Problem:
Binary Search Tree II

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.

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.

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.

Sample Input 1

10
insert 30
insert 88
insert 12
insert 1
insert 20
find 12
insert 17
insert 25
find 16
print

Sample Output 1

yes
no
1 12 17 20 25 30 88
30 12 1 20 17 25 88

Reference

Introduction to Algorithms, Thomas H. Cormen, Charles E. Leiserson, Ronald L. Rivest, and Clifford Stein. The MIT Press.

Solution in JavaScript (judge verdict: Accepted)

class _Node {
  constructor(key, left = null, right = null) {
    this.key = key;
    this.left = left;
    this.right = right;
  }
}

class BinaryTree {
  constructor() {
    this.root = null;
  }

  static get Node() { return _Node; }

  insert(key) {
    this.root = new BinaryTree.Node(key);
    this.insert = (key) => {
      let x = this.root, y;
      let newNode = new BinaryTree.Node(key);
      while (x !== null) {
        y = x;
        x = x[key < x.key ? 'left' : 'right'];
      }
      y[key < y.key ? 'left' : 'right'] = newNode;
    }
  }

  find(key, n = this.root) {
    if (n === null) return false;
    if (n.key === key) return true;
    return this.find(key, n[key < n.key ? 'left' : 'right']);
  }

  printByIneorder() {
    let str = '';
    const innerFunc = (n) => {
      if (n === null) return;
      innerFunc(n.left);
      str += ` ${n.key}`;
      innerFunc(n.right);
    }
    innerFunc(this.root);
    console.log(str);
  }

  printByPreorder() {
    let str = '';
    const innerFunc = (n) => {
      if (n === null) return;
      str += ` ${n.key}`;
      innerFunc(n.left);
      innerFunc(n.right);
    }
    innerFunc(this.root);
    console.log(str);
  }

  print() {
    this.printByIneorder();
    this.printByPreorder();
  }
}

(function main(){
  const lines = require('fs').readFileSync('/dev/stdin', 'utf8').trim().split('\n');
  const n = Number(lines.shift());

  const tree = new BinaryTree();
  lines.forEach(function(cmd) {
    switch(cmd.charAt(0)) {
    case 'i': tree.insert(Number(cmd.split(' ')[1])); break;
    case 'f': console.log(tree.find(Number(cmd.split(' ')[1])) ? 'yes' : 'no'); break;
    default: tree.print();
    }
  });
})();