
    Given a list of drug interaction scores between sequential medications in a patient's treatment plan, find the highest potential cumulative interaction risk by selecting medications that have progressively increasing interaction scores. The selected medications must maintain their relative order from the original prescription sequence, and the risk is calculated by multiplying their respective interaction scores.
    

    
def max_product(arr):
    """
    Given a list of drug interaction scores between sequential medications in a patient's treatment plan, find the highest potential cumulative interaction risk by selecting medications that have progressively increasing interaction scores. The selected medications must maintain their relative order from the original prescription sequence, and the risk is calculated by multiplying their respective interaction scores.
    

    """
def max_product(arr):
    """
    Given a list of drug interaction scores between sequential medications in a patient's treatment plan, find the highest potential cumulative interaction risk by selecting medications that have progressively increasing interaction scores. The selected medications must maintain their relative order from the original prescription sequence, and the risk is calculated by multiplying their respective interaction scores.
    

    """
    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)