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 JAVA (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    static Node nodeRoot;
    static StringBuilder sb = new StringBuilder();

    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(br.readLine());
        for (int i = 0; i < n; i++) {
            String s = br.readLine();
            if (s.charAt(0) == 'i') {
                int m = Integer.parseInt(s.substring(7));
                if (nodeRoot == null) {
                    nodeRoot = new Node(m);
                    continue;
                }
                insert(m, nodeRoot);
            } else if (s.charAt(0) == 'p') {
                sb.append(" ");
                inorder(nodeRoot);
                sb.deleteCharAt(sb.length() - 1).append("\n").append(" ");
                preorder(nodeRoot);
                sb.deleteCharAt(sb.length() - 1).append("\n");
            } else {
                int m = Integer.parseInt(s.substring(5));
                sb.append(find(m, nodeRoot) ? "yes\n" : "no\n");

            }
        }
        System.out.print(sb);
    }

    private static boolean find(int m, Node node) {
        if (node == null) return false;
        if (m > node.value) {
            return find(m, node.right);
        } else if (m < node.value) {
            return find(m, node.left);
        } else {
            return true;
        }
    }

    private static void preorder(Node node) {
        if (node == null) return;
        sb.append(node.value).append(" ");
        preorder(node.left);
        preorder(node.right);
    }

    private static void inorder(Node node) {
        if (node == null) return;
        inorder(node.left);
        sb.append(node.value).append(" ");
        inorder(node.right);
    }

    private static void insert(int m, Node node) {
        if (m > node.value) {
            if (node.right == null) node.right = new Node(m);
            else insert(m, node.right);
        } else {
            if (node.left == null) node.left = new Node(m);
            else insert(m, node.left);
        }
    }

    static class Node {
        int value;
        Node left;
        Node right;

        public Node(int value) {
            this.value = value;
        }
    }
}