public static int sumOfSets(int n,List<String> edges){
        // contruct graph

        List<List<Integer>> graph = new ArrayList<>();
        for(int i=0;i<=n;i++){
            graph.add(new ArrayList<>());
        }

        for(String edge:edges){
            String[] nodes = edge.split(" ");
            int node1 = Integer.parseInt(nodes[0]);
            int node2 = Integer.parseInt(nodes[1]);
            graph.get(node1).add(node2);
            graph.get(node2).add(node1);
        }

        // find size of each connected component
        int sum = 0;
        List<Integer> sizes = new ArrayList<>();
        boolean[] visited = new boolean[n+1];
        for(int i=1;i<=n;i++){
            if(!visited[i]){
                int size = dfs(i,graph,visited);
                sizes.add(size);
            }
        }

        // print sizes

        for(int i=0;i<sizes.size();i++){

            double tmp = Math.log(sizes.get(i));
            // System.out.println(tmp);
            sum += tmp;
        }

        return sum;

    }

    public static int dfs(int node,List<List<Integer>> graph,boolean[] visited){
        visited[node] = true;
        int size = 1;
        for(int neighbour:graph.get(node)){
            if(!visited[neighbour]){
                size += dfs(neighbour,graph,visited);
            }
        }
        return size;
    }