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;
import java.util.ArrayList;
public class Main {

  public static class Node {
    int key;
    Node left;
    Node right;
    Node p;
    public Node(int key) {
      this.key = key;
      this.left = null;
      this.right = null;
      this.p = null;
    }
  }

  public static class Tree {
    Node root;
    public Tree() {
      this.root = null;
    }
  }

  public static void insert(Tree 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 static boolean find_helper(Node x, int k) {
    if (x == null)
      return false;
    if (x.key == k)
      return true;
    if (k <= x.key)
      return find_helper(x.left, k);
    else
      return find_helper(x.right, k);
  }

  public static String find(Node x, int k) {
    if (find_helper(x, k))
      return "yes";
    return "no";
  }

  public static Node find_to_delete(Node x, int k) {
    if (x == null)
      return null;
    if (x.key == k)
      return x;
    if (k <= x.key)
      return find_to_delete(x.left, k);
    else
      return find_to_delete(x.right, k);
  }

  public static void splice_successor_and_replace_key(Node z) {
    Node y = z.right;
    Node p = z;
    while (y.left != null) {
      p = y;
      y = y.left;
    }
    if (z.key == p.key)  // Successor was z's right child
      z.right = null;
    else
      p.left = null;
    z.key = y.key;
  }

  public static void update_parent_with(Tree t, Node z, Node y) {
    // Z has no parent
    if (z.p == null)
      t.root = y;
    // Z is left child of parent
    else if (z.p.left != null && z.p.left.key == z.key)
      z.p.left = y;
    // Z is right child of parent
    else
      z.p.right = y;
    if (y != null)
      y.p = z.p;
  }

  public static void delete(Tree t, int k) {
    Node z = find_to_delete(t.root, k);
    if (z == null)  // K does not exist in tree
      return;
    if (z.left == null && z.right == null)  // Z has no children
      update_parent_with(t, z, null);
    else if (z.right == null)               // Z has only a left child
      update_parent_with(t, z, z.left);
    else if (z.left == null)                // Z has only a right child
      update_parent_with(t, z, z.right);
    else                                    // Z has two children
      splice_successor_and_replace_key(z);
  }

  public static String print_inorder(Node x) {
    String a = "";
    if (x != null) {
      a = a + print_inorder(x.left);
      a = a + " " + x.key;
      a = a + print_inorder(x.right);
    }
    return a;
  }

  public static String print_preorder(Node x) {
    String a = "";
    if (x != null) {
      a = a + " " + x.key;
      a = a + print_preorder(x.left);
      a = a + print_preorder(x.right);
    }
    return a;
  }

  public static void main(String[] args) {
    Scanner s = new Scanner(System.in);
    int m = s.nextInt();
    ArrayList<String> results = new ArrayList<String>();
    Tree T = new Tree();
    for (int i = 0; i < m; i++) {
      String cmd = s.next();
      switch(cmd) {
        case "insert":
          int key = s.nextInt();
          Node x = new Node(key);
          insert(T, x);
          break;
        case "find":
          int k = s.nextInt();
          results.add(find(T.root, k));
          break;
        case "delete":
          k = s.nextInt();
          delete(T, k);
          break;
        case "print":
          results.add(print_inorder(T.root));
          results.add(print_preorder(T.root));
          break;
        default:
          break;
      }
    }
    s.close();
    for (String result : results) {
      System.out.println(result);
    }
  }
}

