In a social network, each user can influence their direct connections. The level of influence for each user is given in the Influences file where the first column represents the user and the second column represents the influence score of the user. You need to find the longest chain of influence in the network such that the influence score of a user in the chain is strictly greater than the previous user. Task: $1.$ Implement a dynamic programming algorithm to find the longest increasing path in terms of influence scores in the graph.

$2.$ Return the maximum length of the chain and the sequence of users in the chain.

provide a complete implementation code for above in c$++$ language.