
    Design an algorithm to determine the optimal bus route segment that maximizes total passenger pickups while following an increasing passenger demand pattern from the starting stop to the current stop position, and must include a specific strategic future stop. The route segment must maintain a strictly increasing passenger count between consecutive selected stops to ensure efficient capacity utilization. The algorithm should analyze passenger count data from multiple stops along the route, considering both the immediate section up to the current position and the mandatory inclusion of the designated future stop. The solution should help transit planners identify the most efficient route segment that serves the highest possible cumulative passenger demand while adhering to these operational constraints.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design an algorithm to determine the optimal bus route segment that maximizes total passenger pickups while following an increasing passenger demand pattern from the starting stop to the current stop position, and must include a specific strategic future stop. The route segment must maintain a strictly increasing passenger count between consecutive selected stops to ensure efficient capacity utilization. The algorithm should analyze passenger count data from multiple stops along the route, considering both the immediate section up to the current position and the mandatory inclusion of the designated future stop. The solution should help transit planners identify the most efficient route segment that serves the highest possible cumulative passenger demand while adhering to these operational constraints.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design an algorithm to determine the optimal bus route segment that maximizes total passenger pickups while following an increasing passenger demand pattern from the starting stop to the current stop position, and must include a specific strategic future stop. The route segment must maintain a strictly increasing passenger count between consecutive selected stops to ensure efficient capacity utilization. The algorithm should analyze passenger count data from multiple stops along the route, considering both the immediate section up to the current position and the mandatory inclusion of the designated future stop. The solution should help transit planners identify the most efficient route segment that serves the highest possible cumulative passenger demand while adhering to these operational constraints.
    

    """
    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]