
    Design an algorithm to analyze bus occupancy patterns that finds the optimal sequence of increasing passenger loads from the start of the route up to a current stop, while ensuring a specific future stop's occupancy is factored into the analysis. The algorithm should identify the maximum total passenger count possible when selecting stops with progressively higher occupancy levels up to the current position, while mandatorily including the passenger count at a designated future stop. This analysis will help transit planners identify the most impactful sequence of stops for capacity planning, with the constraint that passenger counts must increase between selected stops to indicate growing ridership trends. The solution will assist in optimizing bus schedules by understanding the relationship between current ridership patterns and anticipated future demand at specific stops.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design an algorithm to analyze bus occupancy patterns that finds the optimal sequence of increasing passenger loads from the start of the route up to a current stop, while ensuring a specific future stop's occupancy is factored into the analysis. The algorithm should identify the maximum total passenger count possible when selecting stops with progressively higher occupancy levels up to the current position, while mandatorily including the passenger count at a designated future stop. This analysis will help transit planners identify the most impactful sequence of stops for capacity planning, with the constraint that passenger counts must increase between selected stops to indicate growing ridership trends. The solution will assist in optimizing bus schedules by understanding the relationship between current ridership patterns and anticipated future demand at specific stops.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design an algorithm to analyze bus occupancy patterns that finds the optimal sequence of increasing passenger loads from the start of the route up to a current stop, while ensuring a specific future stop's occupancy is factored into the analysis. The algorithm should identify the maximum total passenger count possible when selecting stops with progressively higher occupancy levels up to the current position, while mandatorily including the passenger count at a designated future stop. This analysis will help transit planners identify the most impactful sequence of stops for capacity planning, with the constraint that passenger counts must increase between selected stops to indicate growing ridership trends. The solution will assist in optimizing bus schedules by understanding the relationship between current ridership patterns and anticipated future demand at specific stops.
    

    """
    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]