
    Design a credit risk assessment algorithm that evaluates a customer's financial stability by analyzing their transaction history. The algorithm should find the most favorable sequence of increasing monthly transactions up to the current assessment period that demonstrates consistent financial growth. Additionally, the assessment must incorporate a predicted future transaction amount to gauge potential creditworthiness. The goal is to maximize the total transaction value while maintaining an upward trend in spending patterns, which serves as an indicator of the customer's improving financial capacity. The algorithm should consider all possible combinations of transactions that show progressive increase in spending up to the current month, while ensuring the predicted future transaction fits within this growth pattern.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a credit risk assessment algorithm that evaluates a customer's financial stability by analyzing their transaction history. The algorithm should find the most favorable sequence of increasing monthly transactions up to the current assessment period that demonstrates consistent financial growth. Additionally, the assessment must incorporate a predicted future transaction amount to gauge potential creditworthiness. The goal is to maximize the total transaction value while maintaining an upward trend in spending patterns, which serves as an indicator of the customer's improving financial capacity. The algorithm should consider all possible combinations of transactions that show progressive increase in spending up to the current month, while ensuring the predicted future transaction fits within this growth pattern.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a credit risk assessment algorithm that evaluates a customer's financial stability by analyzing their transaction history. The algorithm should find the most favorable sequence of increasing monthly transactions up to the current assessment period that demonstrates consistent financial growth. Additionally, the assessment must incorporate a predicted future transaction amount to gauge potential creditworthiness. The goal is to maximize the total transaction value while maintaining an upward trend in spending patterns, which serves as an indicator of the customer's improving financial capacity. The algorithm should consider all possible combinations of transactions that show progressive increase in spending up to the current month, while ensuring the predicted future transaction fits within this growth pattern.
    

    """
    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]