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 Node:
    def __init__(self, key):
        self.key = key
        self.parent = None
        self.left = None
        self.right = None
        
    def insert(self, z):
        if z.key < self.key:
            if self.left:
                self.left.insert(z)
            else:
                self.left = z
                z.parent = self
        else:
            if self.right:
                self.right.insert(z)
            else:
                self.right = z
                z.parent = self

    def find(self, key):
        if self.key == key:
            return True
        elif not self.left and not self.right:
            return False
        else:
            if key < self.key:
                return self.left.find(key)
            else:
                return self.right.find(key)
            
    def delete(self, key):
        if self.key == key:
            if not self.left and not self.right:
                if self.key < self.parent.key:
                    self.parent.left = None
                else:
                    self.parent.right = None
            elif self.left and self.right:
                A = [int(i) for i in self.ino().split()]
                ind = A.index(self.key)
                y = A[ind+1]
                self.delete(y)
                self.key = y
            else:
                if self.left:
                    self.left.parent = self.parent
                    if self.key < self.parent.key:
                        self.parent.left = self.left
                    else:
                        self.parent.right = self.left
                else:
                    self.right.parent = self.parent
                    if self.key < self.parent.key:
                        self.parent.left = self.right
                    else:
                        self.parent.right = self.right
        else:
            if self.key < key:
                self.right.delete(key)
            else:
                self.left.delete(key)
        
    def preo(self):
        tmp = ""
        tmp += " " + str(self.key)
        if self.left:
            tmp += self.left.preo()
        if self.right:
            tmp += self.right.preo()
        return tmp
    
    def ino(self):
        tmp = ""
        if self.left:
            tmp += self.left.ino()
        tmp += " " + str(self.key)
        if self.right:
            tmp += self.right.ino()
        return tmp
m = int(input())
root = None
for i in range(m):
    com = input().split()
    if com[0] == "insert":
        node = Node(int(com[1]))
        try:
            root.insert(node)
        except AttributeError :
            root = node
    elif com[0] == "find":
        try:
            if root.find(int(com[1])):
                print("yes")
            else:
                print("no")
        except AttributeError:
            print("no")
    elif com[0] == "delete":
        try:
            root.delete(int(com[1]))
        except AttributeError:
            print("failed deletion")
    else:
        try:
            print(root.ino())
            print(root.preo())
        except AttributeError:
            print("None")
