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 <stdio.h>
#include <stdlib.h>


// I/O
int get_int() {
    int n = 0;
    int c = getchar_unlocked();
    if(c == 45) {
        c = getchar_unlocked();
        while(47 < c && c < 58) n = 10 * n + (c & 0xf), c = getchar_unlocked();
        return -n;
    } else if(c < 48 || 57 < c) return c;
    while(47 < c && c < 58) n = 10 * n + (c & 0xf), c = getchar_unlocked();
    return n;
}
int get_str(char *str) {
    int c;
    while((c = getchar_unlocked()) > 32) *str++ = (char)c;
    *str = 0;
    return c;
}
void put_int(int n) {
    if(!n) {
        putchar_unlocked('0');
        return;
    }
    if(n < 0) n = -n, putchar_unlocked('-');
    char buf[11];
    int i = 0;
    while(n) buf[i++] = (char)(n % 10 + '0'), n /= 10;
    while(i--)putchar_unlocked(buf[i]);
}
void put_str(char *str) { while(*str) putchar_unlocked(*str++); }
//


// Binary Search Tree
typedef struct Node {
    int key;
    struct Node *left, *right;
} Node;
typedef struct BST {
    Node *root;
    size_t size;
} BST;
void bst_init(BST *BST) {
    BST->root = NULL;
    BST->size = 0;
}
void bst_insert(BST *BST, int key) {
    Node *new_node = malloc(sizeof(Node));
    new_node->key = key;
    new_node->left = NULL;
    new_node->right = NULL;
    Node *tmp;
    Node *root = BST->root;
    while(root != NULL) {
        tmp = root;
        if(key < root->key) root = root->left;
        else root = root->right;
    }
    if(BST->size == 0) BST->root = new_node;
    else if(key < tmp->key) tmp->left = new_node;
    else tmp->right = new_node;
    BST->size++;
}
int bst_find(Node *root, int key) {
    if(root == NULL) return 0;
    else if(root->key == key) return 1;
    else if(root->key > key) return bst_find(root->left, key);
    else return bst_find(root->right, key);
}
void bst_inorder(Node *root) {
    if(root == NULL) return;
    bst_inorder(root->left);
    putchar_unlocked(' '), put_int(root->key);
    bst_inorder(root->right);
}
void bst_preorder(Node *root) {
    if(root == NULL) return;
    putchar_unlocked(' '), put_int(root->key);
    bst_preorder(root->left);
    bst_preorder(root->right);
}
//


int main(int argc, char **argv) {
    BST BST;
    bst_init(&BST);
    int m = get_int();
    int key;
    char c[8];
    for(int i = 0; i < m; ++i) {
        get_str(c);
        switch(*c) {
        case 'i':
            key = get_int();
            bst_insert(&BST, key);
            break;
        case 'f':
            key = get_int();
            put_str(bst_find(BST.root, key) ? "yes\n" : "no\n");
            break;
        default:
            bst_inorder(BST.root);
            putchar_unlocked('\n');
            bst_preorder(BST.root);
            putchar_unlocked('\n');
            break;
        }
    }
    return 0;
}