
    Given a sequence of historical credit scores from a loan applicant's records, develop a risk assessment function that determines the strongest upward trend in creditworthiness up to a specific evaluation point in their history, while also considering a projected future credit score. The function should analyze all possible combinations of increasing credit scores from the beginning of the records up to the current evaluation point, including the forecasted score at a future date. The assessment must identify the combination that yields the highest sum of credit scores while maintaining an upward trend, which will help determine the applicant's credit risk trajectory. The goal is to find patterns that indicate sustained improvement in creditworthiness while accounting for both historical performance and future projections.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Given a sequence of historical credit scores from a loan applicant's records, develop a risk assessment function that determines the strongest upward trend in creditworthiness up to a specific evaluation point in their history, while also considering a projected future credit score. The function should analyze all possible combinations of increasing credit scores from the beginning of the records up to the current evaluation point, including the forecasted score at a future date. The assessment must identify the combination that yields the highest sum of credit scores while maintaining an upward trend, which will help determine the applicant's credit risk trajectory. The goal is to find patterns that indicate sustained improvement in creditworthiness while accounting for both historical performance and future projections.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Given a sequence of historical credit scores from a loan applicant's records, develop a risk assessment function that determines the strongest upward trend in creditworthiness up to a specific evaluation point in their history, while also considering a projected future credit score. The function should analyze all possible combinations of increasing credit scores from the beginning of the records up to the current evaluation point, including the forecasted score at a future date. The assessment must identify the combination that yields the highest sum of credit scores while maintaining an upward trend, which will help determine the applicant's credit risk trajectory. The goal is to find patterns that indicate sustained improvement in creditworthiness while accounting for both historical performance and future projections.
    

    """
    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]