Hướng dẫn quicksort 3-way partition python

I'm a new to algorithms and I'm confused as to where are the errors in my code that I'm writing as an assignment. I'm trying to implement a quicksort algorithm in Python 3 that deals with equal values in the array.

Here's a quicksort function (a stands for the array):

def randomized_quick_sort(a, l, r):
    if l >= r:
        return
    k = random.randint(l, r)
    a[l], a[k] = a[k], a[l]
    m1, m2 = partition3(a, l, r)
    randomized_quick_sort(a, l, m1 - 1);
    randomized_quick_sort(a, m2 + 1, r);

And here's my partition function:

def partition3(a, l, r):
    x, j, t = a[l], l, r
    for i in range(l + 1, r + 1):
        if a[i] < x:
            j +=1
            a[i], a[j] = a[j], a[i]
        elif a[i] > x:
            a[i], a[t] = a[t], a[i]
            t -=1
        else:
            j +=1
    a[l], a[j] = a[j], a[l]
    return j, t

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