/**
 * date   : 2023-06-01 21:05:40
 * author : Nyaan
 */

#define NDEBUG

using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility

namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N,F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}

template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

}  // namespace Nyaan


// bit operation

namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan


// inout

namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan


// debug


#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif


// macro

#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)


namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }


//








namespace atcoder {
namespace internal {

template <class E> struct csr {
    std::vector<int> start;
    std::vector<E> elist;
    csr(int n, const std::vector<std::pair<int, E>>& edges)
        : start(n + 1), elist(edges.size()) {
        for (auto e : edges) {
            start[e.first + 1]++;
        }
        for (int i = 1; i <= n; i++) {
            start[i] += start[i - 1];
        }
        auto counter = start;
        for (auto e : edges) {
            elist[counter[e.first]++] = e.second;
        }
    }
};

}  // namespace internal

}  // namespace atcoder





namespace atcoder {

namespace internal {

template <class T> struct simple_queue {
    std::vector<T> payload;
    int pos = 0;
    void reserve(int n) { payload.reserve(n); }
    int size() const { return int(payload.size()) - pos; }
    bool empty() const { return pos == int(payload.size()); }
    void push(const T& t) { payload.push_back(t); }
    T& front() { return payload[pos]; }
    void clear() {
        payload.clear();
        pos = 0;
    }
    void pop() { pos++; }
};

}  // namespace internal

}  // namespace atcoder



namespace atcoder {

template <class Cap, class Cost> struct mcf_graph {
  public:
    mcf_graph() {}
    mcf_graph(int n) : _n(n) {}

    int add_edge(int from, int to, Cap cap, Cost cost) {
        assert(0 <= from && from < _n);
        assert(0 <= to && to < _n);
        assert(0 <= cap);
        assert(0 <= cost);
        int m = int(_edges.size());
        _edges.push_back({from, to, cap, 0, cost});
        return m;
    }

    struct edge {
        int from, to;
        Cap cap, flow;
        Cost cost;
    };

    edge get_edge(int i) {
        int m = int(_edges.size());
        assert(0 <= i && i < m);
        return _edges[i];
    }
    std::vector<edge> edges() { return _edges; }

    std::pair<Cap, Cost> flow(int s, int t) {
        return flow(s, t, std::numeric_limits<Cap>::max());
    }
    std::pair<Cap, Cost> flow(int s, int t, Cap flow_limit) {
        return slope(s, t, flow_limit).back();
    }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t) {
        return slope(s, t, std::numeric_limits<Cap>::max());
    }
    std::vector<std::pair<Cap, Cost>> slope(int s, int t, Cap flow_limit) {
        assert(0 <= s && s < _n);
        assert(0 <= t && t < _n);
        assert(s != t);

        int m = int(_edges.size());
        std::vector<int> edge_idx(m);

        auto g = [&]() {
            std::vector<int> degree(_n), redge_idx(m);
            std::vector<std::pair<int, _edge>> elist;
            elist.reserve(2 * m);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] = degree[e.from]++;
                redge_idx[i] = degree[e.to]++;
                elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}});
                elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}});
            }
            auto _g = internal::csr<_edge>(_n, elist);
            for (int i = 0; i < m; i++) {
                auto e = _edges[i];
                edge_idx[i] += _g.start[e.from];
                redge_idx[i] += _g.start[e.to];
                _g.elist[edge_idx[i]].rev = redge_idx[i];
                _g.elist[redge_idx[i]].rev = edge_idx[i];
            }
            return _g;
        }();

        auto result = slope(g, s, t, flow_limit);

        for (int i = 0; i < m; i++) {
            auto e = g.elist[edge_idx[i]];
            _edges[i].flow = _edges[i].cap - e.cap;
        }

        return result;
    }

  private:
    int _n;
    std::vector<edge> _edges;

    // inside edge
    struct _edge {
        int to, rev;
        Cap cap;
        Cost cost;
    };

    std::vector<std::pair<Cap, Cost>> slope(internal::csr<_edge>& g,
                                            int s,
                                            int t,
                                            Cap flow_limit) {
        // variants (C = maxcost):
        // -(n-1)C <= dual[s] <= dual[i] <= dual[t] = 0
        // reduced cost (= e.cost + dual[e.from] - dual[e.to]) >= 0 for all edge

        // dual_dist[i] = (dual[i], dist[i])
        std::vector<std::pair<Cost, Cost>> dual_dist(_n);
        std::vector<int> prev_e(_n);
        std::vector<bool> vis(_n);
        struct Q {
            Cost key;
            int to;
            bool operator<(Q r) const { return key > r.key; }
        };
        std::vector<int> que_min;
        std::vector<Q> que;
        auto dual_ref = [&]() {
            for (int i = 0; i < _n; i++) {
                dual_dist[i].second = std::numeric_limits<Cost>::max();
            }
            std::fill(vis.begin(), vis.end(), false);
            que_min.clear();
            que.clear();

            // que[0..heap_r) was heapified
            size_t heap_r = 0;

            dual_dist[s].second = 0;
            que_min.push_back(s);
            while (!que_min.empty() || !que.empty()) {
                int v;
                if (!que_min.empty()) {
                    v = que_min.back();
                    que_min.pop_back();
                } else {
                    while (heap_r < que.size()) {
                        heap_r++;
                        std::push_heap(que.begin(), que.begin() + heap_r);
                    }
                    v = que.front().to;
                    std::pop_heap(que.begin(), que.end());
                    que.pop_back();
                    heap_r--;
                }
                if (vis[v]) continue;
                vis[v] = true;
                if (v == t) break;
                // dist[v] = shortest(s, v) + dual[s] - dual[v]
                // dist[v] >= 0 (all reduced cost are positive)
                // dist[v] <= (n-1)C
                Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
                for (int i = g.start[v]; i < g.start[v + 1]; i++) {
                    auto e = g.elist[i];
                    if (!e.cap) continue;
                    // |-dual[e.to] + dual[v]| <= (n-1)C
                    // cost <= C - -(n-1)C + 0 = nC
                    Cost cost = e.cost - dual_dist[e.to].first + dual_v;
                    if (dual_dist[e.to].second - dist_v > cost) {
                        Cost dist_to = dist_v + cost;
                        dual_dist[e.to].second = dist_to;
                        prev_e[e.to] = e.rev;
                        if (dist_to == dist_v) {
                            que_min.push_back(e.to);
                        } else {
                            que.push_back(Q{dist_to, e.to});
                        }
                    }
                }
            }
            if (!vis[t]) {
                return false;
            }

            for (int v = 0; v < _n; v++) {
                if (!vis[v]) continue;
                // dual[v] = dual[v] - dist[t] + dist[v]
                //         = dual[v] - (shortest(s, t) + dual[s] - dual[t]) +
                //         (shortest(s, v) + dual[s] - dual[v]) = - shortest(s,
                //         t) + dual[t] + shortest(s, v) = shortest(s, v) -
                //         shortest(s, t) >= 0 - (n-1)C
                dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second;
            }
            return true;
        };
        Cap flow = 0;
        Cost cost = 0, prev_cost_per_flow = -1;
        std::vector<std::pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
        while (flow < flow_limit) {
            if (!dual_ref()) break;
            Cap c = flow_limit - flow;
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap);
            }
            for (int v = t; v != s; v = g.elist[prev_e[v]].to) {
                auto& e = g.elist[prev_e[v]];
                e.cap += c;
                g.elist[e.rev].cap -= c;
            }
            Cost d = -dual_dist[s].first;
            flow += c;
            cost += c * d;
            if (prev_cost_per_flow == d) {
                result.pop_back();
            }
            result.push_back({flow, cost});
            prev_cost_per_flow = d;
        }
        return result;
    }
};

}  // namespace atcoder





struct RollbackUnionFind {
  vector<int> data;
  stack<pair<int, int> > history;
  int inner_snap;

  RollbackUnionFind(int sz) : inner_snap(0) { data.assign(sz, -1); }

  bool unite(int x, int y) {
    x = find(x), y = find(y);
    history.emplace(x, data[x]);
    history.emplace(y, data[y]);
    if (x == y) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  int find(int k) {
    if (data[k] < 0) return k;
    return find(data[k]);
  }

  int same(int x, int y) { return find(x) == find(y); }

  int size(int k) { return (-data[find(k)]); }

  void undo() {
    data[history.top().first] = history.top().second;
    history.pop();
    data[history.top().first] = history.top().second;
    history.pop();
  }

  void snapshot() { inner_snap = int(history.size() >> 1); }

  int get_state() { return int(history.size() >> 1); }

  void rollback(int state = -1) {
    if (state == -1) state = inner_snap;
    state <<= 1;
    assert(state <= (int)history.size());
    while (state < (int)history.size()) undo();
  }
};

/**
 * @brief RollbackつきUnion Find
 * @docs docs/data-structure/rollback-union-find.md
 */






template <typename T>
struct edge {
  int src, to;
  T cost;

  edge(int _to, T _cost) : src(-1), to(_to), cost(_cost) {}
  edge(int _src, int _to, T _cost) : src(_src), to(_to), cost(_cost) {}

  edge &operator=(const int &x) {
    to = x;
    return *this;
  }

  operator int() const { return to; }
};
template <typename T>
using Edges = vector<edge<T>>;
template <typename T>
using WeightedGraph = vector<Edges<T>>;
using UnweightedGraph = vector<vector<int>>;

// Input of (Unweighted) Graph
UnweightedGraph graph(int N, int M = -1, bool is_directed = false,
                      bool is_1origin = true) {
  UnweightedGraph g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    if (is_1origin) x--, y--;
    g[x].push_back(y);
    if (!is_directed) g[y].push_back(x);
  }
  return g;
}

// Input of Weighted Graph
template <typename T>
WeightedGraph<T> wgraph(int N, int M = -1, bool is_directed = false,
                        bool is_1origin = true) {
  WeightedGraph<T> g(N);
  if (M == -1) M = N - 1;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    cin >> c;
    if (is_1origin) x--, y--;
    g[x].emplace_back(x, y, c);
    if (!is_directed) g[y].emplace_back(y, x, c);
  }
  return g;
}

// Input of Edges
template <typename T>
Edges<T> esgraph(int N, int M, int is_weighted = true, bool is_1origin = true) {
  Edges<T> es;
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    es.emplace_back(x, y, c);
  }
  return es;
}

// Input of Adjacency Matrix
template <typename T>
vector<vector<T>> adjgraph(int N, int M, T INF, int is_weighted = true,
                           bool is_directed = false, bool is_1origin = true) {
  vector<vector<T>> d(N, vector<T>(N, INF));
  for (int _ = 0; _ < M; _++) {
    int x, y;
    cin >> x >> y;
    T c;
    if (is_weighted)
      cin >> c;
    else
      c = 1;
    if (is_1origin) x--, y--;
    d[x][y] = c;
    if (!is_directed) d[y][x] = c;
  }
  return d;
}

/**
 * @brief グラフテンプレート
 * @docs docs/graph/graph-template.md
 */


// 一般のグラフのstからの距離！！！！
// unvisited nodes : d = -1
vector<int> Depth(const UnweightedGraph &g, int start = 0) {
  int n = g.size();
  vector<int> ds(n, -1);
  ds[start] = 0;
  queue<int> q;
  q.push(start);
  while (!q.empty()) {
    int c = q.front();
    q.pop();
    int dc = ds[c];
    for (auto &d : g[c]) {
      if (ds[d] == -1) {
        ds[d] = dc + 1;
        q.push(d);
      }
    }
  }
  return ds;
}

// Depth of Rooted Weighted Tree
// unvisited nodes : d = -1
template <typename T>
vector<T> Depth(const WeightedGraph<T> &g, int start = 0) {
  vector<T> d(g.size(), -1);
  auto dfs = [&](auto rec, int cur, T val, int par = -1) -> void {
    d[cur] = val;
    for (auto &dst : g[cur]) {
      if (dst == par) continue;
      rec(rec, dst, val + dst.cost, cur);
    }
  };
  dfs(dfs, start, 0);
  return d;
}

// Diameter of Tree
// return value : { {u, v}, length }
pair<pair<int, int>, int> Diameter(const UnweightedGraph &g) {
  auto d = Depth(g, 0);
  int u = max_element(begin(d), end(d)) - begin(d);
  d = Depth(g, u);
  int v = max_element(begin(d), end(d)) - begin(d);
  return make_pair(make_pair(u, v), d[v]);
}

// Diameter of Weighted Tree
// return value : { {u, v}, length }
template <typename T>
pair<pair<int, int>, T> Diameter(const WeightedGraph<T> &g) {
  auto d = Depth(g, 0);
  int u = max_element(begin(d), end(d)) - begin(d);
  d = Depth(g, u);
  int v = max_element(begin(d), end(d)) - begin(d);
  return make_pair(make_pair(u, v), d[v]);
}

// nodes on the path u-v ( O(N) )
template <typename G>
vector<int> Path(G &g, int u, int v) {
  vector<int> ret;
  int end = 0;
  auto dfs = [&](auto rec, int cur, int par = -1) -> void {
    ret.push_back(cur);
    if (cur == v) {
      end = 1;
      return;
    }
    for (int dst : g[cur]) {
      if (dst == par) continue;
      rec(rec, dst, cur);
      if (end) return;
    }
    if (end) return;
    ret.pop_back();
  };
  dfs(dfs, u);
  return ret;
}

/**
 * @brief グラフユーティリティ
 * @docs docs/graph/graph-utility.md
 */






struct UnionFind {
  vector<int> data;
  UnionFind(int N) : data(N, -1) {}

  int find(int k) { return data[k] < 0 ? k : data[k] = find(data[k]); }

  int unite(int x, int y) {
    if ((x = find(x)) == (y = find(y))) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    return true;
  }

  // f ... merge function
  template<typename F>
  int unite(int x, int y,const F &f) {
    if ((x = find(x)) == (y = find(y))) return false;
    if (data[x] > data[y]) swap(x, y);
    data[x] += data[y];
    data[y] = x;
    f(x, y);
    return true;
  }

  int size(int k) { return -data[find(k)]; }

  int same(int x, int y) { return find(x) == find(y); }
};

/**
 * @brief Union Find(Disjoint Set Union)
 * @docs docs/data-structure/union-find.md
 */


template <typename T>
T kruskal(int N, Edges<T> &es) {
  sort(begin(es), end(es),
       [&](edge<T> a, edge<T> b) { return a.cost < b.cost; });
  UnionFind uf(N);
  T ret = 0;
  for (edge<T> &e : es) {
    if (uf.same(e.src, e.to)) continue;
    ret += e.cost;
    uf.unite(e.src, e.to);
  }
  return ret;
}





template <typename T>
struct has_cost {
 private:
  template <typename U>
  static auto confirm(U u) -> decltype(u.cost, std::true_type());
  static auto confirm(...) -> std::false_type;

 public:
  enum : bool { value = decltype(confirm(std::declval<T>()))::value };
};

template <typename T>
vector<vector<T>> inverse_tree(const vector<vector<T>>& g) {
  int N = (int)g.size();
  vector<vector<T>> rg(N);
  for (int i = 0; i < N; i++) {
    for (auto& e : g[i]) {
      if constexpr (is_same<T, int>::value) {
        rg[e].push_back(i);
      } else if constexpr (has_cost<T>::value) {
        rg[e].emplace_back(e.to, i, e.cost);
      } else {
        assert(0);
      }
    }
  }
  return rg;
}

template <typename T>
vector<vector<T>> rooted_tree(const vector<vector<T>>& g, int root = 0) {
  int N = (int)g.size();
  vector<vector<T>> rg(N);
  vector<char> v(N, false);
  v[root] = true;
  queue<int> que;
  que.emplace(root);
  while (!que.empty()) {
    auto p = que.front();
    que.pop();
    for (auto& e : g[p]) {
      if (v[e] == false) {
        v[e] = true;
        que.push(e);
        rg[p].push_back(e);
      }
    }
  }
  return rg;
}

/**
 * @brief 根付き木・逆辺からなる木への変換
 */


using namespace Nyaan;

void q() {
  inl(N, M, G);
  Edges<ll> es;

  rep(i, M) {
    inl(u, v, w);
    --u, --v;
    es.emplace_back(u, v, w);
  }
  vvi v;
  rep(i, G) {
    ini(n);
    vi a(n);
    in(a);
    each(x, a)-- x;
    v.push_back(a);
  }
  sort(all(es), [](auto& e1, auto& e2) { return e1.cost < e2.cost; });
  {
    RollbackUnionFind uf(N);
    Edges<ll> nes;
    each(e, es) {
      if (uf.same(e.src, e.to)) {
        continue;
      }
      nes.push_back(e);
      uf.unite(e.src, e.to);
    }
    es = nes;
  }

  WeightedGraph<ll> g(N);
  each(e, es) {
    g[e.src].emplace_back(e.src, e.to, e.cost);
    g[e.to].emplace_back(e.to, e.src, e.cost);
  }
  g = rooted_tree(g);
  trc(g);

  atcoder::mcf_graph<ll, ll> flow(G + 2 * N + 2);
  int S = G + 2 * N + 0;
  int T = G + 2 * N + 1;

  rep(i, G) flow.add_edge(S, i, 1, 0);
  rep(i, G) each(j, v[i]) flow.add_edge(i, G + j, 1, 0);
  rep(i, N) flow.add_edge(G + i, G + N + i, 1, 0);

  ll ans = 0, INF = TEN(9);
  flow.add_edge(G + N + 0, T, 1, INF - INF);
  auto dfs = [&](auto rc, int c) -> void {
    for (auto& d : g[c]) {
      ans += d.cost;
      flow.add_edge(G + N + d, T, 1, INF - d.cost);
      flow.add_edge(G + N + d, G + c, 1, 0);
      rc(rc, d);
    }
  };
  dfs(dfs, 0);

  auto [fl, co] = flow.flow(S, T);
  trc(fl, co);
  if (fl != G) die(-1);
  co = INF * G - co;
  out(ans - (co - TEN(9)));
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}