
    Given a sequence of student mastery scores from consecutive learning modules, determine the highest potential achievement impact by finding the maximum product of scores from any continuously improving learning path. The scores must represent a steadily increasing pattern of mastery levels to be considered valid for the calculation.
    

    
def max_product(arr):
    """
    Given a sequence of student mastery scores from consecutive learning modules, determine the highest potential achievement impact by finding the maximum product of scores from any continuously improving learning path. The scores must represent a steadily increasing pattern of mastery levels to be considered valid for the calculation.
    

    """
def max_product(arr):
    """
    Given a sequence of student mastery scores from consecutive learning modules, determine the highest potential achievement impact by finding the maximum product of scores from any continuously improving learning path. The scores must represent a steadily increasing pattern of mastery levels to be considered valid for the calculation.
    

    """
    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)