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

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

Node *root,*NIL;

void insert(int k){
    Node *y=NIL;
    Node *x=root;
    Node *z;

    z=(Node*)malloc(sizeof(Node));
    z->key=k;
    z->l=z->r=NIL;
    while(x!=NIL){
        y=x;
        if(z->key<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;
    }
}

Node* find(int k){
    Node *x;
    x=root;
    while(x!=NIL&&(x->key)!=k){
        if(k<x->key){
            x=x->l;
        }
        else{
            x=x->r;
        }
    }
    return x;
}

void inorder(Node *u){
    if(u==NIL) return;
    inorder(u->l);
    cout<<' '<<(u->key);
    inorder(u->r);
}

void preorder(Node *u){
    if(u==NIL) return;
    cout<<' '<<(u->key);
    preorder(u->l);
    preorder(u->r);
}

int main(){
    int m;
    cin>>m;
    for(int i=0;i<m;i++){
        char com[10];
        int a;
        scanf("%s%d",com,&a);
        if(com[0]=='p'){
            inorder(root);
            cout<<endl;
            preorder(root);
            cout<<endl;
        }
        else if(com[0]=='i'){
            insert(a);
        }
        else{
            if(find(a)==NIL) cout<<"no"<<endl;
            else cout<<"yes"<<endl;
        }
    }
}

### Prompt

Please formulate a cpp solution to 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 key;
    Node *p,*l,*r;
};

Node *root,*NIL;

void insert(int k){
    Node *y=NIL;
    Node *x=root;
    Node *z;

    z=(Node*)malloc(sizeof(Node));
    z->key=k;
    z->l=z->r=NIL;
    while(x!=NIL){
        y=x;
        if(z->key<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;
    }
}

Node* find(int k){
    Node *x;
    x=root;
    while(x!=NIL&&(x->key)!=k){
        if(k<x->key){
            x=x->l;
        }
        else{
            x=x->r;
        }
    }
    return x;
}

void inorder(Node *u){
    if(u==NIL) return;
    inorder(u->l);
    cout<<' '<<(u->key);
    inorder(u->r);
}

void preorder(Node *u){
    if(u==NIL) return;
    cout<<' '<<(u->key);
    preorder(u->l);
    preorder(u->r);
}

int main(){
    int m;
    cin>>m;
    for(int i=0;i<m;i++){
        char com[10];
        int a;
        scanf("%s%d",com,&a);
        if(com[0]=='p'){
            inorder(root);
            cout<<endl;
            preorder(root);
            cout<<endl;
        }
        else if(com[0]=='i'){
            insert(a);
        }
        else{
            if(find(a)==NIL) cout<<"no"<<endl;
            else cout<<"yes"<<endl;
        }
    }
}

```