
    Given a sequence of social connection strength scores between a user and potential friend recommendations, find the most impactful chain of connections that follows a natural networking pattern where relationship strength first increases through closer connections and then decreases through distant ones. The goal is to identify the path that maximizes the total connection strength while maintaining this natural progression-regression pattern.
    

    
def max_sum(arr):
    """
    Given a sequence of social connection strength scores between a user and potential friend recommendations, find the most impactful chain of connections that follows a natural networking pattern where relationship strength first increases through closer connections and then decreases through distant ones. The goal is to identify the path that maximizes the total connection strength while maintaining this natural progression-regression pattern.
    

    """
def max_sum(arr):
    """
    Given a sequence of social connection strength scores between a user and potential friend recommendations, find the most impactful chain of connections that follows a natural networking pattern where relationship strength first increases through closer connections and then decreases through distant ones. The goal is to identify the path that maximizes the total connection strength while maintaining this natural progression-regression pattern.
    

    """
    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