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);
}