java.lang.StringIndexOutOfBoundsException on repeating decimal to fraction calculator - java

I'm new to java and I'm trying to code a method that takes a repeating decimal and turns it into a fraction. It takes input like (double decimal without repeating, int number of trailing digits to repeat) i.e. (0.3,1) would be 0.3333.... and (1.583,2) would be 1.5838383....
I am getting this error and I can't seem to find out what the problem is. The current input is (10.3,1)
Exception in thread "main" java.lang.StringIndexOutOfBoundsException: String index out of range: -1
at java.lang.String.substring(String.java:1967)
at Fraction.<init>(Fraction.java:44)
at Main.main(Main.java:12)
exited with non-zero status
Heres my code:
public Fraction(double t, int repeating)
{
double decRight = t, decLeft = t;
String rStr = "0000000000000000000" + String.valueOf(decRight);
String lStr = "0000000000000000000" + String.valueOf(decLeft);
int count1 = 0, count2 = 0, rDecIndex = rStr.indexOf("."), lDecIndex = lStr.indexOf(".");
while(!lStr.substring(lDecIndex - repeating,lDecIndex).replace("\\.","").equals(lStr)) //this is line 44, the problem area
{
decLeft *= 10;
count1++;
lStr = "0000000000000000000" + String.valueOf(decLeft);
lDecIndex = lStr.indexOf(".");
}
while(!rStr.substring(rDecIndex,repeating).replace("\\.","").equals(rStr))
{
decRight*= 10;
count2++;
rStr = "0000000000000000000" + String.valueOf(decRight);
rDecIndex = rStr.indexOf(".");
}
top = (int)(decLeft - decRight);
bot = (int)(Math.pow(10,count1) - Math.pow(10,count2));
reduce();
}
The error is in the substring.

Based on the comment, you want an integer with the repeating decimal in it and an integer with what is before the repeating part.
I think you've gone about this the hard way rather than just using substring to get the parts of the string that you want.
/**
* Code By Loren CC-BY
*/
public class test
{
public static void fraction(String t, int repeating)
{
int bot = 0;
for (int i = 0; i < repeating; i++) {
bot *= 10;
bot += 9;
}
String dString = t;
// Get the repeating part of the string as an int
int repeat = Integer.valueOf(dString.substring(dString.length()-repeating));
// Get the string from in front of the repeating number
String front = dString.substring(0, dString.length()-repeating);
// Convert it to a double
double before = Double.valueOf(front);
// Debugging information
System.out.println("Before: "+ front+" " +before+" "+dString.substring(dString.length()-repeating));
// Turn the before string into an int and compute the denominator such that 1.5 could become 15/10
int count = 0;
while (Math.abs(Math.round(before) - before) > 0.000001) {
before *= 10;
count++;
}
// Print debugging information
System.out.println(count);
// Compute the top of the combined fraction
int top = ((int)before)*bot+repeat;
bot = (int)Math.pow(10,count) * bot;
System.out.println(top+" "+bot);
// TODO: Reduce fraction
}
public static void main(String[] args) {
fraction("0.3",1);
fraction("1.580",2);
fraction("0.34",1);
fraction("0.34",2);
}
}
Note: You can't pass in the double 1.580 because that as a string is 1.58 not 1.580 as the 0 is omitted which messes up the function.

For Converting repeating decimals to fractions could you try the following:
import java.math.BigInteger;
public class ConvertRepeatingNumbersToFraction {
public static void main(String[] args) {
convertToFraction("0.3",1);
convertToFraction("1.580",2);
convertToFraction("0.16",1);
convertToFraction("0.34",2);
convertToFraction("0.42",2);
convertToFraction("0.34",1);
}
private static void convertToFraction(String x, int numOfRepeatingDigits) {
int denominator = 0;
for (int i = 0; i < numOfRepeatingDigits; i++) {
denominator = denominator * 10 + 9;
}
int repeatingNumber = Integer.valueOf(x.substring(x.length() - numOfRepeatingDigits));
double numerator = Double.valueOf(x.substring(0, x.length() - numOfRepeatingDigits));
int count = 0;
if (numerator % 1 != 0) {
numerator = numerator * 10;
count++;
}
numerator = numerator * denominator + repeatingNumber;
denominator = (int) Math.pow(10, count) * denominator;
int[] fraction = reduce((int)numerator, denominator);
System.out.println(fraction[0] + "/" + fraction[1]);
}
private static int[] reduce(int num, int den) {
// common divisor
int commonDivisor = BigInteger.valueOf(num).gcd(BigInteger.valueOf(den)).intValue();
return new int[]{ num / commonDivisor, den / commonDivisor };
}
}
I have checked the test numbers on http://onlinecalculators.brainmeasures.com/Numbers/RecurringDecimalNumbertoFraction.aspx and the result are the same.
Hope that helps :)

Related

how to convert decimal value in to a Fraction value?

excepted output : 1/4,1/2,3/4,1,5/4,3/2
but my output is coming as in the decimal form . Please help how to print in the form of fraction only.
import java.util.*;
public class Hello {
public static void main(String[] args) {
//Your Code Here
Scanner s=new Scanner(System.in);
int n=s.nextInt();
double d=1/4.0,sum=0;
for(int i=0;i<n;i++) {
sum+=d;
System.out.print(sum+" ");
}
}}
take input in form of string so it will take input in required format and split it by "/" i.e someString.spit("/").
after that make one for loop and take two number and in two different variable store it.
and then take division for both and print it by using "/" in between them.
public class NewClass {
public static void main(String[] args) {
System.out.println(convertype(0.75));
}
public static String convertype(double decimal){
int digitsAfterPoint = String.valueOf(decimal).length() - String.valueOf(decimal).indexOf('.')+1; // get the count of digits after the point // for example 0.75 has two digits
BigInteger numerator = BigInteger.valueOf((long)(decimal*Math.pow(10, digitsAfterPoint))); // multiply 0.75 with 10^2 to get 75
BigInteger denominator = BigInteger.valueOf((long)(Math.pow(10, digitsAfterPoint))); // 10^2 is your denominator
int gcd = numerator.gcd(denominator).intValue(); // calculate the greatest common divisor of numerator and denominator
if (gcd > 1 ){ // gcd(75,100) = 25
return String.valueOf(numerator.intValue()/gcd) +" / " + String.valueOf(denominator.intValue()/gcd); // return 75/25 / 100/25 = 3/4
}
else{
return String.valueOf(numerator) +" / " + String.valueOf(denominator); // if gcd = 1 which means nothing to simplify just return numerator / denominator
}
}
}
Wrote a method where you can convert double numbers to fraction. Use this to convert it and print as below,
import java.util.Scanner;
public class test {
public static void main(String[] args) {
Scanner s=new Scanner(System.in);
int n=s.nextInt();
double d=1/4.0,sum=0;
for(int i=0;i<n;i++) {
sum+=d;
System.out.print(toFraction(sum)+" ");
}
}
static String toFraction(double x) {
int w = (int) x;
int n = (int) (x * 64) % 64;
int a = n & -n;
return n == 0 ? w+"" : (w * (64 / a) + (n / a)) + "/" + 64 / a;
}
}

Output of converting binary to Decimal not expected?

Given a binary number as input convert it into base 10 (decimal system). Note that to convert a number 100111 from binary to decimal, the value is 1*2^5 + 0*2^4 + 0*2^3 + 1*2^2 + 1*2^1+ 1*2^0. Also note that 5 here is the length of the binary number.
MyApproach
To convert to decimal,I first converted the code from String to decimal.Then I solved the number till it is greater than 0 and solved the expression.
For example for number 10=0*2^0+1*2^1 and solved the expression in the code.
I am getting a wrong Ans on the last test case.
Can anyone guide me what is wrong in my code.?
Below is my code:
public int convert(String binary)
{
int p=0;
int decimal=0;
int number=Integer.parseInt(binary);
while(number>0)
{
int temp = number%10;
decimal += temp*Math.pow(2, p);
number = number/10;
p++;
//write your code here
}
return decimal;
}
}
Parameters ActualOutput ExpectedOutput
'10011010010' null 1234
Max value of integer is (2^31-1) and the value that you are parsing to int from string in greater than that. Hence try to use Long in place of int ..
below code is working fine.. please check it below..
public static int convert(String binary)
{
int p=0;
int decimal=0;
long number=Long.parseLong(binary);
while(number>0)
{
long temp = number%10;
decimal += temp*Math.pow(2, p);
number = number/10;
p++;
//write your code here
}
return decimal;
}
Simpler, without pow :
int s=binary.length();
for (int pos=0;pos<s;pos++)
{
char c=binary.charAt(pos);
if (c=='1') decimal+=1;
if (pos<s-1) decimal*=2;
}
Why convert it to decimal first? This is quite easy:
public static void main( String[] args ) {
String str = "10011010010";
int len = str.length();
long mult = 1;
long val = 0;
for (int i = len - 1; i >= 0; i--) {
if ( str.charAt( i ) == '1' ) {
val += mult;
}
mult *= 2;
}
System.out.println( val );
}
Your input is above the limit of int in Java, which is 2,147,483,647.
Even if if you change it to long, you won't be able to convert values above 1000000000000000000 (which is equal to 262144 in decimal). Best solution is to calculate by taking character by character without converting the whole string.
So, try the following code,
public static long convert(String binary) {
long pow = 1, decimal = 0;
for (int i = (binary.length() - 1); i >= 0; i--) {
if (binary.charAt(i) == '1') {
decimal += pow;
}
pow *= 2;
}
return decimal;
}

How to split an Integer into an Array using Java?

I apologise if this has already been asked before, but I was unable to find a conclusive answer after some extensive searching, so I thought I would ask here. I am a beginner to Java (to coding, in general) and was tasked with writing a program that takes a user-inputted 3 digit number, and adds those three digits.
Note: I cannot use loops for this task, and the three digits must all be inputted at once.
String myInput;
myInput =
JOptionPane.showInputDialog(null,"Hello, and welcome to the ThreeDigit program. "
+ "\nPlease input a three digit number below. \nThreeDigit will add those three numbers and display their sum.");
int threedigitinput;
threedigitinput = Integer.parseInt(myInput);
There are a number of ways, one of which would be...
String ss[] = "123".split("");
int i =
Integer.parseInt(ss[0]) +
Integer.parseInt(ss[1]) +
Integer.parseInt(ss[2]);
System.out.println(i);
another would be...
String s = "123";
int i =
Character.getNumericValue(s.charAt(0)) +
Character.getNumericValue(s.charAt(1)) +
Character.getNumericValue(s.charAt(2));
System.out.println(i);
and still another would be...
String s = "123";
int i =
s.charAt(0) +
s.charAt(1) +
s.charAt(2) -
(3 * 48);
System.out.println(i);
BUT hard coding for 3 numbers isn't very useful beyond this simple case. So how about recursion??
public static int addDigis(String s) {
if(s.length() == 1)
return s.charAt(0) - 48;
return s.charAt(0) - 48 + addDigis(s.substring(1, s.length()));
}
Output for each example: 6
you can use integer math to come up with the three numbers seperately
int first = threedigitinput / 100;
int second = (threedigitinput % 100) / 10;
int third = threedigitinput % 10;
If I understand your question, you could use Character.digit(char,int) to get the value for each character with something like -
int value = Character.digit(myInput.charAt(0), 10)
+ Character.digit(myInput.charAt(1), 10)
+ Character.digit(myInput.charAt(2), 10);
Classic example of using divmod:
public class SumIntegerDigits {
public static void main(String[] args) {
System.out.println(sumOfDigitsSimple(248)); // 14
System.out.println(sumOfDigitsIterative(248)); // 14
System.out.println(sumOfDigitsRecursive(248)); // 14
}
// Simple, non-loop solution
public static final int sumOfDigitsSimple(int x) {
int y = x % 1000; // Make sure that the value has no more than 3 digits.
return divmod(y,100)[0]+divmod(divmod(y,100)[1],10)[0]+divmod(y,10)[1];
}
// Iterative Solution
public static final int sumOfDigitsIterative(int x) {
int sum = 0;
while (x > 0) {
int[] y = divmod(x, 10);
sum += y[1];
x = y[0];
}
return sum;
}
// Tail-recursive Solution
public static final int sumOfDigitsRecursive(int x) {
if (x <= 0) {
return 0;
}
int[] y = divmod(x, 10);
return sumOfDigitsRecursive(y[0]) + y[1];
}
public static final int[] divmod(final int x, int m) {
return new int[] { (x / m), (x % m) };
}
}

Double to fraction in Java

So what I'm trying to do is convert double to rational number. I check how many digits there is after decimal point and I want to save the number 123.456 as 123456 / 1000, for example.
public Rational(double d){
String s = String.valueOf(d);
int digitsDec = s.length() - 1 - s.indexOf('.');
for(int i = 0; i < digitsDec; i++){
d *= 10;
}
System.out.println((int)d); //checking purposes
}
However, for the number 123.456 I get a round off error and the result is 123455. I guess it'd be possible to fix this with BigDecimal but I can't get it to work. Also, having calculated what rational number it would be, I would like to call another constructor with parameters (int numerator, int denominator) but I can't obviously call the constructor in the line where println is now. How should I do this?
For the first part of the question, Java is storing .6 as .5999999 (repeating). See this output:
(after first multiply): d=1234.56
(after second multiply): d=12345.599999999999
(after third multiply): d=123455.99999999999
One fix is to use d = Math.round(d) immediately after your loop finishes.
public class Rational {
private int num, denom;
public Rational(double d) {
String s = String.valueOf(d);
int digitsDec = s.length() - 1 - s.indexOf('.');
int denom = 1;
for(int i = 0; i < digitsDec; i++){
d *= 10;
denom *= 10;
}
int num = (int) Math.round(d);
this.num = num; this.denom = denom;
}
public Rational(int num, int denom) {
this.num = num; this.denom = denom;
}
public String toString() {
return String.valueOf(num) + "/" + String.valueOf(denom);
}
public static void main(String[] args) {
System.out.println(new Rational(123.456));
}
}
It works - try it.
For the second part of your question...
In order to call the second constructor from the first, you can use the "this" keyword
this(num, denom)
But it has to be the very first line in the constructor... which doesn't make sense here (we have to do some calculations first). So I wouldn't bother trying to do that.
This code may be overkill for you, but it deals with the rounding error that you're experiencing, and it also takes care of repeating decimals (4.99999999999999 turns into 5, and 0.33333333333333333333 turns into 1/3).
public static Rational toRational(double number){
return toRational(number, 8);
}
public static Rational toRational(double number, int largestRightOfDecimal){
long sign = 1;
if(number < 0){
number = -number;
sign = -1;
}
final long SECOND_MULTIPLIER_MAX = (long)Math.pow(10, largestRightOfDecimal - 1);
final long FIRST_MULTIPLIER_MAX = SECOND_MULTIPLIER_MAX * 10L;
final double ERROR = Math.pow(10, -largestRightOfDecimal - 1);
long firstMultiplier = 1;
long secondMultiplier = 1;
boolean notIntOrIrrational = false;
long truncatedNumber = (long)number;
Rational rationalNumber = new Rational((long)(sign * number * FIRST_MULTIPLIER_MAX), FIRST_MULTIPLIER_MAX);
double error = number - truncatedNumber;
while( (error >= ERROR) && (firstMultiplier <= FIRST_MULTIPLIER_MAX)){
secondMultiplier = 1;
firstMultiplier *= 10;
while( (secondMultiplier <= SECOND_MULTIPLIER_MAX) && (secondMultiplier < firstMultiplier) ){
double difference = (number * firstMultiplier) - (number * secondMultiplier);
truncatedNumber = (long)difference;
error = difference - truncatedNumber;
if(error < ERROR){
notIntOrIrrational = true;
break;
}
secondMultiplier *= 10;
}
}
if(notIntOrIrrational){
rationalNumber = new Rational(sign * truncatedNumber, firstMultiplier - secondMultiplier);
}
return rationalNumber;
}
This provides the following results (results from test cases are shown as comments):
Rational.toRational(110.0/3.0); // 110/3
Rational.toRational(11.0/1000.0); // 11/1000
Rational.toRational(17357.0/33300.0); // 17357/33300
Rational.toRational(215.0/21.0); // 215/21
Rational.toRational(0.123123123123123123123123); // 41/333
Rational.toRational(145731.0/27100.0); // 145731/27100
Rational.toRational(Math.PI); // 62831853/20000000
Rational.toRational(62.0/63.0); // 62/63
Rational.toRational(24.0/25.0); // 24/25
Rational.toRational(-24.0/25.0); //-24/25
Rational.toRational(-0.25333333333333333333333); // -19/75
Rational.toRational(-4.9999999999999999999999); // -5
Rational.toRational(4.9999999999999999999999); // 5
Rational.toRational(123.456); // 15432/125
It's not elegant, however, I believe this does what you're asking.
double a = 123.456;
String aString = Double.toString(a);
String[] fraction = aString.split("\\.");
int denominator = (int)Math.pow(10, fraction[1].length());
int numerator = Integer.parseInt(fraction[0] + "" + fraction[1]);
System.out.println(numerator + "/" + denominator);
Here, d=123.456 then num=123456, j=1000.
/**
* This method calculates a rational number from a double.
* The denominator will always be a multiple of 10.
*
* #param d the double to calculate the fraction from.
* #return the result as Pair of <numerator , denominator>.
*/
private static Pair<Integer,Integer> calculateRational(double d){
int j=1, num;
do{
j=j*10;
}while((d *j)%10!=0);
j=j/10;
num=(int)(d*j);
return new Pair<>(num,j);
}
Here're some tests:
#Test
public void testCalculateRational() {
Assert.assertEquals(new Pair<>(124567, 1000), calculateRational(124.567));
Assert.assertEquals(new Pair<>(12456, 100), calculateRational(124.56));
Assert.assertEquals(new Pair<>(56, 100), calculateRational(0.56));
}
Try
for(int i = 0; i <= digitsDec; i++){
}

Counting trailing zeros of numbers resulted from factorial

I'm trying to count trailing zeros of numbers that are resulted from factorials (meaning that the numbers get quite large). Following code takes a number, compute the factorial of the number, and count the trailing zeros. However, when the number is about as large as 25!, numZeros don't work.
public static void main(String[] args) {
BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
double fact;
int answer;
try {
int number = Integer.parseInt(br.readLine());
fact = factorial(number);
answer = numZeros(fact);
}
catch (NumberFormatException e) {
e.printStackTrace();
} catch (IOException e) {
e.printStackTrace();
}
}
public static double factorial (int num) {
double total = 1;
for (int i = 1; i <= num; i++) {
total *= i;
}
return total;
}
public static int numZeros (double num) {
int count = 0;
int last = 0;
while (last == 0) {
last = (int) (num % 10);
num = num / 10;
count++;
}
return count-1;
}
I am not worrying about the efficiency of this code, and I know that there are multiple ways to make the efficiency of this code BETTER. What I'm trying to figure out is why the counting trailing zeros of numbers that are greater than 25! is not working.
Any ideas?
Your task is not to compute the factorial but the number of zeroes. A good solution uses the formula from http://en.wikipedia.org/wiki/Trailing_zeros (which you can try to prove)
def zeroes(n):
i = 1
result = 0
while n >= i:
i *= 5
result += n/i # (taking floor, just like Python or Java does)
return result
Hope you can translate this to Java. This simply computes [n / 5] + [n / 25] + [n / 125] + [n / 625] + ... and stops when the divisor gets larger than n.
DON'T use BigIntegers. This is a bozosort. Such solutions require seconds of time for large numbers.
You only really need to know how many 2s and 5s there are in the product. If you're counting trailing zeroes, then you're actually counting "How many times does ten divide this number?". if you represent n! as q*(2^a)*(5^b) where q is not divisible by 2 or 5. Then just taking the minimum of a and b in the second expression will give you how many times 10 divides the number. Actually doing the multiplication is overkill.
Edit: Counting the twos is also overkill, so you only really need the fives.
And for some python, I think this should work:
def countFives(n):
fives = 0
m = 5
while m <= n:
fives = fives + (n/m)
m = m*5
return fives
The double type has limited precision, so if the numbers you are working with get too big the double will be only an approximation. To work around this you can use something like BigInteger to make it work for arbitrarily large integers.
You can use a DecimalFormat to format big numbers. If you format your number this way you get the number in scientific notation then every number will be like 1.4567E7 this will make your work much easier. Because the number after the E - the number of characters behind the . are the number of trailing zeros I think.
I don't know if this is the exact pattern needed. You can see how to form the patterns here
DecimalFormat formater = new DecimalFormat("0.###E0");
My 2 cents: avoid to work with double since they are error-prone. A better datatype in this case is BigInteger, and here there is a small method that will help you:
public class CountTrailingZeroes {
public int countTrailingZeroes(double number) {
return countTrailingZeroes(String.format("%.0f", number));
}
public int countTrailingZeroes(String number) {
int c = 0;
int i = number.length() - 1;
while (number.charAt(i) == '0') {
i--;
c++;
}
return c;
}
#Test
public void $128() {
assertEquals(0, countTrailingZeroes("128"));
}
#Test
public void $120() {
assertEquals(1, countTrailingZeroes("120"));
}
#Test
public void $1200() {
assertEquals(2, countTrailingZeroes("1200"));
}
#Test
public void $12000() {
assertEquals(3, countTrailingZeroes("12000"));
}
#Test
public void $120000() {
assertEquals(4, countTrailingZeroes("120000"));
}
#Test
public void $102350000() {
assertEquals(4, countTrailingZeroes("102350000"));
}
#Test
public void $1023500000() {
assertEquals(5, countTrailingZeroes(1023500000.0));
}
}
This is how I made it, but with bigger > 25 factorial the long capacity is not enough and should be used the class Biginteger, with witch I am not familiar yet:)
public static void main(String[] args) {
// TODO Auto-generated method stub
Scanner in = new Scanner(System.in);
System.out.print("Please enter a number : ");
long number = in.nextLong();
long numFactorial = 1;
for(long i = 1; i <= number; i++) {
numFactorial *= i;
}
long result = 0;
int divider = 5;
for( divider =5; (numFactorial % divider) == 0; divider*=5) {
result += 1;
}
System.out.println("Factorial of n is: " + numFactorial);
System.out.println("The number contains " + result + " zeroes at its end.");
in.close();
}
}
The best with logarithmic time complexity is the following:
public int trailingZeroes(int n) {
if (n < 0)
return -1;
int count = 0;
for (long i = 5; n / i >= 1; i *= 5) {
count += n / i;
}
return count;
}
shamelessly copied from http://www.programcreek.com/2014/04/leetcode-factorial-trailing-zeroes-java/
I had the same issue to solve in Javascript, and I solved it like:
var number = 1000010000;
var str = (number + '').split(''); //convert to string
var i = str.length - 1; // start from the right side of the array
var count = 0; //var where to leave result
for (;i>0 && str[i] === '0';i--){
count++;
}
console.log(count) // console shows 4
This solution gives you the number of trailing zeros.
var number = 1000010000;
var str = (number + '').split(''); //convert to string
var i = str.length - 1; // start from the right side of the array
var count = 0; //var where to leave result
for (;i>0 && str[i] === '0';i--){
count++;
}
console.log(count)
Java's doubles max out at a bit over 9 * 10 ^ 18 where as 25! is 1.5 * 10 ^ 25. If you want to be able to have factorials that high you might want to use BigInteger (similar to BigDecimal but doesn't do decimals).
I wrote this up real quick, I think it solves your problem accurately. I used the BigInteger class to avoid that cast from double to integer, which could be causing you problems. I tested it on several large numbers over 25, such as 101, which accurately returned 24 zeros.
The idea behind the method is that if you take 25! then the first calculation is 25 * 24 = 600, so you can knock two zeros off immediately and then do 6 * 23 = 138. So it calculates the factorial removing zeros as it goes.
public static int count(int number) {
final BigInteger zero = new BigInteger("0");
final BigInteger ten = new BigInteger("10");
int zeroCount = 0;
BigInteger mult = new BigInteger("1");
while (number > 0) {
mult = mult.multiply(new BigInteger(Integer.toString(number)));
while (mult.mod(ten).compareTo(zero) == 0){
mult = mult.divide(ten);
zeroCount += 1;
}
number -= 1;
}
return zeroCount;
}
Since you said you don't care about run time at all (not that my first was particularly efficient, just slightly more so) this one just does the factorial and then counts the zeros, so it's cenceptually simpler:
public static BigInteger factorial(int number) {
BigInteger ans = new BigInteger("1");
while (number > 0) {
ans = ans.multiply(new BigInteger(Integer.toString(number)));
number -= 1;
}
return ans;
}
public static int countZeros(int number) {
final BigInteger zero = new BigInteger("0");
final BigInteger ten = new BigInteger("10");
BigInteger fact = factorial(number);
int zeroCount = 0;
while (fact.mod(ten).compareTo(zero) == 0){
fact = fact.divide(ten);
zeroCount += 1;
}
}

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