Practice AP CS Test - java

I've got a student studying for the AP CS test (he takes it next week). I was hired mid/end year to basically be a long term sub for the rest of the school year for these IT classes. I don't know enough about java or programming to explain to him why the answer to this practice test problem is B and not A (according to the answer sheet).
I'm hoping this might be a decent place to get an explanation I can take to him...
/** Precondition: arr contains only positive values.
*/
public static void doSome(int[]arr, int lim)
{
int v = 0;
int k = 0;
while (k < arr.length && arr[k] < lim)
{
if (arr[k] > v)
{
v = arr[k]; /* Statement S */
}
k++; /* Statement T */
}
}
Assume that doSome is called and executes without error. Which of the following are possible combinations for the value of lim, the number of times Statement S is executed, and the number of times Statement T is executed?
possible combinations for the value of lim
(A) I only
(B) II only
(C) III only
(D) I and III only
(E) II and III only

III is not a valid combination because you can't execute S more times than you execute T.
From a test-taking perspective: In this problem, this is the most important insight because figuring this out immediately knocks out 3 options and takes you down to a 50/50 shot on a guess.
I is not a valid combination because the array contains only positive values, all of which are > 0, so the conditional if(arr[k]>v) must return true at least once, meaning that S is executed at least once if the while loop body gets executed at least once. In option I, statement T (also in the body of the while loop) is executed 5 times, so S must be executed at least once.
II is a valid combination of values.
From a test-taking perspective: It's not worth taking the time to prove this (e.g. by providing sample inputs that produce this combination), as process of elimination has already taken you down to one answer.
Therefore, option B, II only, is the correct answer.
Props to the AP test question writer.

Related

How to create statistics from output of Java code?

Summary: I need a function based on the output. The problem is
connecting Eclipse or a Java code with another software.
I'm studying Physics. I needed a code that works the following way:
first, it declares a random number n;
then it outputs a "winner" number (based on some rules; the code
itself is irrelevant now I think), 20 times (but should be more,
first I need something to record the values, though).
I have n and 20 other numbers which are each between 1 and n (including 1 and n). I want, after compiling the code once, to see the 20 values, how they are distributed (for example, are they around one particular number, or in a region, is there a pattern (this is based on the rules, of course)).
The problem is, I'm only familiar with basic Java (I used eclipse), and have no clue on how I should register for example 2000 instead of the 20 numbers (so for an n number the code should print 2000 or more numbers, which should appear on a function: domain of the function is 1, 2, ..., n, and range is 0, 1, ..., 2000, as it might happen that all 2000 numbers are the same). I thought of Excel, but how could I connect a Java code with it? Visual interpretation is not necessary, although it would make my work easier (I hope, at least).
The code:
import java.util.Random;
public class korbeadosjo {
public static void main(String Args[]){
Random rand = new Random();
int n = (rand.nextInt(300)+2);
System.out.println("n= " + n);
int narrayban = n-1;
int jatekmester = n/2;
int jatekmesterarrayban = jatekmester-1;
System.out.println("n/2: " + jatekmester);
for(int i=0; i<400; i++){
int hanyembernelvoltmar = 1;
int voltmar[] = new int[n];
voltmar[jatekmesterarrayban]=1;
int holvan=jatekmester;
int holvanarrayban = holvan-1;
fori: for(;;){
int jobbravagybalra = rand.nextInt(2);
switch(jobbravagybalra){
case 0: //balra
if(holvanarrayban ==0){
holvanarrayban = narrayban;
}else {
--holvanarrayban;
};
if(voltmar[holvanarrayban]==0){
voltmar[holvanarrayban] =1;
++hanyembernelvoltmar;
}
break;
case 1: //jobbra
if(holvanarrayban == narrayban){
holvanarrayban = 0;
} else {++holvanarrayban;};
if(voltmar[holvanarrayban]==0){
voltmar[holvanarrayban]=1;
++hanyembernelvoltmar;
}
break;
}if(hanyembernelvoltmar==n){
System.out.println(holvanarrayban+1);
break fori;
}}}}}
basic Java (I used eclipse)
Unrelated.
I could only find two prompts in your question:
How to create statistics from output of Java code?
You are likely not wanting to get the output alone. Use those numbers in your Java program to find what you want and output it.
How did you store 2000 values? An array, list, queue...? So also iterate on that data structure and generate the statistics you need.
I thought of Excel, but how could I connect a Java code with it?
There is this site.

How to breakdown a method and process it [closed]

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I am preparing for an exam next week, and I decided to look for some exam questions online for better preparation.
I came across this question and the answer is c. But I really want to know how or the step by step process to answer to answer a question like this. The part where I got stuck is trying to logically understand how a int m = mystery(n); How can a number equal a method? Whenever I get to a question like this is their anything important I should breakdown first?
private int[] myStuff;
/** Precondition : myStuff contains int values in no particular order.
/*/
public int mystery(int num)
{
for (int k = myStuff.length - 1; k >= 0; k--)
{
if (myStuff[k] < num)
{
return k;
}
}
return -1;
}
Which of the following best describes the contents of myStuff after the
following statement has been executed?
int m = mystery(n);
(a) All values in positions 0 through m are less than n.
(b) All values in positions m+1 through myStuff.length-1 are
less than n.
(c) All values in positions m+1 through myStuff.length-1 are
greater than or equal to n.
(d) The smallest value is at position m.
(e) The largest value that is smaller than n is at position m.
See this page to understand a method syntax
http://www.tutorialspoint.com/java/java_methods.htm
int m = mystery(n); means this method going to return int value and you are assigning that value to a int variable m. So your final result is m. the loop will run from the array's end position to 0. loop will break down when array's current position value is less than your parameter n. on that point it will return the loop's current position. s o now m=current loop position. If all the values of the loop is greater than n it will return -1 because if condition always fails.
Place the sample code into a Java IDE such as Eclipse, Netbeans or IntelliJ and then step through the code in the debugger in one of those environments.
Given that you are starting out I will give you the remainder of the code that you need to make this compile and run
public class MysteriousAlright {
private int[] myStuff;
public int mystery(int num)
{
for (int k = myStuff.length - 1; k >= 0; k--) {
if (myStuff[k] < num) {
return k;
}
}
return -1;
}
public static void main(String[] args) {
MysteriousAlright ma = new MysteriousAlright();
ma.setMyStuff(new int[] {4,5,6,7});
int m = ma.mystery(5);
System.out.println("I called ma.mystery(5) and now m is set to " + m);
m = ma.mystery(3);
System.out.println("I called ma.mystery(3) and now m is set to " + m);
m = ma.mystery(12);
System.out.println("I called ma.mystery(12) and now m is set to " + m);
}
public void setMyStuff(int[] myStuff) {
this.myStuff = myStuff;
}
}
You then need to learn how to use the debugger and/or write simple Unit Tests.
Stepping through the code a line at a time and watching the values of the variables change will help you in this learning context.
Here are two strategies that you can use to breakdown nonsense code like that which you have sadly encountered in this "educational" context.
Black Box examination Strategy
Temporarily ignore the logic in the mystery function, we treat the function as a black box that we cannot see into.
Look at what data gets passed in, what data is returned.
So for the member function called mystery we have
What goes in? : int num
What gets returned : an int, so a whole number.
There are two places where data is returned.
Sometimes it returns k
Sometimes it returns -1
Now we move on.
White Box examination Strategy
As the code is poorly written, a black box examination is insufficient to interpret its purpose.
A white box reading takes examines the member function's internal logic (In this case, pretty much the for loop)
The for loop visits every element in the array called myStuff, starting at the end of the array
k is the number that tracks the position of the visited element of the array. (Note we count down from the end of the array to 0)
If the number stored at the visited element is less than num (which is passed in) then return the position of that element..
If none of elements of the array are less than num then return -1
So mystery reports on the first position of the element in the array (starting from the end of the array) where num is bigger than that element.
do you understand what a method is ?
this is pretty basic, the method mystery receives an int as a parameter and returns an int when you call it.
meaning, the variable m will be assigned the value that returns from the method mystery after you call it with n which is an int of some value.
"The part where I got stuck is trying to logically understand how a int m = mystery(n); How can a number equal a method?"
A method may or may not return a value. One that doesn't return a value has a return type of void. A method can return a primitive value (like in your case int) or an object of any class. The name of the return type can be any of the eight primitive types defined in Java, the name of any class, or an interface.
If a method doesn't return a value, you can't assign the result of that method to a variable.
If a method returns a value, the calling method may or may not bother to store the returned value from a method in a variable.

Why use recursion if the same task can be accomplished with loop control structures?

As I start learning recursion different questions are crossing my mind. Recursion uses more memory for the stack and it's usually slower due to maintaining the stack.
What is the benefit of using recursion if I still can use for loops? We describe actions to be repeated over and over until a condition is true, and we can use both recursion or for loops.
Why would I choose recursive version while I have faster control structures as an option?
Recursion uses more memory for the stack and it usually slower due to maintaining the stack
That statement is far from being universally true. It applies in situations when you do not need to save the state for more than a fixed number of levels, but that does not cover many important tasks that can be solved recursively. For example, if you want to implement a depth-first search on a graph, you need to make your own data structure to store the state that would otherwise go on the stack.
What is the benefit of using Recursion if I still can use for loop?
You get more clarity when you apply a recursive algorithm to a task that is best understood through recursion, such as processing recursively-defined structures. In cases like that, a loop by itself is no longer sufficient: you need a data structure to go along with your loop.
Why would I choose recursive version while I have faster control structure?
You wouldn't necessarily choose recursion when you could implement the same algorithm with faster control structures that are easy to understand. However, there are situations when you may want to code a recursion to improve readability, even though you know that you can code the algorithm using a loop, with no additional data structures. Modern compilers can detect situations like that, and "rewrite" your recursive code behind the scene to make it use iterations. This lets you have the best of both worlds - a recursive program that matches reader's expectations, and an iterative implementation that does not waste space on the stack.
Unfortunately, demonstrating examples of situations when recursion gives you clear advantages requires knowledge of advanced topics, so many educators take shortcuts by demonstrating recursion using wrong examples, such as factorials and Fibonacci numbers. One relatively simple example is implementing a parser for an expression with parentheses. You can do it in many different ways, with or without recursion, but the recursive way of parsing expressions gives you an amazingly concise solution that is easy to understand.
The great example of when the recursive solution is better than the itterative one is the tower of Hanoi. Consider the following two solutions -
Recursive (from this question):
public class Hanoi {
public static void main(String[] args) {
playHanoi (2,"A","B","C");
}
//move n disks from position "from" to "to" via "other"
private static void playHanoi(int n, String from , String other, String to) {
if (n == 0)
return;
if (n > 0)
playHanoi(n-1, from, to, other);
System.out.printf("Move one disk from pole %s to pole %s \n ", from, to);
playHanoi(n-1, other, from, to);
}
}
Iterative (copied from RIT):
import java.io.*;
import java.lang.*;
public class HanoiIterative{
// -------------------------------------------------------------------------
// All integers needed for program calculations.
public static int n;
public static int numMoves;
public static int second = 0;
public static int third;
public static int pos2;
public static int pos3;
public static int j;
public static int i;
public static void main(String args[]) {
try{
if( args.length == 1 ){
System.out.println();
n = Integer.parseInt(args[0]); //Sets n to commandline int
int[] locations = new int[ n + 2 ]; //Sets location size
for ( j=0; j < n; j++ ){ //For loop - Initially all
locations[j] = 0; //discs are on tower 1
}
locations[ n + 1 ] = 2; //Final disk destination
numMoves = 1;
for ( i = 1; i <= n; i++){ //Calculates minimum steps
numMoves *= 2; //based on disc size then
} //subtracts one. ( standard
numMoves -= 1; //algorithm 2^n - 1 )
//Begins iterative solution. Bound by min number of steps.
for ( i = 1; i <= numMoves; i++ ){
if ( i%2 == 1 ){ //Determines odd or even.
second = locations[1];
locations[1] = ( locations[1] + 1 ) % 3;
System.out.print("Move disc 1 to ");
System.out.println((char)('A'+locations[1]));
}
else { //If number is even.
third = 3 - second - locations[1];
pos2 = n + 1;
for ( j = n + 1; j >=2; j-- ) //Iterative vs Recursive.
if ( locations[j] == second )
pos2 = j;
pos3 = n + 1;
for ( j = n + 1; j >= 2; j-- ) //Iterative vs Recursive.
if ( locations[j] == third )
pos3 = j;
System.out.print("Move disc "); //Assumes something is moving.
//Iterative set. Much slower here than Recursive.
if ( pos2 < pos3 ){
System.out.print( pos2 );
System.out.print(" to ");
System.out.println((char)('A' + third));
locations[pos2] = third;
}
//Iterative set. Much slower here than Recursive.
else {
System.out.print( pos3 );
System.out.print(" to ");
System.out.println((char)('A' + second));
locations[ pos3 ] = second;
}
}
}
}
} //Protects Program Integrity.
catch( Exception e ){
System.err.println("YOU SUCK. ENTER A VALID INT VALUE FOR #");
System.err.println("FORMAT : java HanoiIterative #");
} //Protects Program Integrity.
finally{
System.out.println();
System.out.println("CREATED BY: KEVIN SEITER");
System.out.println();
}
}
}//HanoiIterative
//--------------------------------------------------------------------------------
Im guessing you didnt really read that iterative one. I didnt either. Its much more complicated. You change change some stuff here and there, but ultimately its always going to be complicated and there is no way around it. While any recursive algorithm CAN be converted to iterative form, it is sometimes much more complicated code wise, and sometimes even significantly less efficient.
How would you search a directory full of sub directories that are themselves full of sub directories and so on (like JB Nizet stated, tree nodes) or calculate a Fibonacci sequence with less ease than using recursion?
All algorithms can be translated from recursive to iterative. Worst case scenario you can explicitly use a stack to keep track of your data (as opposed to the call stack). So if efficiency is really paramount and you know recursion is slowing you down significantly, it's always possible to fall back on the iterative version. Note that some languages have compilers that convert tail recursive methods to their iterative counterparts, e.g., Scala.
The advantage of recursive methods is that most of the time they are much easier to write and understand because they are so intuitive. It is good practice to understand and write recursive programs since many algorithms can be naturally expressed that way. Recursion is just a tool to write expressive and correct programs. And again, once you know your recursive code is correct, it's easier to convert it to its iterative counterpart.
Recursion is usually more elegant and intuitive than other methods. But it's not the universal solution to everything.
Take the Fibonacci sequence for example. You can find the nth term by recursively using the definition of fibonacci number (and the base case with n == 1). But you'll find yourself calculating the mth term ( m < n - 2 ) more than once .
Use instead an array [1, 1] and append the next ith term as the sum of a[i-1] + a[i-2]. You'll find a linear algorithm a lot faster than the other.
BUT you'll love recursion.
It's elegant and often powerful.
Imagine you want to traverse a tree to print something in order. It could be something like:
public void print (){
if( this == null )
return;
left.print();
System.out.println(value);
right.print();
}
To make this with a while loop you need to do your own backtracking stack because it has calls which are not in tail position (though one call is). It won't be as easy to understand as this though and IMO technically it would still be recursion since goto+stack is recursion.
If your trees are not too deep you won't blow the stack and the program works. There is no need to do premature optimizations. I even would have increased the JVM's stack before changing this to do it's own stack.
Now in a future version of the runtime even JVM can get tail call optimization just like proper runtimes should have. Then all recursions in tail positions won't grow the stack and then it's no difference from other control structures so you choose which has the most clear syntax.
My understanding is that standard iterative loops are more applicable when your data set is small, has minimal edge cases, and for which the logical conditions are simple for determining how many times to iterate one or more dedicated functions.
More importantly, recursive functions are more useful when applied to more complex nested data structures, in which you may not be able to intuitively or accurately estimate how many times you need to loop, because the amount of times you need dedicated functions to reiterate is based on a handful of conditions, some of which may not be mutually exclusive, and for which you care to specifically deliberate the order of the call stack and an intuitive path to a base case, for ease of readability and debugging***.
Recursion is recommended for prototype programming for non programmers or junior programmers. For more serious programming you should avoid recursion as much as you can. Please read
NASA coding standard

homework and overloading in java

Ok so this is my homework assignment, and I am having a heck of a time figuring out how to correctly use overloading to allow for a certain number of terms to print out.
"Create a class that contains a method that accepts an integer from the user to display the next 5 terms in the following pattern: (n-7) * 3.
So, if the user enters 5, the output should be:
-6
-39
-138
-435
-1326
Add an overloaded method so the user can enter how many termss they want to print out in a pattern:
So, the user would enter 5 as the starting number and 3 as the number of terms to print out in the pattern.
The output would be:
-6
-39
-435
Add different method that displays the formula and provides calculation to the formula: (should get starting number from user input) and prints out the next 5 terms.
(5-7) * 3 = -6
(-6-7) * 3= -39
(-39-7) * 3 = -435
Add an overloaded method that displays the formula and the calculation to the formula and takes in how many times it should print: (should get from user input).
For example: User enters 5 as the starting number and print out 4 times.
(5-7) * 3 = -6
(-6-7) * 3= -39
(-39-7) * 3 = -435
(-435-7) * 3 = -1326
Specifics:
You have a separate class that contains all your methods.
You should have 4 methods in this class.
Your main should call these four methods getting user input where appropriate.
"
I'm not asking for anyone to do this for me, I just would appreciate a steer in the right direction.
At the moment trying to collect the number of terms wanted by the user in the main class then pass it to the Numberpattern class and then from their have the program determine which Calc method to use is not working.
Okay i feel dirty for doing your homework for you but i'll get you started
the first method is
public void printPattern(int n){
int prevAnswer = n;
for(int i =0; i < 5; i ++){
int newAnswer = (prevAnswer - 7) * 3;
System.out.println(newAnswer);
prevAnswer = newAnswer;
}
}
The first overload is
public void printPattern(int n, int c){ //this is the overload
public void printPattern(int n){
int prevAnswer = n;
for(int i =0; i < c; i ++){ // i < c to print that many numbers in the sequence
int newAnswer = (prevAnswer - 7) * 3;
System.out.println(newAnswer);
prevAnswer = newAnswer;
}
}
To Overload a method simply provide different parameters and write the extended new functionality
By overloading a method, you are using the same methods with different parameter lists. This allows the program to decide which method is best to be used with only one call of that method name.
It looks like your first method would have a loop of a fixed number and only one parameter (n). Your second method will have the same name, but now allow for two parameters - the (n) and the number of times to loop.
public static void nextTerms (int n) {
Your fixed count loop and print out of n code...
}
public static void nextTerms (int n, int loopCount) {
Your changeable loopCount count loop and print out of n code...
}
To run that nextTerms method, your main Class could either call:
nextTerms(5);
or
nextTerms(5, 3);
The program will then decide which of the two nextTerms methods are appropriate.
For more information, I suggest - http://docs.oracle.com/javase/tutorial/java/javaOO/methods.html
Cheers!
Chris

Problem with recursive backtracking

Hey guys, recently posted up about a problem with my algorithm.
Finding the numbers from a set which give the minimum amount of waste
Ive amended the code slightly, so it now backtracks to an extent, however the output is still flawed. Ive debugged this considerablychecking all the variable values and cant seem to find out the issue.
Again advice as opposed to an outright solution would be of great help. I think there is only a couple of problems with my code, but i cant work out where.
//from previous post:
Basically a set is passed to this method below, and a length of a bar is also passed in. The solution should output the numbers from the set which give the minimum amount of waste if certain numbers from the set were removed from the bar length. So, bar length 10, set includes 6,1,4, so the solution is 6 and 4, and the wastage is 0. Im having some trouble with the conditions to backtrack though the set. Ive also tried to use a wastage "global" variable to help with the backtracking aspect but to no avail.
SetInt is a manually made set implementation, which can add, remove, check if the set is empty and return the minimum value from the set.
/*
* To change this template, choose Tools | Templates
* and open the template in the editor.
*/
package recursivebacktracking;
/**
*
* #author User
*/
public class RecBack {
int WASTAGE = 10;
int BESTWASTAGE;
int BARLENGTH = 10;
public void work()
{
int[] nums = {6,1,2,5};
//Order Numbers
SetInt ORDERS = new SetInt(nums.length);
SetInt BESTSET = new SetInt(nums.length);
SetInt SOLUTION = new SetInt(nums.length);
//Set Declarration
for (int item : nums)ORDERS.add(item);
//Populate Set
SetInt result = tryCutting(ORDERS, SOLUTION, BARLENGTH, WASTAGE);
result.printNumbers();
}
public SetInt tryCutting(SetInt possibleOrders, SetInt solution, int lengthleft, int waste)
{
for (int i = 0; i < possibleOrders.numberInSet(); i++) // the repeat
{
int a = possibleOrders.min(); //select next candidate
System.out.println(a);
if (a <= lengthleft) //if accecptable
{
solution.add(a); //record candidate
lengthleft -= a;
WASTAGE = lengthleft;
possibleOrders.remove(a); //remove from original set
if (!possibleOrders.isEmpty()) //solution not complete
{
System.out.println("this time");
tryCutting(possibleOrders, solution, lengthleft, waste);//try recursive call
BESTWASTAGE = WASTAGE;
if ( BESTWASTAGE <= WASTAGE )//if not successfull
{
lengthleft += a;
solution.remove(a);
System.out.println("never happens");
}
} //solution not complete
}
} //for loop
return solution;
}
}
Instead of using backtracking, have you considered using a bitmask algorithm instead? I think it would make your algorithm much simpler.
Here's an outline of how you would do this:
Let N be number of elements in your set. So if the set is {6,1,2,5} then N would be 4. Let max_waste be the maximum waste we can eliminate (10 in your example).
int best = 0; // the best result so far
for (int mask = 1; mask <= (1<<N)-1; ++mask) {
// loop over each bit in the mask to see if it's set and add to the sum
int sm = 0;
for (int j = 0; j < N; ++j) {
if ( ((1<<j)&mask) != 0) {
// the bit is set, add this amount to the total
sm += your_set[j];
// possible optimization: if sm is greater than max waste, then break
// out of loop since there's no need to continue
}
}
// if sm <= max_waste, then see if this result produces a better one
// that our current best, and store accordingly
if (sm <= max_waste) {
best = max(max_waste - sm);
}
}
This algorithm is very similar to backtracking and has similar complexity, it just doesn't use recursion.
The bitmask basically is a binary representation where 1 indicates that we use the item in the set, and 0 means we don't. Since we are looping from 1 to (1<<N)-1, we are considering all possible subsets of the given items.
Note that running time of this algorithm increases very quickly as N gets larger, but with N <= around 20 it should be ok. The same limitation applies with backtracking, by the way. If you need faster performance, you'd need to consider another technique like dynamic programming.
For the backtracking, you just need to keep track of which element in the set you are on, and you either try to use the element or not use it. If you use it, you add it to your total, and if not, you proceeed to the next recursive call without increasing your total. Then, you decrement the total (if you incremented it), which is where the backtracking comes in.
It's very similar to the bitmask approach above, and I provided the bitmask solution to help give you a better understanding of how the backtracking algorithm would work.
EDIT
OK, I didn't realize you were required to use recursion.
Hint1
First, I think you can simplify your code considerably by just using a single recursive function and putting the logic in that function. There's no need to build all the sets ahead of time then process them (I'm not totally sure that's what you're doing but it seems that way from your code). You can just build the sets and then keep track of where you are in the set. When you get to the end of the set, see if your result is better.
Hint2
If you still need more hints, try to think of what your backtracking function should be doing. What are the terminating conditions? When we reach the terminating condition, what do we need to record (e.g. did we get a new best result, etc.)?
Hint3
Spoiler Alert
Below is a C++ implementation to give you some ideas, so stop reading here if you want to work on it some more by yourself.
int bestDiff = 999999999;
int N;
vector< int > cur_items;
int cur_tot = 0;
int items[] = {6,1,2,5};
vector< int > best_items;
int max_waste;
void go(int at) {
if (cur_tot > max_waste)
// we've exceeded max_waste, so no need to continue
return;
if (at == N) {
// we're at the end of the input, see if we got a better result and
// if so, record it
if (max_waste - cur_tot < bestDiff) {
bestDiff = max_waste - cur_tot;
best_items = cur_items;
}
return;
}
// use this item
cur_items.push_back(items[at]);
cur_tot += items[at];
go(at+1);
// here's the backtracking part
cur_tot -= items[at];
cur_items.pop_back();
// don't use this item
go(at+1);
}
int main() {
// 4 items in the set, so N is 4
N=4;
// maximum waste we can eliminiate is 10
max_waste = 10;
// call the backtracking algo
go(0);
// output the results
cout<<"bestDiff = "<<bestDiff<<endl;
cout<<"The items are:"<<endl;
for (int i = 0; i < best_items.size(); ++i) {
cout<<best_items[i]<<" ";
}
return 0;
}

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