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

struct Node{
	int key;
	Node *parent;
	Node *left;
	Node *right; 
};
Node *root, *NIL;
void insert(int k){
	Node *x = root,*y = NIL,*z;
	z = (Node *)malloc(sizeof(Node));
	z->key = k;
	z->left = NIL;
	z->right = NIL;
	while(x!=NIL){
		y = x;
		if(z->key<x->key)
			x = x->left;
		else
			x = x->right;
	}
	z->parent = y;
	if(y==NIL)
		root = z;
	else{
		if(z->key<y->key)
			y->left = z;
		else
			y->right = z;
	}
}
int find(Node *n,int key){
	while(n!=NIL){
		if(key<n->key)
			n = n->left;
		else if(key>n->key)
			n = n->right;
		else
			return 1;
	}
	return 0;
}
void pre(Node *n){
	if(n==NIL) return;
	printf(" %d",n->key);
	pre(n->left);
	pre(n->right);
}
void in(Node *n){
	if(n==NIL) return;
	in(n->left);
	printf(" %d",n->key);
	in(n->right);
}
int main() {
	int n,x;
	char s[10];
	scanf("%d",&n);
	while(n--){
		scanf("%s",s);
		if(s[0]=='i'){
			scanf("%d",&x);
			insert(x);
		}else if(s[0]=='p'){
			in(root);
			printf("\n");
			pre(root);
			printf("\n");
		}else{
			scanf("%d",&x);
			if(find(root,x))
				printf("yes\n");
			else
				printf("no\n");
		}
	}
	return 0;
}

### Prompt

Develop a solution in CPP to the problem described below:

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 <cstdio>
#include <cstdlib>
#include <string>
using namespace std;

struct Node{
	int key;
	Node *parent;
	Node *left;
	Node *right; 
};
Node *root, *NIL;
void insert(int k){
	Node *x = root,*y = NIL,*z;
	z = (Node *)malloc(sizeof(Node));
	z->key = k;
	z->left = NIL;
	z->right = NIL;
	while(x!=NIL){
		y = x;
		if(z->key<x->key)
			x = x->left;
		else
			x = x->right;
	}
	z->parent = y;
	if(y==NIL)
		root = z;
	else{
		if(z->key<y->key)
			y->left = z;
		else
			y->right = z;
	}
}
int find(Node *n,int key){
	while(n!=NIL){
		if(key<n->key)
			n = n->left;
		else if(key>n->key)
			n = n->right;
		else
			return 1;
	}
	return 0;
}
void pre(Node *n){
	if(n==NIL) return;
	printf(" %d",n->key);
	pre(n->left);
	pre(n->right);
}
void in(Node *n){
	if(n==NIL) return;
	in(n->left);
	printf(" %d",n->key);
	in(n->right);
}
int main() {
	int n,x;
	char s[10];
	scanf("%d",&n);
	while(n--){
		scanf("%s",s);
		if(s[0]=='i'){
			scanf("%d",&x);
			insert(x);
		}else if(s[0]=='p'){
			in(root);
			printf("\n");
			pre(root);
			printf("\n");
		}else{
			scanf("%d",&x);
			if(find(root,x))
				printf("yes\n");
			else
				printf("no\n");
		}
	}
	return 0;
}

```