public static int lilysHomework(List<Integer> arr) {
        // The key to solving this problem is to create a sorted indexs
        // and count the number of the swaps it takes to get things
        // in the corrector order.
        List<Integer> indicesAssending = IntStream.range(0, arr.size())
            .boxed()
            .sorted(Comparator.comparingInt(i -> arr.get(i)))
            .collect(Collectors.toList()) ;
            
        List<Integer> indicesDesending = indicesAssending.stream()
            .collect(Collectors.toList());
        Collections.reverse(indicesDesending);
        
        int resultAssending = swapToOrder(indicesAssending);
        int resultDesending = swapToOrder(indicesDesending);
        
        return Math.min(resultAssending, resultDesending);
    }
    
    /** Swap each sorted indice into it proper location **/
    private static int swapToOrder(List<Integer> indices) {
        int result = 0 ;
        
        for (int i=0; i<indices.size();) {
            if (i != indices.get(i).intValue() ) {
                ++result;
                swap(indices, i, indices.get(i)) ;
            } else {
                ++i;
            }            
        }
        return result;
    }
    
    /** Simple swaping of two indices values**/
    private static void swap(List<Integer> arr, int i1, int i2) {
        Integer v1 = arr.get(i1);
        arr.set(i1, arr.get(i2));
        arr.set(i2, v1); 
    }