CF843D.Dynamic Shortest Path

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 $l_{1},l_{2},...,l_{c}$ .

The first line of input data contains integers $n$ , $m$ , $q$ ( $1<=n,m<=10^{5}$ , $1<=q<=2000$ ) — 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 $a_{i}$ , $b_{i}$ , $c_{i}$ ( $1<=a_{i},b_{i}<=n$ , $0<=c_{i}<=10^{9}$ ) — 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 $10^{6}$ .

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.

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

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