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>
const int inf = 0x3f3f3f3f, Inf = 0x7fffffff;
const long long INF = 0x3f3f3f3f3f3f3f3f;
__inline__ __attribute__((always_inline)) unsigned int rnd() {
  static unsigned int seed = 416;
  return seed ^= seed >> 5, seed ^= seed << 17, seed ^= seed >> 13;
}
template <typename _Tp>
_Tp gcd(const _Tp &a, const _Tp &b) {
  return (!b) ? a : gcd(b, a % b);
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) _Tp abs(const _Tp &a) {
  return a >= 0 ? a : -a;
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) _Tp max(const _Tp &a, const _Tp &b) {
  return a < b ? b : a;
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) _Tp min(const _Tp &a, const _Tp &b) {
  return a < b ? a : b;
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) void chmax(_Tp &a, const _Tp &b) {
  (a < b) && (a = b);
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) void chmin(_Tp &a, const _Tp &b) {
  (b < a) && (a = b);
}
template <typename _Tp>
__inline__ __attribute__((always_inline)) void read(_Tp &x) {
  char ch(getchar());
  bool f(false);
  while (!isdigit(ch)) f |= ch == 45, ch = getchar();
  x = ch & 15, ch = getchar();
  while (isdigit(ch)) x = (((x << 2) + x) << 1) + (ch & 15), ch = getchar();
  f && (x = -x);
}
template <typename _Tp, typename... Args>
__inline__ __attribute__((always_inline)) void read(_Tp &t, Args &...args) {
  read(t);
  read(args...);
}
template <typename _Tp, typename... Args>
__inline__ __attribute__((always_inline)) _Tp min(const _Tp &a, const _Tp &b,
                                                  const Args &...args) {
  return a < b ? min(a, args...) : min(b, args...);
}
template <typename _Tp, typename... Args>
__inline__ __attribute__((always_inline)) _Tp max(const _Tp &a, const _Tp &b,
                                                  const Args &...args) {
  return a < b ? max(b, args...) : max(a, args...);
}
__inline__ __attribute__((always_inline)) int read_str(char *s) {
  char ch(getchar());
  while (ch == ' ' || ch == '\r' || ch == '\n') ch = getchar();
  char *tar = s;
  *tar = ch, ch = getchar();
  while (ch != ' ' && ch != '\r' && ch != '\n' && ch != EOF)
    *(++tar) = ch, ch = getchar();
  return tar - s + 1;
}
const int N = 100005;
struct edge {
  int v, nxt, w;
} c[N << 1];
int front[N], edge_cnt;
__inline__ __attribute__((always_inline)) void addedge(int u, int v, int w) {
  c[++edge_cnt] = (edge){v, front[u], w};
  front[u] = edge_cnt;
}
struct node {
  int u;
  long long d;
  __inline__ __attribute__((always_inline)) bool operator<(
      const node &o) const {
    return d > o.d;
  }
};
std::priority_queue<node> Q;
long long dis[N];
void dij(int s) {
  memset(dis, 63, sizeof(dis));
  dis[s] = 0, Q.push((node){s, 0});
  while (!Q.empty()) {
    node x = Q.top();
    Q.pop();
    if (x.d != dis[x.u]) continue;
    for (int i = front[x.u]; i; i = c[i].nxt) {
      int v = c[i].v;
      if (dis[x.u] + c[i].w < dis[v]) {
        dis[v] = dis[x.u] + c[i].w;
        Q.push((node){v, dis[v]});
      }
    }
  }
}
int add[N];
std::vector<int> q[N];
int main() {
  int n, m, _;
  read(n, m, _);
  int opt, x, y, z;
  for (int i = 1; i <= m; ++i) {
    read(x, y, z);
    addedge(x, y, z);
  }
  dij(1);
  while (_--) {
    read(opt, x);
    if (opt == 1) {
      if (dis[x] < 1e18)
        printf("%lld\n", dis[x]);
      else
        printf("-1\n");
    } else {
      for (int i = 1; i <= x; ++i) read(y), ++c[y].w;
      memset(add, 63, sizeof(add));
      add[1] = 0;
      for (int i = 0; i <= n; ++i) q[i].clear();
      q[0].push_back(1);
      for (int i = 0; i <= x && i <= n; ++i) {
        while (!q[i].empty()) {
          int it = q[i].back();
          q[i].pop_back();
          if (add[it] != i) continue;
          for (int _ = front[it]; _; _ = c[_].nxt) {
            int v = c[_].v, tmp = dis[it] + add[it] + c[_].w - dis[v];
            if (add[v] > tmp && tmp <= x && tmp <= n)
              add[v] = tmp, q[tmp].push_back(v);
          }
        }
      }
      for (int i = 1; i <= n; ++i)
        if (add[i] < inf) dis[i] += add[i];
    }
  }
  return 0;
}