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

import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		Main bst = new Main();
		int ops = in.nextInt();
		while (in.hasNextLine()) {
			String[] holder;
			holder = in.nextLine().split(" ");
			
			if (holder[0].equals("insert")) {
				bst.insert(bst, new Node(Integer.parseInt(holder[1])));
			}
			else if (holder[0].equals("print")) {
				bst.print();
			}
			else if (holder[0].equals("find")) {
				if (bst.find(bst, Integer.parseInt(holder[1])) != null) {
					System.out.println("yes");
				}
				else {
					System.out.println("no");
				}
			}
			else if (holder[0].equals("delete")) {;
				bst.delete(Integer.parseInt(holder[1]));
			}
		}
		
		
	}
	
	Node root;
	
	public Main() {
		root = null;
	}
	
	public void delete(int k) {
		recurDel(this.root, k);
	}
	
	private Node recurDel(Node r, int k) {
		if (k < r.key) { // if k is less than the current root, then it must be in the left half. So we recur there
			r.left = recurDel(r.left, k);			
		}
		else if (k > r.key) {
			r.right = recurDel(r.right, k);
		}
		else { // In the else case, k must be equal to the value of the root
			if (r.left == null) { // If it has no left child, then just return the right side without the node
				return r.right;
			}
			else if (r.right == null) { // Same idea as before
				return r.left;
			}
			
			// Otherwise, the node has two children. So we pick the successor as the minimum of the right subtree and copy the value
			// Then we will delete the old leaf containing the value
			Node succ = r.right;
			while (succ.left != null) {
				succ = succ.left;
			}
			r.key = succ.key;
			r.right = recurDel(r.right, r.key);
		}
		return r;
	}
	
	public Node find(Main T , int k) {
		Node result = null;
		Node curr = T.root;
		while (curr != null) {
			if (k == curr.key) {
				result = curr;
				return result;
			} 			
			else if (k < curr.key) {
				curr = curr.left;
			} else {
				curr = curr.right;
			}
		}
		return result;
	}
	
	public void insert(Main T, Node z) {
		Node y = null;
		Node x = T.root;
		
		while (x != null) {
			y = x;
			if (z.key < x.key) {
				x = x.left;
			}
			else {
				x = x.right;
			}
		}
		z.p = y;
		
		if (y == null) {
			T.root = z;
		}
		else if (z.key < y.key) {
			y.left = z;
		}
		else {
			y.right = z;
		}
	}
	
	public String inOrder(Node z) {
		String result = "";
		if (z == null) {
			return result;
		}
		else {
			return inOrder(z.left) + " " + z.key + inOrder(z.right); 
		}
	}
	
	public String preOrder(Node z) {
		String result = "";
		if (z == null) {
			return result;
		}
		else {
			return " " + z.key + preOrder(z.left) + preOrder(z.right); 
		}
	}
	
	public void print() {
		System.out.println(this.inOrder(root));
		System.out.println(this.preOrder(root));
	}
}



class Node {
	int key; // Key of the node
	Node p; // Parent of the node
	Node left; // Left child
	Node right; // Right child
	
	public Node(int val) {
		key = val;
		p = null;
		left = null;
		right = null;
	}
	
	public String toString() {
		return key + "";
	}
	
	
}


