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 \le n \le 1000~) — amount of employees in the company. The following line contains n space-separated numbers ~q_j~ (~0 \le q_j \le 10^6~)— the employees' qualifications. The following line contains number m (~0 \le m \le 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 \le a_i, b_i \le n, 0 \le c_i \le 10^6~). 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.

This problem was taken from Codeforces problem 17B.