E. Railway Constructiontime limit per test2.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputBecause the railway system in Gensokyo is often congested, as an enthusiastic engineer, Kawasiro Nitori plans to construct more railway to ease the congestion.There are n stations numbered from 1 to n and m two-way railways in Gensokyo. Every two-way railway connects two different stations and has a positive integer length d. No two two-way railways connect the same two stations. Besides, it is possible to travel from any station to any other using those railways. Among these n stations, station 1 is the main station. You can get to any station from any other station using only two-way railways.Because of the technological limitation, Nitori can only construct one-way railways, whose length can be arbitrary positive integer. Constructing a one-way railway from station u will costs w_u units of resources, no matter where the railway ends. To ease the congestion, Nitori plans that after construction there are at least two shortest paths from station 1 to any other station, and these two shortest paths do not pass the same station except station 1 and the terminal. Besides, Nitori also does not want to change the distance of the shortest path from station 1 to any other station.Due to various reasons, sometimes the cost of building a new railway will increase uncontrollably. There will be a total of q occurrences of this kind of incident, and the i-th event will add additional amount of x_i to the cost of building a new railway from the station k_i.To save resources, before all incidents and after each incident, Nitori wants you to help her calculate the minimal cost of railway construction.InputThe first line contains three integers n, m, and q (1 \le n \le 2 \cdot 10^5, 1 \le m \le 3 \cdot 10^5, 0 \le q \le 2\cdot10^5).The second line contains n integers w_1,w_2,\ldots,w_n (1 \le w_i \le 10^9).Each of the next m lines contains three integers u, v, d (1 \le u,v \le n, u \ne v, 1 \le d \le 10^9), denoting a two-way railway connecting station u and station v, with length d.The i-th of the next q lines contains two integers k_i,x_i (1 \le k_i \le n, 1 \le x_i \le 4 \times 10^8).OutputPrint q+1 lines, and the i-th of these lines contains one integer, denoting the minimal cost of railway construction after the i-1-th incident (especially, the 0-th incident means no incident occurred).ExamplesInput
5 5 1
1 1 1 1 1
1 2 1
2 3 1
2 4 1
3 5 1
4 5 1
1 2
Output
3
9
Input
8 11 0
14 4 16 15 1 3 1 14
4 2 1
1 2 3
7 5 4
2 3 1
8 6 2
8 5 5
5 4 5
7 6 7
3 5 5
1 6 6
8 1 4
Output
46
Input
10 16 8
29 1 75 73 51 69 24 17 1 97
1 2 18
2 3 254
2 4 546
2 5 789
5 6 998
6 7 233
7 8 433
1 9 248
5 10 488
2 6 1787
10 8 1176
3 8 2199
4 8 1907
2 10 1277
4 10 731
9 10 1047
1 11
1 9
8 8
1 3
2 19
9 5
9 4
7 6
Output
34
45
54
54
57
76
96
112
112
NoteIn the second example, Nitori can build railways as follows: 1 \rightarrow 2, 1 \rightarrow 3, 1 \rightarrow 4, 2 \rightarrow 8, and the cost is 14 + 14 + 14 + 4 = 46.
5 5 1
1 1 1 1 1
1 2 1
2 3 1
2 4 1
3 5 1
4 5 1
1 2

3 9 
['brute force', 'constructive algorithms', 'data structures', 'graphs', 'shortest paths', '*3400']