
    Design a fraud detection algorithm that analyzes a customer's transaction history to find the largest possible total spend during a single normal spending cycle, where a normal cycle is characterized by gradually increasing transaction amounts followed by gradually decreasing amounts. The algorithm should help distinguish between legitimate spending patterns and potential fraudulent activities by identifying the maximum sum possible during such a typical spending cycle.
    

    
def max_sum(arr):
    """
    Design a fraud detection algorithm that analyzes a customer's transaction history to find the largest possible total spend during a single normal spending cycle, where a normal cycle is characterized by gradually increasing transaction amounts followed by gradually decreasing amounts. The algorithm should help distinguish between legitimate spending patterns and potential fraudulent activities by identifying the maximum sum possible during such a typical spending cycle.
    

    """
def max_sum(arr):
    """
    Design a fraud detection algorithm that analyzes a customer's transaction history to find the largest possible total spend during a single normal spending cycle, where a normal cycle is characterized by gradually increasing transaction amounts followed by gradually decreasing amounts. The algorithm should help distinguish between legitimate spending patterns and potential fraudulent activities by identifying the maximum sum possible during such a typical spending cycle.
    

    """
    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