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

struct node {
	int k;
	node *p, *l, *r;
};
node *r, *NIL;

void insert(node *u) {
	node *p = NIL, *c = r;
	while (c != NIL) {
		p = c;
		if (u->k < c->k)
			c = c->l;
		else
			c = c->r;
	}
	u->p = p;
	if (p == NIL)
		r = u;
	else if (u->k < p->k)
		p->l = u;
	else
		p->r = u;
}

void inparse(node *u) {
	if (u == NIL)
		return;
	inparse(u->l);
	cout << " " << u->k;
	inparse(u->r);
}

void preparse(node *u) {
	if (u == NIL)
		return;
	cout << " " << u->k;
	preparse(u->l);
	preparse(u->r);
}

void print() {
	inparse(r);
	cout << endl;
	preparse(r);
	cout << endl;
}

node* find(int k, node *u) {
	if (u == NIL)
		return NIL;
	else if (k == u->k)
		return u;
	else if (k < u->k)
		return find(k, u->l);
	else if (k > u->k)
		return find(k, u->r);
}

void del(int k) {
//	node u = find(k);
}

int main() {
	int m;
	cin >> m;
	for (int i = 0; i < m; i++) {
		string cmd;
		cin >> cmd;
		if (cmd[0] == 'i') {
			node *u = (node*) malloc(sizeof(node));
			int k;
			cin >> k;
			u->k = k;
			u->l = NIL;
			u->r = NIL;
			insert(u);
		} else if (cmd[0] == 'f') {
			int k;
			cin >> k;
			cout << (find(k, r) != NIL ? "yes" : "no") << endl;
		} else if (cmd[0] == 'p') {
			print();
		} else if (cmd[0] == 'd') {
			int k;
			cin >> k;
			del(k);
		}
	}
	return 0;
}


### Prompt

In cpp, your task is to solve 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 k;
	node *p, *l, *r;
};
node *r, *NIL;

void insert(node *u) {
	node *p = NIL, *c = r;
	while (c != NIL) {
		p = c;
		if (u->k < c->k)
			c = c->l;
		else
			c = c->r;
	}
	u->p = p;
	if (p == NIL)
		r = u;
	else if (u->k < p->k)
		p->l = u;
	else
		p->r = u;
}

void inparse(node *u) {
	if (u == NIL)
		return;
	inparse(u->l);
	cout << " " << u->k;
	inparse(u->r);
}

void preparse(node *u) {
	if (u == NIL)
		return;
	cout << " " << u->k;
	preparse(u->l);
	preparse(u->r);
}

void print() {
	inparse(r);
	cout << endl;
	preparse(r);
	cout << endl;
}

node* find(int k, node *u) {
	if (u == NIL)
		return NIL;
	else if (k == u->k)
		return u;
	else if (k < u->k)
		return find(k, u->l);
	else if (k > u->k)
		return find(k, u->r);
}

void del(int k) {
//	node u = find(k);
}

int main() {
	int m;
	cin >> m;
	for (int i = 0; i < m; i++) {
		string cmd;
		cin >> cmd;
		if (cmd[0] == 'i') {
			node *u = (node*) malloc(sizeof(node));
			int k;
			cin >> k;
			u->k = k;
			u->l = NIL;
			u->r = NIL;
			insert(u);
		} else if (cmd[0] == 'f') {
			int k;
			cin >> k;
			cout << (find(k, r) != NIL ? "yes" : "no") << endl;
		} else if (cmd[0] == 'p') {
			print();
		} else if (cmd[0] == 'd') {
			int k;
			cin >> k;
			del(k);
		}
	}
	return 0;
}


```