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
# coding: utf-8
# Your code here!

class Node:
    def __init__(self, id):
        self.id = id
        self.parent = None
        self.left = None
        self.right = None
    
    def __str__(self):
        return 'id={}'.format(self.id)

class BinaryTree:
    def __init__(self):
        self.root = None
        
    def insert(self, node, current_node=None):
        if self.root is None:
            self.root = node
            return
        
        if current_node is None:
            current_node = self.root
            
        if node.id < current_node.id:
            if current_node.left:
                self.insert(node, current_node.left)
            else:
                current_node.left = node
                node.parent = current_node
        else:
            if current_node.right:
                self.insert(node, current_node.right)
            else:
                current_node.right = node
                node.parent = current_node
    
    def delete(self, id, current_node=None):
        if current_node is None:
            current_node = self.root
        
        if id == current_node.id:
            if current_node.left is None and current_node.right is None:
                
                if current_node.parent.left and current_node.parent.left.id == id:
                    current_node.parent.left = None
                else:
                    current_node.parent.right = None
            elif current_node.left and current_node.right:
                result = []
                self.walk_inorder(result, current_node)
                in_id = result[result.index(current_node.id)+1]
                current_node.id = in_id
                self.delete(in_id, current_node.right)
            else:
                child = None
                if current_node.left:
                    child = current_node.left
                else:
                    child = current_node.right
                
                if current_node.parent.left and current_node.parent.left.id == id:
                    child.parent = current_node.parent
                    current_node.parent.left = child
                else:
                    child.parent = current_node.parent
                    current_node.parent.right = child
        elif id < current_node.id:
            if current_node.left:
                self.delete(id, current_node.left)
        elif current_node.id < id:
            if current_node.right:
                self.delete(id, current_node.right)
                
    def walk_inorder(self, result, current_node=None):
        if current_node is None:
            current_node = self.root
        
        if current_node.left:
            self.walk_inorder(result, current_node.left)
            
        result.append(current_node.id)
        
        if current_node.right:
            self.walk_inorder(result, current_node.right)
    
    def walk_preorder(self, result, current_node=None):
        if current_node is None:
            current_node = self.root
        
        result.append(current_node.id)
        
        if current_node.left:
            self.walk_preorder(result, current_node.left)
            
        if current_node.right:
            self.walk_preorder(result, current_node.right)

    def find(self, id, current_node=None):
        if current_node is None:
            current_node = self.root
            
        if current_node.id == id:
            return True
        if id < current_node.id:
            if current_node.left and self.find(id, current_node.left):
                return True
        else:
            if current_node.right and self.find(id, current_node.right):
                return True
        return False

def main():
    n = int(input())
    tree = BinaryTree()
    
    for _ in range(n):
        cmd = input()
        if cmd[0] == 'p':
            result = []
            tree.walk_inorder(result)
            print('', *result)
            
            result = []
            tree.walk_preorder(result)
            print('', *result)
        elif cmd[0] == 'i':
            id = int(cmd.split()[1])
            node = Node(id)
            tree.insert(node)
        elif cmd[0] == 'd':
            id = int(cmd.split()[1])
            tree.delete(id)
        elif cmd[0] == 'f':
            id = int(cmd.split()[1])
            if tree.find(id):
                print('yes')
            else:
                print('no')

if __name__=='__main__':
    main()
