
    Design a fraud detection system that analyzes a sequence of transaction amounts and identifies the largest possible sum of transactions that follow a pattern where amounts first increase and then decrease, as this could indicate potential money laundering. The system should examine all possible subsequences of transactions and determine the maximum total value of any such pattern found.
    

    
def max_sum(arr):
    """
    Design a fraud detection system that analyzes a sequence of transaction amounts and identifies the largest possible sum of transactions that follow a pattern where amounts first increase and then decrease, as this could indicate potential money laundering. The system should examine all possible subsequences of transactions and determine the maximum total value of any such pattern found.
    

    """
def max_sum(arr):
    """
    Design a fraud detection system that analyzes a sequence of transaction amounts and identifies the largest possible sum of transactions that follow a pattern where amounts first increase and then decrease, as this could indicate potential money laundering. The system should examine all possible subsequences of transactions and determine the maximum total value of any such pattern found.
    

    """
    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