.. I have to use a piece of code in java but I don't understand some parts of it.
The code uses methods (.isEmpty() etc. ) from a simple Queue i made in another document.
It is suppposed to investigate an array (which has linked lists in each address) and do some sort of processing with its values.
The problem is that i dont know what marked[s] = true; ,marked[t.v] = true; and parent[t.v] = k; are and how do they work as variables (?)
void BFS(int s)
{
Queue<Integer> Q = new Queue<Integer>();
marked[s] = true;
Q.put(s);
while (!Q.isEmpty())
{
k = Q.get();
for (Node t = adj[k]; t != null; t = t.next)
if (!marked[t.v]) {
marked[t.v] = true;
parent[t.v] = k;
Q.put(t.v);
}
}
}
}
edit: I wrote matrix instead of array, sorry.
marked[] parent and adj are all arrays.
t as you can see from the code, is a Node object. That node object will have a member variable called v. t.v therefore fetches the value of the variable v in the Node object t.
marked[t.v] finds the element in the array with index equal to t.v. e.g. if t.v is equal to 0, then you are fetching marked[0] which is the first element in the marked array.
Related
How would I reverse a queue without having a parameter. I'm trying to copy elements from another queue not in the method and reverse the elements. I have the algorithm but I don't know how to access original queue to copy.
public QueueInterface<T> reverseQueue() {
// TODO 8
Queue<T> a = new Queue<T>();
Stack<T> b = new Stack<T>();
while(!a.isEmpty()){
b.push(a.dequeue());
}
while(!b.isEmpty()){
a.enqueue(b.pop());
}
return a;
}
So I added this condition to add elements to a variable temp and run it through a recursive loop but it gives an error message that would be shown if the queue is empty, NoSuchElementException. Would it be easier to create another Queue instead of temp and place elements inside that or some other way.
public QueueInterface<T> reverseQueue() {
T temp = null;
Queue<T> a = new Queue<T>();
if (temp == null) {
temp = dequeue();
a.enqueue(temp);
reversed();
}
Beginner here using Java (first year student), and am unable to get the below function to work. The goal is to use recursion and a helper function to compute the size of a singly linked list. When running the code against test lists, it keeps returning List changed to [].
I'm struggling in general with Java, so any help is appreciated. Thank you
public class MyLinked {
static class Node {
public Node(double item, Node next) {
this.item = item;
this.next = next;
}
public double item;
public Node next;
}
int N;
Node first;
public int sizeForward() {
return sizeForwardHelper(first);
}
public int sizeForwardHelper(Node n) {
Node current = first;
if (current == null) {
return 0;
} else {
first = first.next;
return sizeForward() + 1;
}
}
I believe I have the first portion set up to return 0 if there are no elements in the List. I believe it's the second part that isn't setting up correctly?
Thanks
Because it’s important for your learning to not spoonfeed you, I’ll describe an approach rather than provide code.
Use this fact:
The length of the list from any given node to the end is 1 plus the length measured from the next node (if there is one).
Usually (as would work here), recursive functions take this form:
If the terminating condition is true, return some value
Otherwise, return some value plus the recursively calculated value
When writing a recursive function, first decide on the terminating condition. In this case, n == null is the obvious choice, and you’d return 0, because you’ve run off the end of the list and the length of nothing (ie no node) is nothing. This also handles the empty list (when first is null) without any special code.
Otherwise, return 1 (the length of one node) plus the length of next.
Put that all together and you’ll have your answer.
——
Hint: The body of the recursive helper method can be coded using one short line if you use a ternary expression.
Instead of calling your wrapper function call your helper function recursively. Try the following:
public int sizeForward () {
return sizeForwardHelper (first);
}
public int sizeForwardHelper(Node n) {
if (n == null) // base case
return 0;
return sizeForwardHelper(n.next) + 1; // count this node + rest of list
}
Your method that computes the size of the list actually modifies the list in the process (with first = first.next; you set the first element to the next, and since there is a recursion, the first element always end up being null which is equivalent to an empty list with your design). Your method will work once, but your list will be empty afterwards.
To illustrate this, I added a print next to the instruction first = first.next; and wrote the following main:
public static void main(String[] args) {
Node n2 = new Node(2d, null);
Node n1 = new Node(1d, n2);
Node n = new Node(0, n1);
MyLinked l = new MyLinked(n);
System.out.println("The first element is: "+l.first.item);
System.out.println("The size is: "+l.sizeForward());
System.out.println("The first element is: "+l.first);
}
It yields:
The first element is: 0.0
first is set to 1.0
first is set to 2.0
first is set to null
The size is: 3
The first element is: null
Clearly, you should not modify the list while computing its size. The helper method should return 0 if the node is null (empty list), and 1 plus the size of the rest of the list otherwise. Here is the code.
public int sizeForwardHelper(Node n) {
if (n == null)
return 0;
else
return sizeForwardHelper(n.next) +1;
}
The goal of the arg free method sizeForward() is just to call the helper. The helper should not use it though.
I am trying to converting a for loop to functional code. I need to look ahead one value and also look behind one value. Is it possible using streams?
The following code is to convert the Roman text to numeric value.
Not sure if reduce method with two/three arguments can help here.
int previousCharValue = 0;
int total = 0;
for (int i = 0; i < input.length(); i++) {
char current = input.charAt(i);
RomanNumeral romanNum = RomanNumeral.valueOf(Character.toString(current));
if (previousCharValue > 0) {
total += (romanNum.getNumericValue() - previousCharValue);
previousCharValue = 0;
} else {
if (i < input.length() - 1) {
char next = input.charAt(i + 1);
RomanNumeral nextNum = RomanNumeral.valueOf(Character.toString(next));
if (romanNum.getNumericValue() < nextNum.getNumericValue()) {
previousCharValue = romanNum.getNumericValue();
}
}
if (previousCharValue == 0) {
total += romanNum.getNumericValue();
}
}
}
No, this is not possible using streams, at least not easily. The stream API abstracts away from the order in which the elements are processed: the stream might be processed in parallel, or in reverse order. So "the next element" and "previous element" do not exist in the stream abstraction.
You should use the API best suited for the job: stream are excellent if you need to apply some operation to all elements of a collection and you are not interested in the order. If you need to process the elements in a certain order, you have to use iterators or maybe access the list elements through indices.
I haven't see such use case with streams, so I can not say if it is possible or not. But when I need to use streams with index, I choose IntStream#range(0, table.length), and then in lambdas I get the value from this table/list.
For example
int[] arr = {1,2,3,4};
int result = IntStream.range(0, arr.length)
.map(idx->idx>0 ? arr[idx] + arr[idx-1]:arr[idx])
.sum();
By the nature of the stream you don't know the next element unless you read it. Therefore directly obtaining the next element is not possible when processing current element. However since you are reading current element you obiously know what was read before, so to achieve such goal as "accesing previous element" and "accessing next element", you can rely on the history of elements which were already processed.
Following two solutions are possible for your problem:
Get access to previously read elements. This way you know the current element and defined number of previously read elements
Assume that at the moment of stream processing you read next element and that current element was read in previous iteration. In other words you consider previously read element as "current" and currently processed element as next (see below).
Solution 1 - implemenation
First we need a data structure which will allow keeping track of data flowing through the stream. Good choice could be an instance of Queue because queues by their nature allows data flowing through them. We only need to bound the queue to the number of last elements we want to know (that would be 3 elements for your use case). For this we create a "bounded" queue keeping history like this:
public class StreamHistory<T> {
private final int numberOfElementsToRemember;
private LinkedList<T> queue = new LinkedList<T>(); // queue will store at most numberOfElementsToRemember
public StreamHistory(int numberOfElementsToRemember) {
this.numberOfElementsToRemember = numberOfElementsToRemember;
}
public StreamHistory save(T curElem) {
if (queue.size() == numberOfElementsToRemember) {
queue.pollLast(); // remove last to keep only requested number of elements
}
queue.offerFirst(curElem);
return this;
}
public LinkedList<T> getLastElements() {
return queue; // or return immutable copy or immutable view on the queue. Depends on what you want.
}
}
The generic parameter T is the type of actual elements of the stream. Method save returns reference to instance of current StreamHistory for better integration with java Stream api (see below) and it is not really required.
Now the only thing to do is to convert the stream of elements to the stream of instances of StreamHistory (where each next element of the stream will hold last n instances of actual objects going through the stream).
public class StreamHistoryTest {
public static void main(String[] args) {
Stream<Character> charactersStream = IntStream.range(97, 123).mapToObj(code -> (char) code); // original stream
StreamHistory<Character> streamHistory = new StreamHistory<>(3); // instance of StreamHistory which will store last 3 elements
charactersStream.map(character -> streamHistory.save(character)).forEach(history -> {
history.getLastElements().forEach(System.out::print);
System.out.println();
});
}
}
In above example we first create a stream of all letters in alphabet. Than we create instance of StreamHistory which will be pushed to each iteration of map() call on original stream. Via call to map() we convert to stream containing references to our instance of StreamHistory.
Note that each time the data flows through original stream the call to streamHistory.save(character) updates the content of the streamHistory object to reflect current state of the stream.
Finally in each iteration we print last 3 saved characters. The output of this method is following:
a
ba
cba
dcb
edc
fed
gfe
hgf
ihg
jih
kji
lkj
mlk
nml
onm
pon
qpo
rqp
srq
tsr
uts
vut
wvu
xwv
yxw
zyx
Solution 2 - implementation
While solution 1 will in most cases do the job and is fairly easy to follow, there are use cases were the possibility to inspect next element and previous is really convenient. In such scenario we are only interested in three element tuples (pevious, current, next) and having only one element does not matter (for simple example consider following riddle: "given a stream of numbers return a tupple of three subsequent numbers which gives the highest sum"). To solve such use cases we might want to have more convenient api than StreamHistory class.
For this scenario we introduce a new variation of StreamHistory class (which we call StreamNeighbours). The class will allow to inspect the previous and the next element directly. Processing will be done in time "T-1" (that is: the currently processed original element is considered as next element, and previously processed original element is considered to be current element). This way we, in some sense, inspect one element ahead.
The modified class is following:
public class StreamNeighbours<T> {
private LinkedList<T> queue = new LinkedList(); // queue will store one element before current and one after
private boolean threeElementsRead; // at least three items were added - only if we have three items we can inspect "next" and "previous" element
/**
* Allows to handle situation when only one element was read, so technically this instance of StreamNeighbours is not
* yet ready to return next element
*/
public boolean isFirst() {
return queue.size() == 1;
}
/**
* Allows to read first element in case less than tree elements were read, so technically this instance of StreamNeighbours is
* not yet ready to return both next and previous element
* #return
*/
public T getFirst() {
if (isFirst()) {
return queue.getFirst();
} else if (isSecond()) {
return queue.get(1);
} else {
throw new IllegalStateException("Call to getFirst() only possible when one or two elements were added. Call to getCurrent() instead. To inspect the number of elements call to isFirst() or isSecond().");
}
}
/**
* Allows to handle situation when only two element were read, so technically this instance of StreamNeighbours is not
* yet ready to return next element (because we always need 3 elements to have previos and next element)
*/
public boolean isSecond() {
return queue.size() == 2;
}
public T getSecond() {
if (!isSecond()) {
throw new IllegalStateException("Call to getSecond() only possible when one two elements were added. Call to getFirst() or getCurrent() instead.");
}
return queue.getFirst();
}
/**
* Allows to check that this instance of StreamNeighbours is ready to return both next and previous element.
* #return
*/
public boolean areThreeElementsRead() {
return threeElementsRead;
}
public StreamNeighbours<T> addNext(T nextElem) {
if (queue.size() == 3) {
queue.pollLast(); // remove last to keep only three
}
queue.offerFirst(nextElem);
if (!areThreeElementsRead() && queue.size() == 3) {
threeElementsRead = true;
}
return this;
}
public T getCurrent() {
ensureReadyForReading();
return queue.get(1); // current element is always in the middle when three elements were read
}
public T getPrevious() {
if (!isFirst()) {
return queue.getLast();
} else {
throw new IllegalStateException("Unable to read previous element of first element. Call to isFirst() to know if it first element or not.");
}
}
public T getNext() {
ensureReadyForReading();
return queue.getFirst();
}
private void ensureReadyForReading() {
if (!areThreeElementsRead()) {
throw new IllegalStateException("Queue is not threeElementsRead for reading (less than two elements were added). Call to areThreeElementsRead() to know if it's ok to call to getCurrent()");
}
}
}
Now, assuming that three elements were already read, we can directly access current element (which is the element going through the stream at time T-1), we can access next element (which is the element going at the moment through the stream) and previous (which is the element going through the stream at time T-2):
public class StreamTest {
public static void main(String[] args) {
Stream<Character> charactersStream = IntStream.range(97, 123).mapToObj(code -> (char) code);
StreamNeighbours<Character> streamNeighbours = new StreamNeighbours<Character>();
charactersStream.map(character -> streamNeighbours.addNext(character)).forEach(neighbours -> {
// NOTE: if you want to have access the values before instance of StreamNeighbours is ready to serve three elements
// you can use belows methods like isFirst() -> getFirst(), isSecond() -> getSecond()
//
// if (curNeighbours.isFirst()) {
// Character currentChar = curNeighbours.getFirst();
// System.out.println("???" + " " + currentChar + " " + "???");
// } else if (curNeighbours.isSecond()) {
// Character currentChar = curNeighbours.getSecond();
// System.out.println(String.valueOf(curNeighbours.getFirst()) + " " + currentChar + " " + "???");
//
// }
//
// OTHERWISE: you are only interested in tupples consisting of three elements, so three elements needed to be read
if (neighbours.areThreeElementsRead()) {
System.out.println(neighbours.getPrevious() + " " + neighbours.getCurrent() + " " + neighbours.getNext());
}
});
}
}
The output of this is following:
a b c
b c d
c d e
d e f
e f g
f g h
g h i
h i j
i j k
j k l
k l m
l m n
m n o
n o p
o p q
p q r
q r s
r s t
s t u
t u v
u v w
v w x
w x y
x y z
By StreamNeighbours class it is easier to track the previous/next element (because we have method with appropriate names), while in StreamHistory class this is more cumbersome since we need to manually "reverse" the order of the queue to achieve this.
As others stated, it's not feasable, to get next elements from within an iterated Stream.
If IntStream is used as a for loop surrogate, which merely acts as an index iteration provider, it's possible use its range iteration index just like with for; one needs to provide a means of skipping the next element on the next iteration, though, e. g. by means of an external skip var, like this:
AtomicBoolean skip = new AtomicBoolean();
List<String> patterns = IntStream.range(0, ptrnStr.length())
.mapToObj(i -> {
if (skip.get()) {
skip.set(false);
return "";
}
char c = ptrnStr.charAt(i);
if (c == '\\') {
skip.set(true);
return String.valueOf(new char[] { c, ptrnStr.charAt(++i) });
}
return String.valueOf(c);
})
It's not pretty, but it works.
On the other hand, with for, it can be as simple as:
List<String> patterns = new ArrayList();
for (char i=0, c=0; i < ptrnStr.length(); i++) {
c = ptrnStr.charAt(i);
patternList.add(
c != '\\'
? String.valueOf(c)
: String.valueOf(new char[] { c, ptrnStr.charAt(++i) })
);
}
EDIT:
Condensed code and added for example.
I'm trying to iterate over an Object array. Using the next() method works so I'm guessing that my iterator class and constructors are working.
For some reason i'm not getting any output while the hasNext() method is running.
Iterator it = hej.iterator();
Object j = it.next();
System.out.println(j);
while(it.hasNext()){
Object i = it.next();
System.out.println(i + " ");
}
With "hej" being my Object array.
My code for the next(); and hasNext() methods are as follows:
public class StackIterator implements Iterator<Object>{
// fields
private int element = 0;
private final Object[] elements;
private final int max;
// constructor
public StackIterator(Object[] values, int maxIndex) {
elements = values;
max = maxIndex;
}
// methods
public boolean hasNext() {
return element < max;
}
public Object next() {
return elements[element++];
}
}
The file that constructs the Object Array and the Object Array depends on an interface:
public interface Stack {
int size();
boolean isEmpty();
void push(Object element);
Object pop();
Object peek();
Iterator<Object> iterator();
}
The methods are then explained in another file:
public class StackExample implements Stack {
// fields
int length = 0;
Object[] arr;
// constructor
public StackExample() {arr = new Object[length];}
// method returns size of object array
public int size() {
return arr.length;
}
// method checks if object is empty
public boolean isEmpty() {
boolean result = false;
if (arr.length == 0){
result = true;
}
return result;
}
// method for push
public void push(Object element) {
newBiggerObj();
arr[0] = element;
}
// returns the first object of the stack
public Object pop() {
Object[] temp = new Object[arr.length-1];
Object first = arr[0];
for (int i = 0; i<arr.length-1; i++){
temp[i] = arr[i+1];
}arr = temp;
return first;
}
// returns the object on top of stack
public Object peek() {
if (isEmpty()){
try{
throw new Exception("Stack empty, can't peek!");
}
catch(Exception e){
return e.getMessage();
}
}
else {
Object first = arr[0];
return first;
}
}
// method for push method
private void newBiggerObj(){
Object[] temp = new Object[arr.length+1];
for (int i = 0; i<arr.length; i++){
temp[i+1] = arr[i];
}
arr = temp;
}
public String toString(){
String str = "";
for (int i = 0; i < arr.length; i++){
str = str + arr[i] + " , ";
}return str;
}
public Iterator<Object> iterator() {
return new StackIterator(arr, length);
}
}
What bothers me is that the method Iterator is within itself returning an instance of the class Stack Iterator. Which i posted above. So my real problem seems to be that my fields are not being given any value, since I am not myself giving the any values within the constructor.
My main method in which I'm testing all of this is as follows:
public class Teststack {
public static void main(String[] args){
// new instane of class StackExample
StackExample hej = new StackExample();
// test for the different methods
System.out.println(hej.isEmpty());
System.out.println(hej.size());
hej.push(4);
hej.push("hej");
hej.push(6);
hej.push(5);
System.out.println(hej.size());
System.out.println(hej.peek());
System.out.println(hej.pop());
System.out.println(hej.toString());
System.out.println(hej.isEmpty());
System.out.println("Testing Iterator: ");
// test for iterator
Iterator it = hej.iterator();
Object j = it.next();
System.out.println(j);
while(it.hasNext()){
Object i = it.next();
System.out.println(i + " ");
}
}
}
In your StackExample class, I don't see the length variable being updated when elements are pushed or popped. Due to this, length will always be 0 and calls to it.hasNext() will always return false.
You don't need to pass the length as a separate argument. You can find the array's length in the StackIterator constructor and use it.
Also note that since you're creating a new array on every push and pop, the iterator returned by StackExample#iterator() will become stale after every push/pop since it will work on an old copy/state of the stack.
The problem is here:
public Iterator<Object> iterator() {
return new StackIterator(arr, length);
}
length field is never changed, so its value is always 0. You can change the code to this:
public Iterator<Object> iterator() {
return new StackIterator(arr, arr.length);
}
Also, before retrieving elements from the iterator, you should always call it.hasNext. The fact you did this:
Iterator it = hej.iterator();
Object j = it.next();
And worked was just pure luck.
Apart of this, I can sense you have a bad design on your stack implementation. Here are some hints to improve your code:
The inner array should be initialized with a default size different than 0. E.g. 10 (as done in java.util.ArrayList implementation).
You should avoid creating a new array when adding (push) or removing (pop) an element from your stack. Instead of this, you should use the length field to control how many elements are in your stack.
The value of the new size should be based on another formula rather than array.length + 1. For example, try using something like int newSize = array.length / 2 * 3;.
Resize the inner array only when necessary. When calling push, do it only if you precisely need to increase the size of the array. When calling pop, do it if the current length of the array (this is, array.length) is far greater than the value of length field of your class.
Never forget to update the value of length on push and pop methods.
Couple of issues:
You are calling Object j = it.next(); after creating iterator and then check for hasNext. You are incrementing the element index. Hence if you just have one element, you wont enter the while loop. In addition, if your custom datastructure is empty i.e. array has no elements then you are prone to ArrayIndexOutOfBoundException.
You will always iterate and print n-1 elements instead to n elements.
Once you iterated, then your pointer will always point to last element and never get resetted. So very next time you wont be able to iterate over your elements. Its a one time iterator.
Try not to call
Object j = it.next() statement, but just while cycle. Seems you have an array of just 1 element.
There are a number of problems with this code:
In the StackIterator constructor there is no bounds checking on maxIndex. Callers can pass in a number greater than values.length, less that 0, etc.
In the next method, there is no check of the end condition, either directly or by calling hasNext(). Callers can keep calling next() and see elements beyond max or even get an ArrayIndexOutOfBoundsException, when they should be getting a NoSuchElementException.
The Stack class never increments or decrements its length field when elements are pushed or popped.
The Stack class tracks the length separately from the array, even though it always resizes the array on every push or pop, but Java arrays already know their size. (But see the next item.)
The Stack class resizes the array on every push or pop, which is very inefficient. Typically classes like this only resize the array when necessary, allowing 'slack' space, to give amortized constant time performance (see ArrayList). If you do this, however, it is necessary to null out popped items to avoid unintentional object retention.
The Stack adds and removes elements at the beginning of the array. This is incredibly inefficient since it means a O(n) reshuffling must be done on every push or pop.
The peek() method takes into account the possibility that the Stack may be empty, but the pop() method does not. A pop() on an empty Stack will throw an ArrayIndexOutOfBoundsException.
Stack is not a generic class. It holds Object. Users of the Stack will have to cast the return values from peek() or pop(), and it isn't type safe. In your example, you show a stack that is a heterogeneous mixture of String and Integer. This is a very Java 1.2 way of doing things, and while it isn't necessarily wrong, you should consider parameterizing Stack.
I need to write a method that starts with a single linked list of integers and a special value called the splitting value. The elements of the list are in no particular order. The method divides the nodes into two linked lists: one containing all the nodes that contain an element less than the splitting value and one that contains all the other nodes. If the original linked list had any repeated integers (i.e., any two or more nodes with the same element in them), then the new linked list that has this element should have the same number of nodes that repeat this element. The method returns two head references - one for each of the linked lists that were created.
I have been spent countless hours trying to get this right and think this is the closest but I have an error while compiling that my copyTail* IntNodes may not be initialized. I also may be completely wrong with my code....
Any help pointing in me in the right direction??
public static IntNode[ ] listSplitLessGreater(IntNode source, int splitter)
{
IntNode copyHeadLess;
IntNode copyTailLess;
IntNode copyHeadGreater;
IntNode copyTailGreater;
IntNode[ ] answer = new IntNode[2];
boolean less = true;
boolean greater = true;
// Handle the special case of the empty list.
if (source == null)
return answer; // The answer has two null references .
//Split list into two lists less and greater/equal than splitter.
while (source.link != null)
{
if (splitter < source.data)
{
if (less)
{
copyHeadLess = new IntNode(source.data, null);
copyTailLess = copyHeadLess;
less=false;
}
else
{
source = source.link;
copyTailLess.addNodeAfter(source.data);
copyTailLess = copyTailLess.link;
}
}
else
{
if (greater)
{
copyHeadGreater = new IntNode(source.data, null);
copyTailGreater = copyHeadGreater;
greater=false;
}
else
{
source = source.link;
copyTailGreater.addNodeAfter(source.data);
copyTailGreater = copyTailGreater.link;
}
}
}
//Return Head References
answer[0] = copyHeadLess;
answer[1] = copyHeadGreater;
return answer;
}
I think you're making it more complicated than it needs to be, by modelling a list just with a single class (IntNode). If you model it as "the list" and "a node in the list" then it's easy to have an empty list. You also don't need to keep track of both the head and the tail - the list can do that. At that point, it's very simple:
Create two empty lists, one for "lower" and one for "not lower"
Iterate over the original list:
Work out which list to add the element to
Add the element
Return both lists (e.g. using an array as you have done)
Note that even without that, you can make your code simpler by just using null to mean "I haven't got this list yet". At the moment your code won't compile, as copyHeadLess etc aren't definitely assigned when they're used. You know that you won't try to use them until they've been assigned, but the compiler doesn't. I'd still recommend the remodelling approach though :)
If source isn't null, but source.link is null (list is only composed of one element) then you never assign to your copyHeadLess, etc, variables. Try initializing them to null or whatever the default is:
IntNode copyHeadLess = null;
IntNode copyTailLess = null;
IntNode copyHeadGreater = null;
IntNode copyTailGreater = null;
IntNode[ ] answer = new IntNode[2];
boolean less = true;
boolean greater = true;
// Handle the special case of the empty list.
if (source == null)
return answer; // The answer has two null references .
//Split list into two lists less and greater/equal than splitter.
while (source.link != null)
{
// what about case where source isn't null but source.link is null?
}
//Return Head References
answer[0] = copyHeadLess; // this may have never been assigned in your original code
answer[1] = copyHeadGreater; // this may have never been assigned in your original code
return answer;
}