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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class Main{
    static private node t = null;
    final static private StringBuilder sb = new StringBuilder();
    public static void main(String[] Args) throws IOException{
        final BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        final int n = Integer.parseInt(br.readLine());
        String in;
        for(int i = 0; i<n; i++){
            in = br.readLine();
            if(in.charAt(0)=='p'){
                inorder(t);
                sb.append('\n');
                preorder(t);
                sb.append('\n');
            }else if(in.charAt(0)=='i'){
                insert(new node(Integer.parseInt(in.substring(7))));
            }else if(in.charAt(0)=='f'){
                sb.append(find(Integer.parseInt(in.substring(5))) ? "yes\n" : "no\n");
            }else{
                delete(Integer.parseInt(in.substring(7)));
            }
        }
        System.out.print(sb);
    }
    static void insert(node z){
        node y = null;
        node x = t;
        while(x!=null){
            y = x;
            if(z.key<x.key){
                x = x.left;
            }else{
                x = x.right;
            }
        }
        if(y==null){
            t = z;
        }else if(z.key<y.key){
            y.left = z;
        }else{
            y.right = z;
        }
    }
    static boolean find(int key){
        node x;
        for(x = t; x!=null&&x.key!=key; x = key<x.key ? x.left : x.right);
        return x!=null&&x.key==key;
    }
    static void delete(int key){
        node y = null;
        node x;
        for(x = t; x!=null&&x.key!=key; y = x, x = key<x.key ? x.left : x.right);
        if(x==null||x.key!=key) return;
        if(x.left==null){
            if(key<y.key) y.left = x.right;
            else y.right = x.right;
        }else if(x.right==null){
            if(key<y.key) y.left = x.left;
            else y.right = x.left;
        }else{
            y = x;
            node z;
            for(z = x.right; z.left!=null; y = z, z = z.left);
            x.key = z.key;
            if(z.key<y.key) y.left = z.right;
            else y.right = z.right;
        }
    }
    static void inorder(node t){
        if(t==null) return;
        inorder(t.left);
        sb.append(' ').append(t.key);
        inorder(t.right);
    }
    static void preorder(node t){
        if(t==null) return;
        sb.append(' ').append(t.key);
        preorder(t.left);
        preorder(t.right);
    }
}
class node{
    public int key;
    public node left;
    public node right;
    node(int key){
        this.key = key;
        left = right = null;
    }
}