#include<cstdio>
#include<cstdlib>
#include<string>
#include<iostream>
using namespace std;
struct Node{
 int key;
 Node *right,*left,*parent;
};
Node *root,*NIL;
Node* find(Node *u,int k){
 while(u!=NIL&&k!=u->key){
  if(k<u->key)u=u->left;
  else u=u->right;
 }
 return u;
}
void insert(int k){
 Node *y=NIL;
 Node *x=root;
 Node *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;
 }
}
void inorder(Node *u){
 if(u==NIL)return;
 inorder(u->left);
 printf(" %d",u->key);
 inorder(u->right);
}
void preorder(Node *u){
 if(u==NIL)return;
 printf(" %d",u->key);
 preorder(u->left);
 preorder(u->right);
}
int main(){
 int n,i,x;
 string com;
 scanf("%d",&n);
 for(i=0;i<n;i++){
  cin>>com;
  if(com[0]=='f'){
   scanf("%d",&x);
   Node *t=find(root,x);
   if(t!=NIL)printf("yes\n");
   else printf("no\n");
  }else if(com=="insert"){
   scanf("%d",&x);
   insert(x);
  }else if(com=="print"){
   inorder(root);
   printf("\n");
   preorder(root);
   printf("\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<cstdio>
#include<cstdlib>
#include<string>
#include<iostream>
using namespace std;
struct Node{
 int key;
 Node *right,*left,*parent;
};
Node *root,*NIL;
Node* find(Node *u,int k){
 while(u!=NIL&&k!=u->key){
  if(k<u->key)u=u->left;
  else u=u->right;
 }
 return u;
}
void insert(int k){
 Node *y=NIL;
 Node *x=root;
 Node *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;
 }
}
void inorder(Node *u){
 if(u==NIL)return;
 inorder(u->left);
 printf(" %d",u->key);
 inorder(u->right);
}
void preorder(Node *u){
 if(u==NIL)return;
 printf(" %d",u->key);
 preorder(u->left);
 preorder(u->right);
}
int main(){
 int n,i,x;
 string com;
 scanf("%d",&n);
 for(i=0;i<n;i++){
  cin>>com;
  if(com[0]=='f'){
   scanf("%d",&x);
   Node *t=find(root,x);
   if(t!=NIL)printf("yes\n");
   else printf("no\n");
  }else if(com=="insert"){
   scanf("%d",&x);
   insert(x);
  }else if(com=="print"){
   inorder(root);
   printf("\n");
   preorder(root);
   printf("\n");
  }
 }
 return 0;
}

```