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 ai is ready to become a supervisor of employee bi at extra cost ci». The qualification qj of each employee is known, and for each application the following is true: qai > qbi. 

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 qj (0 ≤ qj ≤ 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: ai, bi and ci (1 ≤ ai, bi ≤ n, 0 ≤ ci ≤ 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 qai > qbi.

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.
import java.io.*;

public class Hierarchy {
    public static void main(String[] args) throws IOException {
        BufferedReader readInput = new BufferedReader(new InputStreamReader(System.in));

        int employees = Integer.parseInt(readInput.readLine());
        String qualifications = readInput.readLine(); // qualifications are actually never needed
        int numApplicants = Integer.parseInt(readInput.readLine());

        int[] hierarchy = new int[employees+1];
        for (int i = 1; i <= employees; i++) {
            hierarchy[i] = -1;
        }
        
        while(numApplicants-- > 0) {
            String[] application = readInput.readLine().split(" ");
            int a = Integer.parseInt(application[0]);
            int b = Integer.parseInt(application[1]);
            int cost = Integer.parseInt(application[2]);
            if(hierarchy[b] == -1) {
                hierarchy[b] = cost;
            }
            else {
                hierarchy[b] = Math.min(hierarchy[b], cost);
            }
        }
        
        int count = 0;
        int total = 0;
        for (int i = 1; i <= employees; i++) {
            if (hierarchy[i] == -1) {
                if(count++ > 1) {
                    System.out.println(-1);
                    return;
                }
            }
            else {
                total += hierarchy[i];
            }
        }
        if(count != 1) {
            System.out.println(-1);
        }
        else {
            System.out.println(total);
        }
    }

}
