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

using namespace std;

struct Node_struct{
	Node_struct *l, *r, *p;
	int key;
};
Node_struct* Root;

void insert(int num){
	Node_struct *x = Root , *y = NULL, *z;
	z=(Node_struct*)malloc(sizeof(Node_struct));
	z->key = num;
	z->l = NULL, z->r = NULL;
	
	while(x != NULL){
		y = x;
		if(z->key > x->key) x = x->r;
		else x = x->l;
	}
	z->p = y;
	if(y == NULL) Root = z;
	else if(z->key > y->key) y->r = z;
	else y->l = z;
}

void in(Node_struct *cur){
	if(cur==NULL)	return;
	in(cur->l);
	printf(" %d",cur->key);
	in(cur->r);
}

void pre(Node_struct *cur){
	if(cur==NULL)	return;
	printf(" %d", cur->key);
	pre(cur->l);
	pre(cur->r);
}

void find(int num){
	bool flag = false;
	Node_struct *x = Root;
	
	while(x != NULL){
		if(num == x->key)flag = true;
		if(num > x->key) x = x->r;
		else x = x->l;
	}
	if(flag) printf("yes\n");
	else printf("no\n");
}

int main(){
	int i, n;
	int id;
	string s;
	scanf("%d", &n);
	
	for(i=0; i<n; ++i){
		cin >> s;
		if(s[0] == 'i'){
			scanf("%d", &id);
			insert(id);
		}
		else if(s[0] == 'p'){
			in(Root);
			printf("\n");
			pre(Root);
			printf("\n");
		}
		else if(s[0] == 'f'){
			scanf("%d", &id);
			find(id);
		}
	}
	
	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 <stdio.h>
#include <iostream>
#include <string>

using namespace std;

struct Node_struct{
	Node_struct *l, *r, *p;
	int key;
};
Node_struct* Root;

void insert(int num){
	Node_struct *x = Root , *y = NULL, *z;
	z=(Node_struct*)malloc(sizeof(Node_struct));
	z->key = num;
	z->l = NULL, z->r = NULL;
	
	while(x != NULL){
		y = x;
		if(z->key > x->key) x = x->r;
		else x = x->l;
	}
	z->p = y;
	if(y == NULL) Root = z;
	else if(z->key > y->key) y->r = z;
	else y->l = z;
}

void in(Node_struct *cur){
	if(cur==NULL)	return;
	in(cur->l);
	printf(" %d",cur->key);
	in(cur->r);
}

void pre(Node_struct *cur){
	if(cur==NULL)	return;
	printf(" %d", cur->key);
	pre(cur->l);
	pre(cur->r);
}

void find(int num){
	bool flag = false;
	Node_struct *x = Root;
	
	while(x != NULL){
		if(num == x->key)flag = true;
		if(num > x->key) x = x->r;
		else x = x->l;
	}
	if(flag) printf("yes\n");
	else printf("no\n");
}

int main(){
	int i, n;
	int id;
	string s;
	scanf("%d", &n);
	
	for(i=0; i<n; ++i){
		cin >> s;
		if(s[0] == 'i'){
			scanf("%d", &id);
			insert(id);
		}
		else if(s[0] == 'p'){
			in(Root);
			printf("\n");
			pre(Root);
			printf("\n");
		}
		else if(s[0] == 'f'){
			scanf("%d", &id);
			find(id);
		}
	}
	
	return 0;
}

```