import java.io.*;
import java.util.*;

class Pair
{
    int first;
    int second;
    Pair(int f, int s)
    {
        first = f;
        second = s;
    }
    Pair(){}
}

class Pair3 implements Comparable<Pair3>
{
    int first;
    int second;
    int third;
    Pair3(int f, int s, int t)
    {
        first = f;
        second = s;
        third = t;
    }
    Pair3(){}
    @Override
    public int compareTo(Pair3 tmp)
    {
        if(first < tmp.first) return -1;
        else if(first == tmp.first)
        {
            if(second < tmp.second) return -1;
            else if(second == tmp.second)
            {
                if(third < tmp.third) return -1;
                else if(third == tmp.third) return 0;
                else return 1;
            }
            else return 1;
        }
        return 1;
    }
}

public class HelloWorld {

    public static void dijsktra(int n, int fishtypes[], List<List<Pair>> adj, List<List<Integer>> totalweight)
    {
        Set<Pair3> set = new TreeSet<>();
        //add Pair3 = [distance, shop, types of fish] of shop 0 to set
        
        set.add(new Pair3(0, 0, fishtypes[0]));
        while(set.isEmpty() == false)
        {
            Pair3 node = set.iterator().next();
            set.remove(set.iterator().next());
            int curdist = node.first;
            int curshop = node.second;
            int curTypesOfFish = node.third;

            if(totalweight.get(curshop).get(curTypesOfFish) <= curdist)
            {
                //we will skip to the next node if the distance from 0 to curshop is smaller than this node's distance with the same types of fish
                continue;
            }
            totalweight.get(curshop).set(curTypesOfFish, curdist);
            for(int i = 0; i < adj.get(curshop).size(); i++)
            {
                Pair3 nextnode = new Pair3();
                nextnode.first = curdist + adj.get(curshop).get(i).second;
                nextnode.second = adj.get(curshop).get(i).first;
                nextnode.third = curTypesOfFish | fishtypes[adj.get(curshop).get(i).first]; //bit-masking
                set.add(nextnode);
            }
        }
    }
    public static void main(String[] args) {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int k = sc.nextInt();
        int fishtypes[] = new int[n];
        // bit-masking for types of fish sold by i-th shop 
        for(int i = 0; i < n; i++)
        {
            int x = sc.nextInt();
            for(int j = 0; j < x; j++)
            {
                int type = sc.nextInt();
                fishtypes[i] = fishtypes[i] | (1 << (type - 1));
            }
        }
        //create adj list
        List<List<Pair>> adj = new ArrayList<>();
        for(int i = 0; i < n; i++)
        {
            adj.add(new ArrayList<>());
        }
        for(int i = 0; i < m; i++)
        {
            int shop1 = sc.nextInt() - 1;
            int shop2 = sc.nextInt() - 1;
            int weight = sc.nextInt();
            adj.get(shop1).add(new Pair(shop2, weight));
            adj.get(shop2).add(new Pair(shop1, weight));
        }
        //totalweight[i][j] save total weight from 1 to i-th shop with j types collected
        List<List<Integer>> totalweight = new ArrayList<>();
        for(int i = 0; i < n; i++)
        {
            totalweight.add(new ArrayList<>());
            for(int j = 0; j < ((1 << k)); j++)
            {
                totalweight.get(i).add(Integer.MAX_VALUE);
            }
        }
        dijsktra(n, fishtypes, adj, totalweight);
        int res = Integer.MAX_VALUE;
        for(int i = 0; i < totalweight.get(n - 1).size(); i++)
        {
            if(totalweight.get(n - 1).get(i) == Integer.MAX_VALUE) continue;
            for(int j = i; j < totalweight.get(n - 1).size(); j++)
            {
                if(totalweight.get(n - 1).get(j) == Integer.MAX_VALUE) continue;
                //check if 2 cats collect enough types of fish
                if((i | j) == (1 << k) - 1) 
                {
                    res = Math.min(res, Math.max(totalweight.get(n - 1).get(i), totalweight.get(n - 1).get(j)));
                }
            }
        }
        System.out.println(res);
        sc.close();
    }
}