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 ... l_c — add 1 to weights of edges with indices l₁, l₂, ..., 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.

Note

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

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

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Dynamic Shortest Path

Examples