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.util.*;
import java.io.*;

public class Main {
    static int parent [];
    static int cost [];
    public static void main (String args []) throws Exception {
        BufferedReader in = new BufferedReader (new InputStreamReader (System.in));
        String read = "";
        while ((read = in.readLine())!=null) {
            int n = Integer.parseInt(read);
            parent = new int [n];
            cost = new int [n];
            for (int i=0; i<n; i++) {
                parent[i] = i;
                cost[i] = Integer.MAX_VALUE;
            }
            in.readLine();
            int app = Integer.parseInt(in.readLine());
            while (app-- > 0) {
                StringTokenizer st = new StringTokenizer (in.readLine());
                int a = Integer.parseInt(st.nextToken())-1;
                int b = Integer.parseInt(st.nextToken())-1;
                int c = Integer.parseInt(st.nextToken());
                if (c<cost[b]) {
                    cost[b] = c;
                    parent[b] = a;
                }
            }
            int total = 0;
            int count = 0;
            for (int i=0; i<n; i++) {
                if (parent[i]==i) {
                    count++;
                    if (count>1) break;
                    continue;
                }
                total += cost[i];
            }
            if (count>1) System.out.println ("-1");
            else System.out.println (total);
        }
    }
}