
    Design an algorithm that analyzes a sequence of patient severity scores in the emergency room to identify the most critical period of deterioration and subsequent improvement, where the severity scores first increase (worsening condition) and then decrease (recovery phase). The algorithm should determine the maximum sum of severity scores in this pattern to quantify the overall impact of the medical event on the patient.
    

    
def max_sum(arr):
    """
    Design an algorithm that analyzes a sequence of patient severity scores in the emergency room to identify the most critical period of deterioration and subsequent improvement, where the severity scores first increase (worsening condition) and then decrease (recovery phase). The algorithm should determine the maximum sum of severity scores in this pattern to quantify the overall impact of the medical event on the patient.
    

    """
def max_sum(arr):
    """
    Design an algorithm that analyzes a sequence of patient severity scores in the emergency room to identify the most critical period of deterioration and subsequent improvement, where the severity scores first increase (worsening condition) and then decrease (recovery phase). The algorithm should determine the maximum sum of severity scores in this pattern to quantify the overall impact of the medical event on the patient.
    

    """
    MSIBS = arr[:]
    for i in range(len(arr)):
        for j in range(0, i):
            if arr[i] > arr[j] and MSIBS[i] < MSIBS[j] + arr[i]:
                MSIBS[i] = MSIBS[j] + arr[i]
    MSDBS = arr[:]
    for i in range(1, len(arr) + 1):
        for j in range(1, i):
            if arr[-i] > arr[-j] and MSDBS[-i] < MSDBS[-j] + arr[-i]:
                MSDBS[-i] = MSDBS[-j] + arr[-i]
    max_sum = float('-Inf')
    for (i, j, k) in zip(MSIBS, MSDBS, arr):
        max_sum = max(max_sum, i + j - k)
    return max_sum