
    Design an algorithm for a content moderation system that analyzes a sequence of post engagement metrics to identify the most significant viral content cycle by finding the highest total engagement score of posts that show an increasing then decreasing pattern. The engagement pattern must follow a rise-and-fall trajectory, where interaction scores first increase and then decrease, helping moderators focus on the most impactful period of viral spread.
    

    
def max_sum(arr):
    """
    Design an algorithm for a content moderation system that analyzes a sequence of post engagement metrics to identify the most significant viral content cycle by finding the highest total engagement score of posts that show an increasing then decreasing pattern. The engagement pattern must follow a rise-and-fall trajectory, where interaction scores first increase and then decrease, helping moderators focus on the most impactful period of viral spread.
    

    """
def max_sum(arr):
    """
    Design an algorithm for a content moderation system that analyzes a sequence of post engagement metrics to identify the most significant viral content cycle by finding the highest total engagement score of posts that show an increasing then decreasing pattern. The engagement pattern must follow a rise-and-fall trajectory, where interaction scores first increase and then decrease, helping moderators focus on the most impactful period of viral spread.
    

    """
    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