D. Dynamic Shortest Path
time limit per test
10 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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 l 1 l 2 ... l c — add 1 to weights of edges with indices l 1, l 2, ..., l c.
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 a i, b i, c i (1 ≤ a i, b i ≤ n, 0 ≤ c i ≤ 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 ≤ l j ≤ m). It's guaranteed that inside single query all l j 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 91 2 02 3 02 1 21 31 22 1 11 31 22 2 1 21 31 2
Output
102142
Input
5 4 92 3 12 4 13 4 11 2 01 51 42 1 22 1 21 42 2 1 31 42 1 41 4
Output
-11234
Note

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

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