I found another way to achieve the objective, this problem is very close to the minimum swaps problem, wich the objective is count the minimum swaps to sort a array (https://www.geeksforgeeks.org/minimum-number-swaps-required-sort-array/):

from collections import defaultdict

def swaps(arr_e):
        vis = defaultdict(bool)
        ans = 0
        j = 0
        for i in range(len(arr_e)):
                if vis[i] or arr_e[i][0] == i:
                        continue

                j = i
                cycles = 0
                while not vis[j]:
                        vis[j] = True
                        j = arr_e[j][0]
                        cycles += 1

                if cycles > 0:
                        ans += cycles - 1

        return ans

# Complete the lilysHomework function below.
def lilysHomework(arr):
        arr_e = list(enumerate(arr))
        arr_s = sorted(arr_e, key=lambda x: x[1])
        ans1 = swaps(arr_s)
        arr_s = sorted(arr_e, key=lambda x: x[1], reverse = True)
        ans2 = swaps(arr_s)

        return min(ans1, ans2)