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.

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.

✓	#	Name		✎	Rating↕	Solved↕
	27B	Tournament bitmasks brute force dfs and similar greedy			1300	6k
	17B	Hierarchy dfs and similar dsu greedy shortest paths			1500	6.6k

Problemset