
    Design an algorithm for a social event recommendation system that analyzes user engagement patterns to identify the most impactful sequence of events, where engagement typically follows a rise-and-fall pattern. Given an array of daily user engagement scores, find the sequence that maximizes total user interaction while maintaining the natural progression of growing interest followed by declining engagement.
    

    
def max_sum(arr):
    """
    Design an algorithm for a social event recommendation system that analyzes user engagement patterns to identify the most impactful sequence of events, where engagement typically follows a rise-and-fall pattern. Given an array of daily user engagement scores, find the sequence that maximizes total user interaction while maintaining the natural progression of growing interest followed by declining engagement.
    

    """
def max_sum(arr):
    """
    Design an algorithm for a social event recommendation system that analyzes user engagement patterns to identify the most impactful sequence of events, where engagement typically follows a rise-and-fall pattern. Given an array of daily user engagement scores, find the sequence that maximizes total user interaction while maintaining the natural progression of growing interest followed by declining engagement.
    

    """
    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