B. Hierarchy
time limit per test
2 seconds
memory limit per test
64 megabytes
input
standard input
output
standard output

Nick's company employed n people. Now Nick needs to build a tree hierarchy of «supervisor-surbodinate» relations in the company (this is to say that each employee, except one, has exactly one supervisor). There are m applications written in the following form: «employee a i is ready to become a supervisor of employee b i at extra cost c i». The qualification q j of each employee is known, and for each application the following is true: q a i > q b i.

Would you help Nick calculate the minimum cost of such a hierarchy, or find out that it is impossible to build it.

Input

The first input line contains integer n (1 ≤ n ≤ 1000) — amount of employees in the company. The following line contains n space-separated numbers q j (0 ≤ q j ≤ 106)— the employees' qualifications. The following line contains number m (0 ≤ m ≤ 10000) — amount of received applications. The following m lines contain the applications themselves, each of them in the form of three space-separated numbers: a i, b i and c i (1 ≤ a i, b i ≤ n, 0 ≤ c i ≤ 106). Different applications can be similar, i.e. they can come from one and the same employee who offered to become a supervisor of the same person but at a different cost. For each application q a i > q b i.

Output

Output the only line — the minimum cost of building such a hierarchy, or -1 if it is impossible to build it.

Examples
Input
4
7 2 3 1
4
1 2 5
2 4 1
3 4 1
1 3 5
Output
11
Input
3
1 2 3
2
3 1 2
3 1 3
Output
-1
Note

In the first sample one of the possible ways for building a hierarchy is to take applications with indexes 1, 2 and 4, which give 11 as the minimum total cost. In the second sample it is impossible to build the required hierarchy, so the answer is -1.