
    Develop a fraud detection algorithm that analyzes a sequence of transaction amounts to identify the highest-risk spending pattern by finding the maximum total value of transactions that show an increase followed by a decrease. The pattern must consist of transactions where amounts initially rise and then fall, which is typical of fraudulent card usage where thieves make increasingly larger purchases before suddenly reducing spending as detection risk increases.
    

    
def max_sum(arr):
    """
    Develop a fraud detection algorithm that analyzes a sequence of transaction amounts to identify the highest-risk spending pattern by finding the maximum total value of transactions that show an increase followed by a decrease. The pattern must consist of transactions where amounts initially rise and then fall, which is typical of fraudulent card usage where thieves make increasingly larger purchases before suddenly reducing spending as detection risk increases.
    

    """
def max_sum(arr):
    """
    Develop a fraud detection algorithm that analyzes a sequence of transaction amounts to identify the highest-risk spending pattern by finding the maximum total value of transactions that show an increase followed by a decrease. The pattern must consist of transactions where amounts initially rise and then fall, which is typical of fraudulent card usage where thieves make increasingly larger purchases before suddenly reducing spending as detection risk increases.
    

    """
    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