
    Design an algorithm for a content moderation system that calculates the highest cumulative severity score from a sequence of flagged posts up to a checkpoint position, while ensuring the inclusion of a specific critical post that appears after the checkpoint. The severity scores must follow an increasing pattern to indicate an escalating trend in concerning content. The algorithm should analyze a batch of posts where each post has been assigned a numerical severity score, and the critical post's position occurs after the checkpoint position in the sequence. The goal is to identify the most severe sequence of escalating violations that leads up to and includes this specific critical post, helping moderators understand the pattern of rule violations.
    

    
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design an algorithm for a content moderation system that calculates the highest cumulative severity score from a sequence of flagged posts up to a checkpoint position, while ensuring the inclusion of a specific critical post that appears after the checkpoint. The severity scores must follow an increasing pattern to indicate an escalating trend in concerning content. The algorithm should analyze a batch of posts where each post has been assigned a numerical severity score, and the critical post's position occurs after the checkpoint position in the sequence. The goal is to identify the most severe sequence of escalating violations that leads up to and includes this specific critical post, helping moderators understand the pattern of rule violations.
    

    """
def max_sum_increasing_subseq(a, n, index, k):
    """
    Design an algorithm for a content moderation system that calculates the highest cumulative severity score from a sequence of flagged posts up to a checkpoint position, while ensuring the inclusion of a specific critical post that appears after the checkpoint. The severity scores must follow an increasing pattern to indicate an escalating trend in concerning content. The algorithm should analyze a batch of posts where each post has been assigned a numerical severity score, and the critical post's position occurs after the checkpoint position in the sequence. The goal is to identify the most severe sequence of escalating violations that leads up to and includes this specific critical post, helping moderators understand the pattern of rule violations.
    

    """
    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]