Problem: You are given a weighted directed graph, consisting of n vertices and m edges. You should answer q queries of two types:

  * 1 v — find the length of shortest path from vertex 1 to vertex v. 
  * 2 c l1 l2 ... lc — add 1 to weights of edges with indices l1, l2, ..., lc. 

Input

The first line of input data contains integers n, m, q (1 ≤ n, m ≤ 105, 1 ≤ q ≤ 2000) — the number of vertices and edges in the graph, and the number of requests correspondingly.

Next m lines of input data contain the descriptions of edges: i-th of them contains description of edge with index i — three integers ai, bi, ci (1 ≤ ai, bi ≤ n, 0 ≤ ci ≤ 109) — the beginning and the end of edge, and its initial weight correspondingly.

Next q lines of input data contain the description of edges in the format described above (1 ≤ v ≤ n, 1 ≤ lj ≤ m). It's guaranteed that inside single query all lj are distinct. Also, it's guaranteed that a total number of edges in all requests of the second type does not exceed 106.

Output

For each query of first type print the length of the shortest path from 1 to v in a separate line. Print -1, if such path does not exists.

Examples

Input

3 2 9
1 2 0
2 3 0
2 1 2
1 3
1 2
2 1 1
1 3
1 2
2 2 1 2
1 3
1 2


Output

1
0
2
1
4
2


Input

5 4 9
2 3 1
2 4 1
3 4 1
1 2 0
1 5
1 4
2 1 2
2 1 2
1 4
2 2 1 3
1 4
2 1 4
1 4


Output

-1
1
2
3
4

Note

The description of changes of the graph in the first sample case:

<image>

The description of changes of the graph in the second sample case:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
static struct FastInput {
  static constexpr int BUF_SIZE = 1 << 20;
  char buf[BUF_SIZE];
  size_t chars_read = 0;
  size_t buf_pos = 0;
  FILE* in = stdin;
  char cur = 0;
  inline char get_char() {
    if (buf_pos >= chars_read) {
      chars_read = fread(buf, 1, BUF_SIZE, in);
      buf_pos = 0;
      buf[0] = (chars_read == 0 ? -1 : buf[0]);
    }
    return cur = buf[buf_pos++];
  }
  inline void tie(int) {}
  inline explicit operator bool() { return cur != -1; }
  inline static bool is_blank(char c) { return c <= ' '; }
  inline bool skip_blanks() {
    while (is_blank(cur) && cur != -1) {
      get_char();
    }
    return cur != -1;
  }
  inline FastInput& operator>>(char& c) {
    skip_blanks();
    c = cur;
    return *this;
  }
  inline FastInput& operator>>(string& s) {
    if (skip_blanks()) {
      s.clear();
      do {
        s += cur;
      } while (!is_blank(get_char()));
    }
    return *this;
  }
  template <typename T>
  inline FastInput& read_integer(T& n) {
    n = 0;
    if (skip_blanks()) {
      int sign = +1;
      if (cur == '-') {
        sign = -1;
        get_char();
      }
      do {
        n += n + (n << 3) + cur - '0';
      } while (!is_blank(get_char()));
      n *= sign;
    }
    return *this;
  }
  template <typename T>
  inline typename enable_if<is_integral<T>::value, FastInput&>::type operator>>(
      T& n) {
    return read_integer(n);
  }
  inline FastInput& operator>>(__int128& n) { return read_integer(n); }
  template <typename T>
  inline typename enable_if<is_floating_point<T>::value, FastInput&>::type
  operator>>(T& n) {
    n = 0;
    if (skip_blanks()) {
      string s;
      (*this) >> s;
      sscanf(s.c_str(), "%lf", &n);
    }
    return *this;
  }
} fast_input;
static struct FastOutput {
  static constexpr int BUF_SIZE = 1 << 20;
  char buf[BUF_SIZE];
  size_t buf_pos = 0;
  static constexpr int TMP_SIZE = 1 << 20;
  char tmp[TMP_SIZE];
  FILE* out = stdout;
  inline void put_char(char c) {
    buf[buf_pos++] = c;
    if (buf_pos == BUF_SIZE) {
      fwrite(buf, 1, buf_pos, out);
      buf_pos = 0;
    }
  }
  ~FastOutput() { fwrite(buf, 1, buf_pos, out); }
  inline FastOutput& operator<<(char c) {
    put_char(c);
    return *this;
  }
  inline FastOutput& operator<<(const char* s) {
    while (*s) {
      put_char(*s++);
    }
    return *this;
  }
  inline FastOutput& operator<<(const string& s) {
    for (int i = 0; i < (int)s.size(); i++) {
      put_char(s[i]);
    }
    return *this;
  }
  template <typename T>
  inline char* integer_to_string(T n) {
    char* p = tmp + TMP_SIZE - 1;
    if (n == 0) {
      *--p = '0';
    } else {
      bool is_negative = false;
      if (n < 0) {
        is_negative = true;
        n = -n;
      }
      while (n > 0) {
        *--p = (char)('0' + n % 10);
        n /= 10;
      }
      if (is_negative) {
        *--p = '-';
      }
    }
    return p;
  }
  template <typename T>
  inline typename enable_if<is_integral<T>::value, char*>::type stringify(T n) {
    return integer_to_string(n);
  }
  inline char* stringify(__int128 n) { return integer_to_string(n); }
  template <typename T>
  inline typename enable_if<is_floating_point<T>::value, char*>::type stringify(
      T n) {
    sprintf(tmp, "%.17f", n);
    return tmp;
  }
  template <typename T>
  inline FastOutput& operator<<(const T& n) {
    auto p = stringify(n);
    for (; *p != 0; p++) {
      put_char(*p);
    }
    return *this;
  }
} fast_output;
const int N = 1e6 + 3;
vector<int> inq[N];
int main() {
  ios::sync_with_stdio(false);
  fast_input.tie(0);
  int n, m, q;
  fast_input >> n >> m >> q;
  vector<vector<int>> edge(n + 1);
  vector<tuple<int, int, int>> edges;
  for (int i = 0; i < m; i++) {
    int u, v, w;
    fast_input >> u >> v >> w;
    edges.emplace_back(u, v, w);
    edge[u].emplace_back(i);
  }
  priority_queue<pair<long long, int>> pq;
  const long long inf = 1e18;
  vector<long long> d(n + 1, inf);
  d[1] = 0;
  pq.emplace(d[1], 1);
  while ((int)pq.size()) {
    auto x = pq.top();
    pq.pop();
    if (-x.first != d[x.second]) continue;
    int v = x.second;
    for (auto& x : edge[v]) {
      int u = get<1>(edges[x]);
      if (d[u] > d[v] + get<2>(edges[x])) {
        d[u] = d[v] + get<2>(edges[x]);
        pq.emplace(-d[u], u);
      }
    }
  }
  vector<int> add(m);
  for (int i = 0; i < m; i++) {
    auto& x = edges[i];
    add[i] = get<2>(x) - (d[get<1>(x)] - d[get<0>(x)]);
  }
  int up = 0;
  while (q--) {
    int type;
    fast_input >> type;
    if (type == 1) {
      int v;
      fast_input >> v;
      if (up) {
        vector<int> dist(n + 1, (int)1e9);
        dist[1] = 0;
        inq[0].emplace_back(1);
        for (int i = 0; i <= up; i++) {
          for (int j = 0; j < (int)inq[i].size(); j++) {
            int v = inq[i][j];
            if (dist[v] != i) continue;
            for (auto& x : edge[v]) {
              int u = get<1>(edges[x]);
              if (dist[u] > dist[v] + add[x]) {
                dist[u] = dist[v] + add[x];
                if (dist[u] <= up) inq[dist[u]].emplace_back(u);
              }
            }
          }
          inq[i].clear();
        }
        for (int i = 1; i <= n; i++) d[i] = min(d[i] + dist[i], inf);
        for (int i = 0; i < m; i++) {
          auto& x = edges[i];
          add[i] -= (dist[get<1>(x)] - dist[get<0>(x)]);
        }
        up = 0;
      }
      if (d[v] != inf)
        fast_output << d[v] << "\n";
      else
        fast_output << "-1\n";
    } else {
      int foo;
      fast_input >> foo;
      for (int i = 0; i < foo; i++) {
        int x;
        fast_input >> x;
        --x;
        add[x]++;
      }
      up += foo;
    }
  }
}