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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Comparator;
import java.util.PriorityQueue;

public class Main {

    static class PotentialBoss implements Comparable<PotentialBoss>{
        int boss;
        int cost;
        PotentialBoss(int b, int c){
            boss = b;
            cost = c;
        }

        @Override
        public int compareTo(PotentialBoss potentialBoss) {
            if(cost == potentialBoss.cost)
                return 0;
            return cost < potentialBoss.cost ? -1 : 1;
        }
    }
    public static void main(String[] args) throws IOException {

        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        // I don't think qualifications are relevant and I know these types of problems will sometimes throw irrelevant information at you.
        String qualifications = in.readLine();
        int m = Integer.parseInt(in.readLine());
        ArrayList<PriorityQueue<PotentialBoss>> potentialBossList = new ArrayList<PriorityQueue<PotentialBoss>>(n + 1);
        for(int i = 0; i < n + 1; i++)
            potentialBossList.add(new PriorityQueue<PotentialBoss>());
        String[] line;
        for(int i = 1; i <= m; i++){
            line = in.readLine().split(" ");
            int a = Integer.parseInt(line[0]);
            int b = Integer.parseInt(line[1]);
            int c = Integer.parseInt(line[2]);
            potentialBossList.get(b).add(new PotentialBoss(a, c));
        }
        // Check for validity
        int ceoIndex = 0;
        for(int i = 1; i <=n; i++){
            if(potentialBossList.get(i).size() == 0) {
                if (ceoIndex != 0) {
                    System.out.println(-1);
                    return;
                }
                else
                    ceoIndex = i;
            }
        }
        // Add up the minimum bosses for each employee. Since we checked that there is only one employee with no bosses, this should work.
        int totalCost = 0;
        for(int i = 1; i <= n; i++){
            if(i != ceoIndex)
                totalCost += potentialBossList.get(i).poll().cost;
        }
        System.out.println(totalCost);

    }
}
