Problem: Dima took up the biology of bacteria, as a result of his experiments, he invented k types of bacteria. Overall, there are n bacteria at his laboratory right now, and the number of bacteria of type i equals ci. For convenience, we will assume that all the bacteria are numbered from 1 to n. The bacteria of type ci are numbered from <image> to <image>.

With the help of special equipment Dima can move energy from some bacteria into some other one. Of course, the use of such equipment is not free. Dima knows m ways to move energy from some bacteria to another one. The way with number i can be described with integers ui, vi and xi mean that this way allows moving energy from bacteria with number ui to bacteria with number vi or vice versa for xi dollars.

Dima's Chef (Inna) calls the type-distribution correct if there is a way (may be non-direct) to move energy from any bacteria of the particular type to any other bacteria of the same type (between any two bacteria of the same type) for zero cost.

As for correct type-distribution the cost of moving the energy depends only on the types of bacteria help Inna to determine is the type-distribution correct? If it is, print the matrix d with size k × k. Cell d[i][j] of this matrix must be equal to the minimal possible cost of energy-moving from bacteria with type i to bacteria with type j.

Input

The first line contains three integers n, m, k (1 ≤ n ≤ 105; 0 ≤ m ≤ 105; 1 ≤ k ≤ 500). The next line contains k integers c1, c2, ..., ck (1 ≤ ci ≤ n). Each of the next m lines contains three integers ui, vi, xi (1 ≤ ui, vi ≤ 105; 0 ≤ xi ≤ 104). It is guaranteed that <image>.

Output

If Dima's type-distribution is correct, print string «Yes», and then k lines: in the i-th line print integers d[i][1], d[i][2], ..., d[i][k] (d[i][i] = 0). If there is no way to move energy from bacteria i to bacteria j appropriate d[i][j] must equal to -1. If the type-distribution isn't correct print «No».

Examples

Input

4 4 2
1 3
2 3 0
3 4 0
2 4 1
2 1 2


Output

Yes
0 2
2 0


Input

3 1 2
2 1
1 2 0


Output

Yes
0 -1
-1 0


Input

3 2 2
2 1
1 2 0
2 3 1


Output

Yes
0 1
1 0


Input

3 0 2
1 2


Output

No

Solution (in JAVA):

Solution:
/**
 * ******* Created  on 20/12/19 2:19 AM*******
 */

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

public class D400 implements Runnable {

    private static final int MAX = (int) (1E5 + 5);
    private static final int MOD = (int) (1E9 + 7);
    private static final long Inf = (long) (1E14 + 10);
    long[][] dp = new long[505][505];
    int n,m,k;
    int[] c = new int[MAX];
    boolean[] visited = new boolean[MAX];
    List<Integer>[] adj = new List[MAX];
    TreeSet<Integer>[] has = new TreeSet[MAX];
    private void solve() throws IOException {
        n= reader.nextInt();
        m = reader.nextInt();
        k = reader.nextInt();
        int ind =0 ;
        for(int i =0;i<n;i++)
            adj[i] = new ArrayList<>();

        for(int i =0;i<k;i++){
            int x = reader.nextInt();
            while(x-- > 0 )c[ind++] = i;
        }
        for(int i=0;i<k;i++)
            for(int j =0;j<k;j++){
              dp[i][j] = ((i==j) ?0 : Inf );
            }
        for(int i =0;i<m;i++){
            int a = reader.nextInt();a--;
            int b = reader.nextInt();b--;
            int w = reader.nextInt();
            if( w == 0){
                adj[a].add(b);
                adj[b].add(a);
            }
            dp[c[a]][c[b]] = Math.min(dp[c[a]][c[b]], w);
            dp[c[b]][c[a]] = Math.min(dp[c[b]][c[a]], w);
        }
        int id =0;
        for(int i=0;i<k;i++)
            has[i]= new TreeSet<>();
        for(int i =0;i<n;i++){
            if(!visited[i]){
                DFS(i, ++id);
            }
        }

        boolean flag =true;
        for(int i=0;i<k;i++)
            if(has[i].size() >1)
                flag =false;
         if(!flag){
             writer.println("No");
             return;
         }

         writer.println("Yes");

         flyodALgo();
         for(int i =0;i<k;i++){
             for(int j=0;j<k;j++)
                 if(dp[i][j]==Inf)
                     writer.print("-1 ");
                 else
                    writer.print(dp[i][j]+" ");
             writer.println();
         }
    }

    private void flyodALgo() {
        for(int i=0;i<k;i++){
            for(int j=0;j<k;j++){
                for(int l=0;l<k;l++){
                    dp[j][l] = Math.min(dp[j][l], dp[j][i] +dp[i][l]);
                }
            }
        }
    }

    private void DFS(int v, int id) {
        if(visited[v])return;
        visited[v] = true;
        has[c[v]].add(id);
        for(int u : adj[v]){
            DFS(u,id);
        }
    }

    public static void main(String[] args) throws IOException {
        try (Input reader = new StandardInput(); PrintWriter writer = new PrintWriter(System.out)) {
            new D400().run();
        }
    }

    StandardInput reader;
    PrintWriter writer;

    @Override
    public void run() {
        try {
            reader = new StandardInput();
            writer = new PrintWriter(System.out);
            solve();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }

    interface Input extends Closeable {
        String next() throws IOException;

        default int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        default long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        default double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        default int[] readIntArray() throws IOException {
            return readIntArray(nextInt());
        }

        default int[] readIntArray(int size) throws IOException {
            int[] array = new int[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        default long[] readLongArray(int size) throws IOException {
            long[] array = new long[size];
            for (int i = 0; i < array.length; i++) {
                array[i] = nextLong();
            }
            return array;
        }
    }

    private static class StandardInput implements Input {
        private final BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        private StringTokenizer stringTokenizer;

        @Override
        public void close() throws IOException {
            reader.close();
        }

        @Override
        public String next() throws IOException {
            if (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                stringTokenizer = new StringTokenizer(reader.readLine());
            }
            return stringTokenizer.nextToken();
        }
    }
}