Efficiently find length of longest Increasing Subsequence
Here given code implementation process.
// C Program
// Efficiently Find longest Increasing Subsequence
#include <stdio.h>
// Print the elements of given array
void printElement(int arr[], int n)
{
for (int i = 0; i < n; ++i)
{
printf(" %d", arr[i]);
}
}
void longestSubsequences(int arr[], int n)
{
if (n <= 0)
{
return;
}
int length = 1;
int mid = 0;
int low = 0;
int high = 0;
// Auxiliary array
int tail[n];
// Set intial value
for (int i = 0; i < n; ++i)
{
tail[i] = 0;
}
for (int i = 0; i < n; ++i)
{
if (arr[i] < arr[tail[0]])
{
tail[0] = i;
}
else if (arr[i] > arr[tail[length - 1]])
{
tail[length] = i;
length++;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + (high - low) / 2;
if (arr[tail[mid]] >= arr[i])
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail[high] = i;
}
}
printf("\n Array : ");
// Display given array
printElement(arr, n);
// Display calculated length
printf("\n Length : %d\n ", length);
}
int main(int argc, char
const *argv[])
{
// Define array of integer elements
int arr1[] = {
8 , 4 , 7 , 5 , 1 , 9 , 3
};
int arr2[] = {
9 , 10 , 3 , 4 , 8 , 7 , 10
};
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
int n = sizeof(arr1) / sizeof(arr1[0]);
longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = sizeof(arr2) / sizeof(arr2[0]);
longestSubsequences(arr2, n);
return 0;
}Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
// Java program for
// Efficiently find length of longest Increasing Subsequence
public class Subsequence
{
// Print the elements of given array
public void printElement(int[] arr, int n)
{
for (int i = 0; i < n; ++i)
{
System.out.print(" " + arr[i]);
}
}
public void longestSubsequences(int[] arr, int n)
{
if (n <= 0)
{
return;
}
int length = 1;
int mid = 0;
int low = 0;
int high = 0;
// Auxiliary array
int[] tail = new int[n];
// Set intial value
for (int i = 0; i < n; ++i)
{
tail[i] = 0;
}
for (int i = 0; i < n; ++i)
{
if (arr[i] < arr[tail[0]])
{
tail[0] = i;
}
else if (arr[i] > arr[tail[length - 1]])
{
tail[length] = i;
length++;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + (high - low) / 2;
if (arr[tail[mid]] >= arr[i])
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail[high] = i;
}
}
System.out.print("\n Array : ");
// Display given array
printElement(arr, n);
System.out.print("\n Length : " + length + "\n ");
}
public static void main(String[] args)
{
Subsequence task = new Subsequence();
// Define array of integer elements
int[] arr1 = {
8 , 4 , 7 , 5 , 1 , 9 , 3
};
int[] arr2 = {
9 , 10 , 3 , 4 , 8 , 7 , 10
};
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
int n = arr1.length;
task.longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = arr2.length;
task.longestSubsequences(arr2, n);
}
}Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
// Include header file
#include <iostream>
using namespace std;
// C++ program for
// Efficiently find length of longest Increasing Subsequence
class Subsequence
{
public:
// Print the elements of given array
void printElement(int arr[], int n)
{
for (int i = 0; i < n; ++i)
{
cout << " " << arr[i];
}
}
void longestSubsequences(int arr[], int n)
{
if (n <= 0)
{
return;
}
int length = 1;
int mid = 0;
int low = 0;
int high = 0;
// Auxiliary array
int tail[n];
// Set intial value
for (int i = 0; i < n; ++i)
{
tail[i] = 0;
}
for (int i = 0; i < n; ++i)
{
if (arr[i] < arr[tail[0]])
{
tail[0] = i;
}
else if (arr[i] > arr[tail[length - 1]])
{
tail[length] = i;
length++;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + (high - low) / 2;
if (arr[tail[mid]] >= arr[i])
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail[high] = i;
}
}
cout << "\n Array : ";
// Display given array
this->printElement(arr, n);
cout << "\n Length : " << length << "\n ";
}
};
int main()
{
Subsequence *task = new Subsequence();
// Define array of integer elements
int arr1[] = {
8 , 4 , 7 , 5 , 1 , 9 , 3
};
int arr2[] = {
9 , 10 , 3 , 4 , 8 , 7 , 10
};
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
int n = sizeof(arr1) / sizeof(arr1[0]);
task->longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = sizeof(arr2) / sizeof(arr2[0]);
task->longestSubsequences(arr2, n);
return 0;
}Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
// Include namespace system
using System;
// Csharp program for
// Efficiently find length of longest Increasing Subsequence
public class Subsequence
{
// Print the elements of given array
public void printElement(int[] arr, int n)
{
for (int i = 0; i < n; ++i)
{
Console.Write(" " + arr[i]);
}
}
public void longestSubsequences(int[] arr, int n)
{
if (n <= 0)
{
return;
}
int length = 1;
int mid = 0;
int low = 0;
int high = 0;
// Auxiliary array
int[] tail = new int[n];
// Set intial value
for (int i = 0; i < n; ++i)
{
tail[i] = 0;
}
for (int i = 0; i < n; ++i)
{
if (arr[i] < arr[tail[0]])
{
tail[0] = i;
}
else if (arr[i] > arr[tail[length - 1]])
{
tail[length] = i;
length++;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + (high - low) / 2;
if (arr[tail[mid]] >= arr[i])
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail[high] = i;
}
}
Console.Write("\n Array : ");
// Display given array
this.printElement(arr, n);
Console.Write("\n Length : " + length + "\n ");
}
public static void Main(String[] args)
{
Subsequence task = new Subsequence();
// Define array of integer elements
int[] arr1 = {
8 , 4 , 7 , 5 , 1 , 9 , 3
};
int[] arr2 = {
9 , 10 , 3 , 4 , 8 , 7 , 10
};
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
int n = arr1.Length;
task.longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = arr2.Length;
task.longestSubsequences(arr2, n);
}
}Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
package main
import "fmt"
// Go program for
// Efficiently find length of longest Increasing Subsequence
type Subsequence struct {}
func getSubsequence() * Subsequence {
var me *Subsequence = &Subsequence {}
return me
}
// Print the elements of given array
func(this Subsequence) printElement(arr[] int, n int) {
for i := 0 ; i < n ; i++ {
fmt.Print(" ", arr[i])
}
}
func(this Subsequence) longestSubsequences(arr[] int, n int) {
if n <= 0 {
return
}
var length int = 1
var mid int = 0
var low int = 0
var high int = 0
// Auxiliary array
var tail = make([] int, n)
// Set intial value
for i := 0 ; i < n ; i++ {
tail[i] = 0
}
for i := 0 ; i < n ; i++ {
if arr[i] < arr[tail[0]] {
tail[0] = i
} else if arr[i] > arr[tail[length - 1]] {
tail[length] = i
length++
} else {
low = -1
high = length - 1
// Find element position in tail array
for (high - low > 1) {
mid = low + (high - low) / 2
if arr[tail[mid]] >= arr[i] {
high = mid
} else {
low = mid
}
}
// Set new position
tail[high] = i
}
}
fmt.Print("\n Array : ")
// Display given array
this.printElement(arr, n)
fmt.Print("\n Length : ", length, "\n ")
}
func main() {
var task * Subsequence = getSubsequence()
// Define array of integer elements
var arr1 = [] int {
8,
4,
7,
5,
1,
9,
3,
}
var arr2 = [] int {
9,
10,
3,
4,
8,
7,
10,
}
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
var n int = len(arr1)
task.longestSubsequences(arr1, n)
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = len(arr2)
task.longestSubsequences(arr2, n)
}Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
<?php
// Php program for
// Efficiently find length of longest Increasing Subsequence
class Subsequence
{
// Print the elements of given array
public function printElement($arr, $n)
{
for ($i = 0; $i < $n; ++$i)
{
echo(" ".$arr[$i]);
}
}
public function longestSubsequences($arr, $n)
{
if ($n <= 0)
{
return;
}
$length = 1;
$mid = 0;
$low = 0;
$high = 0;
// Auxiliary array
// Set intial value
$tail = array_fill(0, $n, 0);
for ($i = 0; $i < $n; ++$i)
{
if ($arr[$i] < $arr[$tail[0]])
{
$tail[0] = $i;
}
else if ($arr[$i] > $arr[$tail[$length - 1]])
{
$tail[$length] = $i;
$length++;
}
else
{
$low = -1;
$high = $length - 1;
// Find element position in tail array
while ($high - $low > 1)
{
$mid = $low + (int)(($high - $low) / 2);
if ($arr[$tail[$mid]] >= $arr[$i])
{
$high = $mid;
}
else
{
$low = $mid;
}
}
// Set new position
$tail[$high] = $i;
}
}
echo("\n Array : ");
// Display given array
$this->printElement($arr, $n);
echo("\n Length : ".$length."\n ");
}
}
function main()
{
$task = new Subsequence();
// Define array of integer elements
$arr1 = array(8, 4, 7, 5, 1, 9, 3);
$arr2 = array(9, 10, 3, 4, 8, 7, 10);
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
$n = count($arr1);
$task->longestSubsequences($arr1, $n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
$n = count($arr2);
$task->longestSubsequences($arr2, $n);
}
main();Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
// Node JS program for
// Efficiently find length of longest Increasing Subsequence
class Subsequence
{
// Print the elements of given array
printElement(arr, n)
{
for (var i = 0; i < n; ++i)
{
process.stdout.write(" " + arr[i]);
}
}
longestSubsequences(arr, n)
{
if (n <= 0)
{
return;
}
var length = 1;
var mid = 0;
var low = 0;
var high = 0;
// Auxiliary array
// Set intial value
var tail = Array(n).fill(0);
for (var i = 0; i < n; ++i)
{
if (arr[i] < arr[tail[0]])
{
tail[0] = i;
}
else if (arr[i] > arr[tail[length - 1]])
{
tail[length] = i;
length++;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + parseInt((high - low) / 2);
if (arr[tail[mid]] >= arr[i])
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail[high] = i;
}
}
process.stdout.write("\n Array : ");
// Display given array
this.printElement(arr, n);
process.stdout.write("\n Length : " + length + "\n ");
}
}
function main()
{
var task = new Subsequence();
// Define array of integer elements
var arr1 = [8, 4, 7, 5, 1, 9, 3];
var arr2 = [9, 10, 3, 4, 8, 7, 10];
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
var n = arr1.length;
task.longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = arr2.length;
task.longestSubsequences(arr2, n);
}
main();Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
# Python 3 program for
# Efficiently find length of longest Increasing Subsequence
class Subsequence :
# Print the elements of given list
def printElement(self, arr, n) :
i = 0
while (i < n) :
print(" ", arr[i], end = "")
i += 1
def longestSubsequences(self, arr, n) :
if (n <= 0) :
return
length = 1
mid = 0
low = 0
high = 0
# Auxiliary list
# Set intial value
tail = [0] * (n)
i = 0
while (i < n) :
if (arr[i] < arr[tail[0]]) :
tail[0] = i
elif (arr[i] > arr[tail[length - 1]]) :
tail[length] = i
length += 1
else :
low = -1
high = length - 1
# Find element position in tail list
while (high - low > 1) :
mid = low + int((high - low) / 2)
if (arr[tail[mid]] >= arr[i]) :
high = mid
else :
low = mid
# Set new position
tail[high] = i
i += 1
print("\n Array : ", end = "")
# Display given list
self.printElement(arr, n)
print("\n Length : ", length ,"\n ", end = "")
def main() :
task = Subsequence()
# Define list of integer elements
arr1 = [8, 4, 7, 5, 1, 9, 3]
arr2 = [9, 10, 3, 4, 8, 7, 10]
# Test Case A
# [ 8 , 4 , 7 , 5 , 1 , 9, 3]
# length of Longest increasing subsequence 3
# (4, 5, 9)
# Result = 3
n = len(arr1)
task.longestSubsequences(arr1, n)
# Test Case B
# [ 9, 10, 3, 4, 8, 7, 10]
# length of Longest increasing subsequence 4
# (3, 4, 8, 10), (3, 4, 7, 10)
# Result = 4
n = len(arr2)
task.longestSubsequences(arr2, n)
if __name__ == "__main__": main()Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
# Ruby program for
# Efficiently find length of longest Increasing Subsequence
class Subsequence
# Print the elements of given array
def printElement(arr, n)
i = 0
while (i < n)
print(" ", arr[i])
i += 1
end
end
def longestSubsequences(arr, n)
if (n <= 0)
return
end
length = 1
mid = 0
low = 0
high = 0
# Auxiliary array
# Set intial value
tail = Array.new(n) {0}
i = 0
while (i < n)
if (arr[i] < arr[tail[0]])
tail[0] = i
elsif (arr[i] > arr[tail[length - 1]])
tail[length] = i
length += 1
else
low = -1
high = length - 1
# Find element position in tail array
while (high - low > 1)
mid = low + (high - low) / 2
if (arr[tail[mid]] >= arr[i])
high = mid
else
low = mid
end
end
# Set new position
tail[high] = i
end
i += 1
end
print("\n Array : ")
# Display given array
self.printElement(arr, n)
print("\n Length : ", length ,"\n ")
end
end
def main()
task = Subsequence.new()
# Define array of integer elements
arr1 = [8, 4, 7, 5, 1, 9, 3]
arr2 = [9, 10, 3, 4, 8, 7, 10]
# Test Case A
# [ 8 , 4 , 7 , 5 , 1 , 9, 3]
# length of Longest increasing subsequence 3
# (4, 5, 9)
# Result = 3
n = arr1.length
task.longestSubsequences(arr1, n)
# Test Case B
# [ 9, 10, 3, 4, 8, 7, 10]
# length of Longest increasing subsequence 4
# (3, 4, 8, 10), (3, 4, 7, 10)
# Result = 4
n = arr2.length
task.longestSubsequences(arr2, n)
end
main()Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
// Scala program for
// Efficiently find length of longest Increasing Subsequence
class Subsequence()
{
// Print the elements of given array
def printElement(arr: Array[Int], n: Int): Unit = {
var i: Int = 0;
while (i < n)
{
print(" " + arr(i));
i += 1;
}
}
def longestSubsequences(arr: Array[Int], n: Int): Unit = {
if (n <= 0)
{
return;
}
var length: Int = 1;
var mid: Int = 0;
var low: Int = 0;
var high: Int = 0;
// Auxiliary array
// Set intial value
var tail: Array[Int] = Array.fill[Int](n)(0);
var i: Int = 0;
while (i < n)
{
if (arr(i) < arr(tail(0)))
{
tail(0) = i;
}
else if (arr(i) > arr(tail(length - 1)))
{
tail(length) = i;
length += 1;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + (high - low) / 2;
if (arr(tail(mid)) >= arr(i))
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail(high) = i;
}
i += 1;
}
print("\n Array : ");
// Display given array
printElement(arr, n);
print("\n Length : " + length + "\n ");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var task: Subsequence = new Subsequence();
// Define array of integer elements
var arr1: Array[Int] = Array(8, 4, 7, 5, 1, 9, 3);
var arr2: Array[Int] = Array(9, 10, 3, 4, 8, 7, 10);
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
var n: Int = arr1.length;
task.longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = arr2.length;
task.longestSubsequences(arr2, n);
}
}Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
import Foundation;
// Swift 4 program for
// Efficiently find length of longest Increasing Subsequence
class Subsequence
{
// Print the elements of given array
func printElement(_ arr: [Int], _ n: Int)
{
var i: Int = 0;
while (i < n)
{
print(" ", arr[i], terminator: "");
i += 1;
}
}
func longestSubsequences(_ arr: [Int], _ n: Int)
{
if (n <= 0)
{
return;
}
var length: Int = 1;
var mid: Int = 0;
var low: Int = 0;
var high: Int = 0;
// Auxiliary array
// Set intial value
var tail: [Int] = Array(repeating: 0, count: n);
var i: Int = 0;
while (i < n)
{
if (arr[i] < arr[tail[0]])
{
tail[0] = i;
}
else if (arr[i] > arr[tail[length - 1]])
{
tail[length] = i;
length += 1;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + (high - low) / 2;
if (arr[tail[mid]] >= arr[i])
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail[high] = i;
}
i += 1;
}
print("\n Array : ", terminator: "");
// Display given array
self.printElement(arr, n);
print("\n Length : ", length ,"\n ", terminator: "");
}
}
func main()
{
let task: Subsequence = Subsequence();
// Define array of integer elements
let arr1: [Int] = [8, 4, 7, 5, 1, 9, 3];
let arr2: [Int] = [9, 10, 3, 4, 8, 7, 10];
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
var n: Int = arr1.count;
task.longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = arr2.count;
task.longestSubsequences(arr2, n);
}
main();Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
// Kotlin program for
// Efficiently find length of longest Increasing Subsequence
class Subsequence
{
// Print the elements of given array
fun printElement(arr: Array < Int > , n: Int): Unit
{
var i: Int = 0;
while (i < n)
{
print(" " + arr[i]);
i += 1;
}
}
fun longestSubsequences(arr: Array < Int > , n: Int): Unit
{
if (n <= 0)
{
return;
}
var length: Int = 1;
var mid: Int;
var low: Int;
var high: Int ;
// Auxiliary array
// Set intial value
val tail: Array < Int > = Array(n)
{
0
};
var i: Int = 0;
while (i < n)
{
if (arr[i] < arr[tail[0]])
{
tail[0] = i;
}
else if (arr[i] > arr[tail[length - 1]])
{
tail[length] = i;
length += 1;
}
else
{
low = -1;
high = length - 1;
// Find element position in tail array
while (high - low > 1)
{
mid = low + (high - low) / 2;
if (arr[tail[mid]] >= arr[i])
{
high = mid;
}
else
{
low = mid;
}
}
// Set new position
tail[high] = i;
}
i += 1;
}
print("\n Array : ");
// Display given array
this.printElement(arr, n);
print("\n Length : " + length + "\n ");
}
}
fun main(args: Array < String > ): Unit
{
val task: Subsequence = Subsequence();
// Define array of integer elements
val arr1: Array < Int > = arrayOf(8, 4, 7, 5, 1, 9, 3);
val arr2: Array < Int > = arrayOf(9, 10, 3, 4, 8, 7, 10);
// Test Case A
// [ 8 , 4 , 7 , 5 , 1 , 9, 3]
// length of Longest increasing subsequence 3
// (4, 5, 9)
// Result = 3
var n: Int = arr1.count();
task.longestSubsequences(arr1, n);
// Test Case B
// [ 9, 10, 3, 4, 8, 7, 10]
// length of Longest increasing subsequence 4
// (3, 4, 8, 10), (3, 4, 7, 10)
// Result = 4
n = arr2.count();
task.longestSubsequences(arr2, n);
}Output
Array : 8 4 7 5 1 9 3
Length : 3
Array : 9 10 3 4 8 7 10
Length : 4
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