void dijkstra(int N, const vector<vector<pair<int, int>>>& edges, vector<vector<long>>& distance, int subset) {
    set<pair<long, int>> S;
    for (int i=1; i <= N; ++i) {
        if (distance[subset][i] != LONG_MAX) S.insert({distance[subset][i], i});
    }
    while (!S.empty()) {
        int shortest = S.begin()->second;
        S.erase(S.begin());
        for (auto e : edges[shortest]) {
            if (distance[subset][e.first] > distance[subset][shortest] + e.second) {
                S.erase({ distance[subset][e.first], e.first});
                distance[subset][e.first] = distance[subset][shortest] + e.second;
                S.insert({ distance[subset][e.first], e.first });
            }
        }
    }
}

int shop(int N, int k, const vector<vector<int>>& fishes, const vector<vector<pair<int, int>>>& roads) {
    int totalSubsets = pow(2, k);
    vector<vector<long>> distance(totalSubsets, vector<long>(N + 1, LONG_MAX));
    distance[0][1] = 0;
    dijkstra(N, roads, distance, 0);
    for (int subset = 1; subset < totalSubsets; ++subset) {
        for (int fish = 1, bit = 1; fish <= k; ++fish, bit <<= 1) {
            if ((subset & bit) == 0) continue;
            for (int shop : fishes[fish]) distance[subset][shop] = min(distance[subset][shop], distance[subset^bit][shop]);
        }
        dijkstra(N, roads, distance, subset);
    }
    long answer = LONG_MAX;
    for (int subset = 0; subset < totalSubsets; ++subset) {
        answer = min(answer, max(distance[subset][N], distance[subset^(totalSubsets - 1)][N]));
    }
    return answer;
}

int main()
{
    int n, m, k, fishTypes, fish, x, y, w;
    cin >> n >> m >> k;
    vector<vector<int>> fishes(k + 1);
    vector<vector<pair<int, int>>> roads(n + 1);
    for (int shop = 1; shop <= n; ++shop) {
        cin >> fishTypes;
        for (int type = 1; type <= fishTypes; ++type) {
            cin >> fish;
            fishes[fish].push_back(shop);
        }
    }
    for (int j=1; j <= m; ++j) {
        cin >> x >> y >> w;
        roads[x].push_back({y, w});
        roads[y].push_back({x, w});
    }
    cout << shop(n, k, fishes, roads);
}

#include<bits/stdc++.h>
using namespace std;

#define Max 100000

void dijsktra(int n, vector<int> &fishtypes, vector<vector<pair<int, int>>> &adj, vector<vector<int>> &totalweight)
{
    //create set of [distance, shop, types of fish]
    set<pair<int, pair<int, int>>> st;
    st.insert({0, {0, fishtypes[0]}});
    while(st.size() != 0)
    {
        pair<int, pair<int, int>> node = *(st.begin());
        st.erase(st.begin());
        int curdist = node.first;
        int curshop = node.second.first;
        int curTypeOfFish = node.second.second;
        //we will skip when we already go to that shop with the same types of fish collected but with smaller total weight
        if(curdist >= totalweight[curshop][curTypeOfFish]) continue;
        totalweight[curshop][curTypeOfFish] = curdist;
        for(int i = 0; i < adj[curshop].size(); i++)
        {
            int newdist = curdist + adj[curshop][i].second;
            int nextshop = adj[curshop][i].first;
            int newtype = curTypeOfFish | fishtypes[nextshop];
            pair<int, pair<int, int>> nextnode(newdist, {nextshop, newtype});
            st.insert(nextnode);
        }
    }
}
int main()
{
    int n, m, k;
    cin >> n >> m >> k;
    vector<int> fishtypes(n, 0);
    //bit-masking for types of fish sold by i-th shop
    for(int i = 0; i < n; i++)
    {
        int x;
        cin >> x;
        for(int j = 0; j < x; j++)
        {
            int type;
            cin >> type;
            fishtypes[i] = fishtypes[i] | (1 << (type - 1));
        }
    }
    //create adj list
    vector<vector<pair<int, int>>> adj(n, vector<pair<int, int>>());
    for(int i = 0; i < m; i++)
    {
        int shop1;
        int shop2;
        int weight;
        cin >> shop1 >> shop2 >> weight;
        adj[shop1 - 1].push_back({shop2 - 1, weight});
        adj[shop2 - 1].push_back({shop1 - 1, weight});
    }
    vector<bool> visited(n, false);
    vector<vector<int>> totalweight(n, vector<int>(1 << k, INT_MAX));
    dijsktra(n, fishtypes, adj, totalweight);
    int res = INT_MAX;
    for(int i = 0; i < (1 << k); i++)
    {
        if(totalweight[n - 1][i] == INT_MAX) continue;
        for(int j = i; j < (1 << k); j++)
        {
            if(totalweight[n - 1][j] == INT_MAX) continue;
            if((i | j) == (1 << k) - 1)
            {
                res = min(res, max(totalweight[n - 1][i], totalweight[n - 1][j]));
            }
        }
    }
    cout << res;
    return 0;
}