
    Given a client's monthly spending data over time, determine the highest total expenditure pattern that shows a single transition from increasing to decreasing spending behavior. This analysis will help identify the most significant period of spending volatility, where expenses first grew and then declined, to better understand the client's financial patterns and develop targeted recommendations.
    

    
def max_sum(arr):
    """
    Given a client's monthly spending data over time, determine the highest total expenditure pattern that shows a single transition from increasing to decreasing spending behavior. This analysis will help identify the most significant period of spending volatility, where expenses first grew and then declined, to better understand the client's financial patterns and develop targeted recommendations.
    

    """
def max_sum(arr):
    """
    Given a client's monthly spending data over time, determine the highest total expenditure pattern that shows a single transition from increasing to decreasing spending behavior. This analysis will help identify the most significant period of spending volatility, where expenses first grew and then declined, to better understand the client's financial patterns and develop targeted recommendations.
    

    """
    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