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

struct node{
	int key;
	node *p,*l,*r;
};

node *root,*nil;

int n;

void insert(int k){
	node *y,*x,*z;
	y=nil;
	x=root;
	z=(node*)malloc(sizeof(node));
	z->key=k;
	z->l=nil;
	z->r=nil;
	while(x!=nil){
		y=x;
		if(k < x->key){
			x=x->l;
		}
		else{
			x=x->r;
		}
	}
	z->p=y;
	if(y==nil){
		root=z;
	}
	else{
		if( z->key  < y->key){
			y->l=z;
		}
		else{
			y->r=z;
		}
	}
}

void ino(node *x){
	if(x==nil){
		return;
	}
	ino(x->l);
	printf(" %d",x->key);
	ino(x->r);
}

void pre(node *x){
	if(x==nil){
		return;
	}
	printf(" %d",x->key);
	pre(x->l);
	pre(x->r);
}

node *find(node *x,int k){
	while(x!=nil&&k!=x->key){
		if(k <x->key){
			x=x->l;
		}
		else{
			x=x->r;
		}
	}
	return x;
}

int main() {
	cin>>n;
	int key;
	char c[20];
	for(int i=0;i<n;i++){
		cin>>c;
		if( c[0]=='i'){
			cin>>key;
			insert(key);
		}
		else if(c[0]=='f'){
			cin>>key;
			node *x=find(root,key);
			if(x==nil){
				printf("no\n");
			}
			else{
				printf("yes\n");
			}
		}
		else{
			ino(root);cout<<endl;
			pre(root);cout<<endl;
		}
	}

	return 0;
}

### Prompt

Please provide a cpp coded solution 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 <bits/stdc++.h>
using namespace std;

struct node{
	int key;
	node *p,*l,*r;
};

node *root,*nil;

int n;

void insert(int k){
	node *y,*x,*z;
	y=nil;
	x=root;
	z=(node*)malloc(sizeof(node));
	z->key=k;
	z->l=nil;
	z->r=nil;
	while(x!=nil){
		y=x;
		if(k < x->key){
			x=x->l;
		}
		else{
			x=x->r;
		}
	}
	z->p=y;
	if(y==nil){
		root=z;
	}
	else{
		if( z->key  < y->key){
			y->l=z;
		}
		else{
			y->r=z;
		}
	}
}

void ino(node *x){
	if(x==nil){
		return;
	}
	ino(x->l);
	printf(" %d",x->key);
	ino(x->r);
}

void pre(node *x){
	if(x==nil){
		return;
	}
	printf(" %d",x->key);
	pre(x->l);
	pre(x->r);
}

node *find(node *x,int k){
	while(x!=nil&&k!=x->key){
		if(k <x->key){
			x=x->l;
		}
		else{
			x=x->r;
		}
	}
	return x;
}

int main() {
	cin>>n;
	int key;
	char c[20];
	for(int i=0;i<n;i++){
		cin>>c;
		if( c[0]=='i'){
			cin>>key;
			insert(key);
		}
		else if(c[0]=='f'){
			cin>>key;
			node *x=find(root,key);
			if(x==nil){
				printf("no\n");
			}
			else{
				printf("yes\n");
			}
		}
		else{
			ino(root);cout<<endl;
			pre(root);cout<<endl;
		}
	}

	return 0;
}

```