
    Design a loan risk assessment algorithm that evaluates an applicant's income stability by finding the maximum sum of consistently increasing monthly incomes up to the current assessment period, while also considering a projected future income. The algorithm must identify the strongest upward income trend that includes both historical income records up to the current assessment month and a specific projected income from a future month. The sequence must maintain a strictly increasing pattern to demonstrate reliable income growth. The assessment should help determine the applicant's loan eligibility based on their proven income progression and future earning potential.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a loan risk assessment algorithm that evaluates an applicant's income stability by finding the maximum sum of consistently increasing monthly incomes up to the current assessment period, while also considering a projected future income. The algorithm must identify the strongest upward income trend that includes both historical income records up to the current assessment month and a specific projected income from a future month. The sequence must maintain a strictly increasing pattern to demonstrate reliable income growth. The assessment should help determine the applicant's loan eligibility based on their proven income progression and future earning potential.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design a loan risk assessment algorithm that evaluates an applicant's income stability by finding the maximum sum of consistently increasing monthly incomes up to the current assessment period, while also considering a projected future income. The algorithm must identify the strongest upward income trend that includes both historical income records up to the current assessment month and a specific projected income from a future month. The sequence must maintain a strictly increasing pattern to demonstrate reliable income growth. The assessment should help determine the applicant's loan eligibility based on their proven income progression and future earning potential.
    

    """
    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]