please help with caclulatePartitions in java. Must be recursive, no iterations and please do not change method header. can add private method helpers.

import java.util.ArrayList;

public class PartitionCalculator $\{$

public static int numOfPartitions $($int N$)\{$

return countPartitions$($N$,$N$)$;$//$ default return statement

$\}$

private static int countPartitions$($int n$,$ int max$)\{$

if $($n $==0)\{$

return $1$;

$\}$ else if $($n $<0)\{$

return $0$;

$\}$ else if $($max $==0)\{$

return $0$;

$\}$ else $\{$

return countPartitions$($n$,$ max $-1)+$ countPartitions$($n $-$ max, max$)$;

$\}$

$\}$

public static ArrayList calculatePartitions $($int N$)\{$

$//$ no loops recursion only

$//$ For example if we call calculatePartitions$(4),$ there are a total of $5$ of them, the returned list

$//$should contain the following partitions $($in any order$)$:

$//1.[4]$

$//2.[3,1][1,3]$

$//3.[2,2]$

$//4.[2,1,1][1,2,1][1,1,2]$

$//5.[1,1,1,1]$

return null;$//$default return statement

$\}$

public static ArrayList calculateAllPermutations$($ArrayList partitions$)\{$

return partitions;

$\}$

public static void main$($String$[]$ args$)\{$

$//$ Testing the function with example given in the problem

System.out.println$("$Number of partitions for $5$: $"+$ numOfPartitions$(5))$; $//$ Output: $7$

$\}$

$\}$