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 Ruby (judge verdict: Accepted)

class Tree
    attr_accessor :key, :left, :right
    def initialize(k, l, r)
        @key   = k
        @left  = l
        @right = r
    end
end

def insert(x, tree)
    if tree == nil
        Tree.new(x, nil, nil)
    elsif x < tree.key
        Tree.new(tree.key, insert(x, tree.left), tree.right)
    elsif x > tree.key
        Tree.new(tree.key, tree.left, insert(x, tree.right))
    else
        tree
    end
end

def find(x, tree)
    if tree == nil then
        false
    elsif x < tree.key
        find(x, tree.left)
    elsif x > tree.key
        find(x, tree.right)
    else
        true
    end
end

def goleft(tree, directions, breadcrambs)
    rt = tree.left
    tree.left = nil
    directions << 'L'
    breadcrambs << tree
    [rt, directions, breadcrambs]
end

def goright(tree, directions, breadcrambs)
    rt = tree.right
    tree.right = nil
    directions << 'R'
    breadcrambs << tree
    [rt, directions, breadcrambs]
end

def goup(tree, directions, breadcrambs)
    d = directions[-1]
    xtree = breadcrambs[-1]
    if d == 'L' then xtree.left = tree
    else xtree.right = tree end
    [xtree, directions[0..-2], breadcrambs[0..-2]]
end

def preorder(tree)
    if tree != nil
        print " #{tree.key}"
        preorder(tree.left)
        preorder(tree.right)
    end
end

def inorder(tree)
    if tree != nil
        inorder(tree.left)
        print " #{tree.key}"
        inorder(tree.right)
    end
end

def postorder(tree)
    if tree != nil
        postorder(tree.left)
        postorder(tree.right)
        print " #{tree.key}"
    end
end

#-- main
#------------------------------------------
tree = nil
paths = []
breads = []

x = gets.chomp.to_i
x.times {
    cmd, n = gets.chomp.split
    case cmd
    when "insert"
        tree = insert(n.to_i, tree)
    when "find"
        if find(n.to_i, tree)
            puts "yes"
        else
            puts "no"
        end
    when "delete"
        tree = delete(n.to_i, tree)
    when "print"
        inorder(tree); puts
        preorder(tree); puts
    end
}