl;
			return;
		}

		if (k < x->key) {
			x = x->le;
			continue;
		}
		else if (k > x->key) {
			x = x->ri;
			continue;
		}
	}

	cout << "no" << endl;
	return;
}


int main()
{
	int n, num;
	string order;

	cin >> n;

	for (int i = 0; i < n; ++i) {
		cin >> order;
		if (order == "insert") {
			cin >> num;
			insert(num);
		}
		else if (order == "print") {
			ino(root);
			cout << endl;
			pre(root);
			cout << endl;
		}
		else if (order == "find") {
			cin >> num;
			find(num);
		}
	}

	return 0;
}


```