
    Given a sequence of medication interaction severity scores, determine the highest risk level by finding the maximum product of scores from a subset of medications when taken in increasing doses. The subset must maintain the order of medications as they appear in the original sequence, but can skip medications in between.
    

    
def max_product(arr):
    """
    Given a sequence of medication interaction severity scores, determine the highest risk level by finding the maximum product of scores from a subset of medications when taken in increasing doses. The subset must maintain the order of medications as they appear in the original sequence, but can skip medications in between.
    

    """
def max_product(arr):
    """
    Given a sequence of medication interaction severity scores, determine the highest risk level by finding the maximum product of scores from a subset of medications when taken in increasing doses. The subset must maintain the order of medications as they appear in the original sequence, but can skip medications in between.
    

    """
    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)