
    Design a credit risk assessment algorithm that analyzes historical credit scores to identify the most reliable sequence of borrowers up to the current application review position. The sequence must show progressively improving creditworthiness (increasing credit scores) and must include a specific future applicant's score in the evaluation. The algorithm should calculate the maximum sum of credit scores that forms such an improving sequence, considering all applications reviewed so far plus the designated future application. The goal is to identify the strongest possible chain of credit reliability that could influence the current risk assessment decision.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a credit risk assessment algorithm that analyzes historical credit scores to identify the most reliable sequence of borrowers up to the current application review position. The sequence must show progressively improving creditworthiness (increasing credit scores) and must include a specific future applicant's score in the evaluation. The algorithm should calculate the maximum sum of credit scores that forms such an improving sequence, considering all applications reviewed so far plus the designated future application. The goal is to identify the strongest possible chain of credit reliability that could influence the current risk assessment decision.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a credit risk assessment algorithm that analyzes historical credit scores to identify the most reliable sequence of borrowers up to the current application review position. The sequence must show progressively improving creditworthiness (increasing credit scores) and must include a specific future applicant's score in the evaluation. The algorithm should calculate the maximum sum of credit scores that forms such an improving sequence, considering all applications reviewed so far plus the designated future application. The goal is to identify the strongest possible chain of credit reliability that could influence the current risk assessment decision.
    

    """
    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]