Write a program which performs the following operations to a binary search tree $T$ by adding delete operation to B: Binary Search Tree II.

* insert  $k$: Insert a node containing $k$ as key into $T$.
* find $k$: Report whether $T$ has a node containing $k$.
* delete $k$: Delete a node containing $k$.
* print: Print the keys of the binary search tree by inorder tree walk and preorder tree walk respectively.



The operation delete $k$ for deleting a given node $z$ containing key $k$ from $T$ can be implemented by an algorithm which considers the following cases:

1. If $z$ has no children, we modify its parent $z.p$ to replace $z$ with NIL as its child (delete $z$).
2. If $z$ has only a single child, we "splice out" $z$ by making a new link between its child and its parent.
3. If $z$ has two children, we splice out $z$'s successor $y$ and replace $z$'s key with $y$'s 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.

Input

In the first line, the number of operations $m$ is given. In the following $m$ lines, operations represented by insert $k$, find $k$, delete $k$ 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

Example

Input

18
insert 8
insert 2
insert 3
insert 7
insert 22
insert 1
find 1
find 2
find 3
find 4
find 5
find 6
find 7
find 8
print
delete 3
delete 7
print


Output

yes
yes
yes
no
no
no
yes
yes
 1 2 3 7 8 22
 8 2 1 3 7 22
 1 2 8 22
 8 2 1 22
class BinarySearchTree:
    def __init__(self):
        self.root = None
        self.order_list = []
    def insert(self, z):
        y = None
        x = self.root
        while x != None:
            y = x
            if z.key < x.key:
                x = x.left
            else:
                x = x.right
        z.parent = y
        if y == None:
            self.root = z
        elif z.key < y.key:
            y.left = z
        else:
            y.right = z
    def find(self, key):
        x = self.root
        while x != None:
            if key == x.key:
                return x
            elif key < x.key:
                x = x.left
            else:
                x = x.right
        return None
    def delete(self, z):
        if z.left == None and z.right == None:
            if z.key < z.parent.key:
                z.parent.left = None
            else:
                z.parent.right = None
        elif z.left != None and z.right == None:
            z.left.parent = z.parent
            if z.key < z.parent.key:
                z.parent.left = z.left
            else:
                z.parent.right = z.left
        elif z.left == None and z.right != None:
            z.right.parent = z.parent
            if z.key < z.parent.key:
                z.parent.left = z.right
            else:
                z.parent.right = z.right
        else:
            next_node = z.right
            while next_node.left:
                next_node = next_node.left
            z.key = next_node.key
            self.delete(next_node)
            
    def walk_preorder(self, node):
        if node == None:
            return None
        self.order_list.append(node.key)
        self.walk_preorder(node.left)
        self.walk_preorder(node.right)
    def walk_inorder(self, node):
        if node == None:
            return None
        self.walk_inorder(node.left)
        self.order_list.append(node.key)
        self.walk_inorder(node.right)
    def print_nodes(self):
        self.order_list = []
        self.walk_inorder(self.root)
        inorder_str = ' '.join(map(str, self.order_list))
        print(' {}'.format(inorder_str))
        self.order_list = []
        self.walk_preorder(self.root)
        preorder_str = ' '.join(map(str, self.order_list))
        print(' {}'.format(preorder_str))
        
class Node:
    def __init__(self, key):
        self.key = key
        self.parent = None
        self.left = None
        self.right = None

n = int(input())
tree = BinarySearchTree()
for _ in range(n):
    command = input().split(' ')
    if len(command) == 1:
        tree.print_nodes()
    else:
        opecode, operand = command[0], int(command[1])
        if opecode == 'insert':
            node = Node(operand)
            tree.insert(node)
        elif opecode == 'find':
            node = tree.find(operand)
            if node != None:
                print('yes')
            else:
                print('no')
        elif opecode == 'delete':
            node = tree.find(operand)
            if node != None:
                tree.delete(node)
