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B. Hierarchy

time limit per test

2 secondsmemory limit per test

64 megabytesinput

standard inputoutput

standard outputNick'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*_{ai} > *q*_{bi}.

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} ≤ 10^{6})— 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} ≤ 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*_{ai} > *q*_{bi}.

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.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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