H. Standard Graph Problemtime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given a weighted directed graph with n vertices and m edges. Each vertex in the graph can be either highlighted or normal. Initially, all vertices are normal. The cost of the graph is defined as the minimum sum of edge weights that need to be selected so that from each normal vertex one can reach at least one highlighted vertex using the selected edges only. If it is not possible to select the edges, the cost is -1 instead.Your task is to compute the cost of the graph after each of the q queries. The queries can be of two types:   +\;v_i makes vertex v_i highlighted; it is guaranteed that the vertex is normal before the query.  -\;v_i makes vertex v_i normal; it is guaranteed that the vertex is highlighted before the query. Output the cost of the graph after each of the q queries.InputThe first line contains three integers n, m, and q (3 \le n \le 2 \cdot 10^5, 1 \le m, q \le 2 \cdot 10^5) — the number of vertices in the graph, the number of edges, and the number of queries.The next m lines contain the edges of the graph, one edge per line. The i-th line contains three integers u_i, v_i, and c_i (1 \leq u_i, v_i \leq n, u_i \ne v_i, 1 \leq c_i \leq 10^6) — the endpoints of the i-th edge (from u_i to v_i) and its weight (c_i).The next q lines contain the queries, one query per line. The i-th line contains +\;v_i, if it is a query of the first type, and -\;v_i, if it is a query of the second type (1 \leq v_i \leq n).OutputOutput q numbers. The i-th number is the cost of the graph after the first i queries.ExamplesInput
4 5 61 2 12 3 53 2 34 1 82 1 4+ 1- 1+ 3+ 1+ 4+ 2Output
15
-1
14
12
4
0
Input
10 14 108 6 42 5 13 5 41 6 31 3 77 2 16 1 34 10 14 6 55 4 15 8 1010 9 19 5 19 7 6+ 7+ 8- 7+ 10+ 2- 10+ 5- 2- 5+ 3Output
28
24
29
19
18
24
18
19
29
20
NoteIn the first test:   After the first query, it is most profitable to select the edges with numbers 3, 4, 5, their total cost is 15.  After the second query, there are no highlighted vertices, which means that there are no suitable sets of edges, the cost of the graph is -1.  After the third query, it is most profitable to select the edges with numbers 1, 2, 5, their total cost is 14.  After the fourth query, it is most profitable to select the edges with numbers 4 and 5, their total cost is 12.  After the fifth query, it is most profitable to select only edge number 5, its cost is 4.  After the sixth query, all vertices are highlighted and there is no need to select any edges, the cost of the graph is 0. 
4 5 61 2 12 3 53 2 34 1 82 1 4+ 1- 1+ 3+ 1+ 4+ 2
15 -1 14 12 4 0 
['data structures', 'graphs', 'greedy', 'trees', '*3500']