In many social networks, users have the option to specify other users as their friends. In addition, there is often a friend recommendation system that shows users people they know indirectly (through one of their friends) and suggests adding these people to the friends list. You have to develop a system for recommending friends. There are n users in the social network we are interested in, each of which is assigned a unique id from 1 to n. Each user of this network has no more than 5 friends. Obviously, no user is a friend to himself, and if user x is in user y's friends list, then user y is also in user x's friends list. Let's describe how the list of possible friends for each user should be formed. For user x, the list should include users y such that: y is not a friend of x and is not the same as x; user y and user x have at least one mutual friend; there is no such user y' who satisfies the first two constraints, and who has strictly more mutual friends with x than y has with x. In other words, the list of possible friends of user x includes all such users who are not his friends, for whom the number of mutual friends with x is maximum. Note that the list of possible friends may be empty. You have to write a program that generates lists of possible friends for all users of the network according to a given structure of the social network.

#include <iostream>
#include <vector>

using namespace std;

struct Relation {
    int user;
    int friend_;
};

class Network {
public:
    Network(int n) : nodes(n), friends(n) {}
    void Add(const Relation& r) {
        nodes[r.user - 1].emplace_back(r.friend_ - 1);
        nodes[r.friend_ - 1].emplace_back(r.user - 1);
    }
    vector<vector<int>> FindPotentialFriends() {
        for (int i = 0; i < nodes.size(); ++i) {
            for (auto fi : nodes[i]) {
                for (auto ffi : nodes[fi]) {
                    if (i == ffi) continue;
                    ++friends[i][ffi];
                }
            }
        }
        vector<vector<int>> res;
        for (int i = 0; i < friends.size(); ++i) {
            vector<int> cur_friends