
    Given a sequence of student mastery scores from different learning modules, determine the highest potential achievement level by finding the maximum product of scores that form a progressively improving learning path. A valid learning path must show increasing mastery levels across modules, and the goal is to identify the combination that results in the highest overall learning effectiveness score when multiplied together.
    

    
def max_product(arr):
    """
    Given a sequence of student mastery scores from different learning modules, determine the highest potential achievement level by finding the maximum product of scores that form a progressively improving learning path. A valid learning path must show increasing mastery levels across modules, and the goal is to identify the combination that results in the highest overall learning effectiveness score when multiplied together.
    

    """
def max_product(arr):
    """
    Given a sequence of student mastery scores from different learning modules, determine the highest potential achievement level by finding the maximum product of scores that form a progressively improving learning path. A valid learning path must show increasing mastery levels across modules, and the goal is to identify the combination that results in the highest overall learning effectiveness score when multiplied together.
    

    """
    n = len(arr)
    mpis = arr[:]
    for i in range(n):
        current_prod = arr[i]
        j = i + 1
        while j < n:
            if arr[j - 1] > arr[j]:
                break
            current_prod *= arr[j]
            if current_prod > mpis[j]:
                mpis[j] = current_prod
            j = j + 1
    return max(mpis)