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 C++ (judge verdict: Accepted)

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

struct Node{
    int key;
    Node *parent, *left, *right;
};

Node *NIL, *root;


void insert(int key){

    Node *x, *y, *z;

    z = new Node;
    z->key = key;
    z->left = NIL;
    z->right = NIL;
    y = NIL;
    x = root;

    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;
}

Node* find(int key){
    Node *x, *y;
    int target = key;
    bool judge = false;
    x = root;
    while(x != NIL){
        if(target > x->key){
            x = x->right;
        }
        else if(target < x->key){
            x = x->left;
        }
        else{
            judge = true;
            break;
        } 
    }
    //if(judge) cout << "yes" << endl;
    //else cout << "no" << endl;
    return x;
}

void preorder(Node *node){
    if(node == NIL) return ;
    cout << " " << node->key;
    if(node->left != NIL) preorder(node->left);
    if(node->right != NIL) preorder(node->right);
}

void inorder(Node *node){
    if(node == NIL) return;
    if(node->left != NIL) inorder(node->left);
    cout << " " << node->key;
    if(node->right != NIL) inorder(node->right);
}


void print(){
    inorder(root);
    cout << endl;
    preorder(root);
    cout << endl;
}

int main(){
    int i, m, key;

    string command;

    cin >> m;
    for(i = 0; i < m ; i++){
        cin >> command;
        if(command[0] == 'i'){
            cin >> key;
            insert(key);
        } else if(command[0] == 'p'){
            print();
        }
        else{
            cin >> key;
            //find(key);
            if (find(key) != NIL) cout << "yes" << endl;
            else cout << "no" << endl;
        }
    }
    return 0;
}