#include <iostream>
#include <cstdlib>
#include <cstdio>
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);
  cout<<" "<<u->key<<flush;
  inorder(u->right);
}
void preorder(Node *u) {
  if (u==NIL) {
    return;
  }
  cout<<" "<<u->key<<flush;
  preorder(u->left);
  preorder(u->right);
}
int main() {
  int n;
  scanf("%d",&n);
  string com;
  int x;
  for (int i=0; i<n; i++) {
    cin>>com;
    if (com=="find") {
      scanf("%d",&x);
      Node *t=find(root,x);
      if (t!=NIL) {
        cout<<"yes"<<endl;
      } else {
        cout<<"no"<<endl;
      }
    } else if (com=="insert") {
      scanf("%d",&x);
      insert(x);
    } else if (com=="print") {
      inorder(root);
      cout<<endl;
      preorder(root);
      cout<<endl;
    }
  }
  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 <cstdlib>
#include <cstdio>
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);
  cout<<" "<<u->key<<flush;
  inorder(u->right);
}
void preorder(Node *u) {
  if (u==NIL) {
    return;
  }
  cout<<" "<<u->key<<flush;
  preorder(u->left);
  preorder(u->right);
}
int main() {
  int n;
  scanf("%d",&n);
  string com;
  int x;
  for (int i=0; i<n; i++) {
    cin>>com;
    if (com=="find") {
      scanf("%d",&x);
      Node *t=find(root,x);
      if (t!=NIL) {
        cout<<"yes"<<endl;
      } else {
        cout<<"no"<<endl;
      }
    } else if (com=="insert") {
      scanf("%d",&x);
      insert(x);
    } else if (com=="print") {
      inorder(root);
      cout<<endl;
      preorder(root);
      cout<<endl;
    }
  }
  return 0;
}



```