
    In a professional networking platform, develop an algorithm to identify the most impactful career trajectory among connected professionals by analyzing their skill progression scores over time. The algorithm should find the maximum combined value of skill ratings that follow a typical career path pattern - where expertise first increases during specialization and then potentially decreases during career transitions or role changes.
    

    
def max_sum(arr):
    """
    In a professional networking platform, develop an algorithm to identify the most impactful career trajectory among connected professionals by analyzing their skill progression scores over time. The algorithm should find the maximum combined value of skill ratings that follow a typical career path pattern - where expertise first increases during specialization and then potentially decreases during career transitions or role changes.
    

    """
def max_sum(arr):
    """
    In a professional networking platform, develop an algorithm to identify the most impactful career trajectory among connected professionals by analyzing their skill progression scores over time. The algorithm should find the maximum combined value of skill ratings that follow a typical career path pattern - where expertise first increases during specialization and then potentially decreases during career transitions or role changes.
    

    """
    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