
    Design a fraud detection algorithm that analyzes credit card transaction patterns by finding the highest total value of legitimate increasing purchases up to a specific transaction, while also considering one future suspicious transaction. The algorithm must identify the maximum sum possible from a sequence of increasing transaction amounts that occurred before the investigation point, plus the value of the suspicious future transaction. The transaction sequence must maintain a strictly increasing pattern to be considered valid, as this reflects normal consumer spending behavior. The solution should help fraud analysts determine if a suspicious future transaction fits within established spending patterns by evaluating it alongside previous legitimate transaction sequences.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a fraud detection algorithm that analyzes credit card transaction patterns by finding the highest total value of legitimate increasing purchases up to a specific transaction, while also considering one future suspicious transaction. The algorithm must identify the maximum sum possible from a sequence of increasing transaction amounts that occurred before the investigation point, plus the value of the suspicious future transaction. The transaction sequence must maintain a strictly increasing pattern to be considered valid, as this reflects normal consumer spending behavior. The solution should help fraud analysts determine if a suspicious future transaction fits within established spending patterns by evaluating it alongside previous legitimate transaction sequences.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a fraud detection algorithm that analyzes credit card transaction patterns by finding the highest total value of legitimate increasing purchases up to a specific transaction, while also considering one future suspicious transaction. The algorithm must identify the maximum sum possible from a sequence of increasing transaction amounts that occurred before the investigation point, plus the value of the suspicious future transaction. The transaction sequence must maintain a strictly increasing pattern to be considered valid, as this reflects normal consumer spending behavior. The solution should help fraud analysts determine if a suspicious future transaction fits within established spending patterns by evaluating it alongside previous legitimate transaction sequences.
    

    """
    dp = [[0 for i in range(n)] for i in range(n)]
    for i in range(n):
        if a[i] > a[0]:
            dp[0][i] = a[i] + a[0]
        else:
            dp[0][i] = a[i]
    for i in range(1, n):
        for j in range(n):
            if a[j] > a[i] and j > i:
                if dp[i - 1][i] + a[j] > dp[i - 1][j]:
                    dp[i][j] = dp[i - 1][i] + a[j]
                else:
                    dp[i][j] = dp[i - 1][j]
            else:
                dp[i][j] = dp[i - 1][j]
    return dp[index][k]