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:
/*
 ID: govind.3, GhpS, govindpatel
 LANG: JAVA
 TASK: Main 
 */

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {

    /**
     * Min segment Tree takes the minimum number at the root
     */
    class MinSegmentTree {

        /**
         * root: Tree root, balance: input array, rl,rr:
         * rl=0,rr=inputArray.length-1 minTree:segment Tree
         */
        private void initMinTree(int root, int rl, int rr, int[] balance, int[] minTree) {
            if (rl == rr) {
                minTree[root] = balance[rl];
                return;
            }
            int rm = (rl + rr) / 2;
            initMinTree(root * 2 + 1, rl, rm, balance, minTree);
            initMinTree(root * 2 + 2, rm + 1, rr, balance, minTree);
            minTree[root] = Math.min(minTree[root * 2 + 1], minTree[root * 2 + 2]);
        }

        /**
         * minTree:segment tree root:0 rl:0,rr:inputarray.length-1
         * l=queryleft-1(If 1 based index),r = queryright(1-based)
         */
        private int getMin(int[] minTree, int root, int rl, int rr, int l, int r) {
            //l = query left-1, r = query right
            if (l > r) {
                return Integer.MAX_VALUE;
            }
            if (l == rl && r == rr) {
                return minTree[root];
            }
            int rm = (rl + rr) / 2;
            return Math.min(getMin(minTree, root * 2 + 1, rl, rm, l, Math.min(r, rm)),
                    getMin(minTree, root * 2 + 2, rm + 1, rr, Math.max(rm + 1, l), r));
        }
    }
    //dsu next operation
    int[] next;

    private int next(int i) {
        if (next[i] == i) {
            return i;
        }
        return next[i] = next(next[i]);
    }

    //segment tree...
    private void set(int[] t, int ind, int val) {
        ind += (t.length / 2);
        t[ind] = val;
        int curr = 0;
        while (ind > 1) {
            ind >>= 1;
            if (curr == 0) {
                t[ind] = t[ind * 2] | t[ind * 2 + 1];
            } else {
                t[ind] = t[ind * 2] ^ t[2 * ind + 1];
            }
            curr ^= 1;
        }
    }

    //Binary Index tree
    class FenwickTree {

        int[] ft;
        int N;

        FenwickTree(int n) {
            this.N = n;
            ft = new int[N];
        }

        private int lowbit(int x) {
            return x & (-x);
        }

        void update(int pos, int val) {
            while (pos < N) {
                ft[pos] += val;
                pos |= pos + 1;//0-index
            }
        }

        int sum(int pos) {
            int sum = 0;
            while (pos >= 0) {
                sum += ft[pos];
                pos = (pos & (pos + 1)) - 1;
            }
            return sum;
        }

        int rangeSum(int left, int right) {
            return sum(right) - sum(left - 1);
        }
    }

    /**
     * BINARY SEARCH IN FENWICK TREE: l=1, r=N(length), at=sumRequired,
     * letter=TreeIndex(if there are many ft), ft=arrays of FT
     */
    private int binarySearch(int l, int r, int at, int letter, FenwickTree[] ft) {
        while (r - l > 0) {
            int mid = (l + r) / 2;
            int sum = ft[letter].sum(mid);
            if (sum < at) {
                l = mid + 1;
            } else {
                r = mid;
            }
        }
        return l;
    }

    private int[] compress(int[] a) {
        int[] b = new int[a.length];
        for (int i = 0; i < a.length; i++) {
            b[i] = a[i];
        }
        Arrays.sort(b);
        int m = 0;
        for (int i = 0; i < b.length;) {
            int j = i;
            while (j < b.length && b[j] == b[i]) {
                j++;
            }
            b[m++] = b[i];
            i = j;
        }
        for (int i = 0; i < a.length; i++) {
            a[i] = Arrays.binarySearch(b, 0, m, a[i]);
        }
        return a;
    }

    class Dijkstra {

        class Edge implements Comparable<Edge> {

            int to;
            long weight;

            Edge(int t, long w) {
                to = t;
                weight = w;
            }

            public int compareTo(Edge other) {
                return (int) Math.signum(weight - other.weight);
            }
        }
        public static final long INF = (long) 1e17;
        private ArrayList<Edge> adj[];
        private int nodes;
        private long[] dist;
        private int[] prev;
        private boolean[] visited;

        public Dijkstra(int n) {
            nodes = n;
            adj = new ArrayList[nodes];
            dist = new long[nodes];
            prev = new int[nodes];
            visited = new boolean[nodes];
            for (int i = 0; i < nodes; i++) {
                adj[i] = new ArrayList<Edge>();
                dist[i] = INF;
                prev[i] = -1;
            }
        }

        public void add(int u, int v, long cost) {
            adj[u].add(new Edge(v, cost));
        }

        public void dist() {
            //src vertex = 0;
            dist[0] = 0;
            Queue<Edge> q = new PriorityQueue<Edge>();
            q.add(new Edge(0, 0));
            while (!q.isEmpty()) {
                Edge e = q.poll();
                int ind = e.to;
                if (visited[ind]) {
                    continue;
                }
                visited[ind] = true;

                for (Edge edge : adj[ind]) {
                    long newDistance = e.weight + edge.weight;
                    if (newDistance < dist[edge.to]) {
                        dist[edge.to] = newDistance;
                        prev[edge.to] = ind;
                        q.add(new Edge(edge.to, dist[edge.to]));
                    }
                }
            }
        }

        public ArrayList<Integer> getPrevList(int last) {
            ArrayList<Integer> al = new ArrayList<Integer>();
            while (last != -1) {
                al.add(last);
                last = prev[last];
            }
            return al;
        }

        public int[] getPrev() {
            return prev;
        }

        public long[] getDistance() {
            return dist;
        }

        public boolean[] getVisited() {
            return visited;
        }
    }

    class Edge {

        int id, to, cap;
        boolean rev;

        Edge(int to, int id, int cap, boolean rev) {
            this.to = to;
            this.id = id;
            this.cap = cap;
            this.rev = rev;
        }
    }
    int[] p;
    int INF = 1000000000;
    boolean[] was;
    int tot;
    int[] color;
    ArrayList<Integer>[] g;

    private void solve() throws IOException {
        int N = nextInt();//initial node...
        int M = nextInt();//edges...
        int K = nextInt();//after...
        int[] c = new int[K];
        for (int i = 0; i < K; i++) {
            c[i] = nextInt();
        }
        int[] type = new int[N];
        int[] first = new int[K];
        int sum = 0;
        for (int i = 0; i < K; i++) {
            for (int j = sum; j < sum + c[i]; j++) {
                type[j] = i;
            }
            first[i] = sum;
            sum += c[i];
        }
        System.err.println(sum + " " + Arrays.toString(type));
        System.err.println(Arrays.toString(first));
        int[][] dist = new int[K][K];
        for (int i = 0; i < K; i++) {
            for (int j = 0; j < K; j++) {
                dist[i][j] = i == j ? 0 : INF;
            }
        }
        was = new boolean[N];
        tot = 0;
        color = new int[N];
        g = new ArrayList[N];
        for (int i = 0; i < N; i++) {
            g[i] = new ArrayList<Integer>();
        }
        for (int i = 0; i < M; i++) {
            int u = nextInt() - 1;
            int v = nextInt() - 1;
            int cost = nextInt();
            dist[type[u]][type[v]] = Math.min(cost, dist[type[u]][type[v]]);
            dist[type[v]][type[u]] = Math.min(cost, dist[type[v]][type[u]]);
            if (cost == 0) {
                g[u].add(v);
                g[v].add(u);
            }
        }
        for (int i = 0; i < N; i++) {
            if (!was[i]) {
                dfs(i);
                tot++;
            }
        }
        for (int i = 0; i < N; i++) {
            if (color[i] != color[first[type[i]]]) {
                out.println("No");
                return;
            }
        }
        for (int k = 0; k < K; k++) {
            for (int i = 0; i < K; i++) {
                for (int j = 0; j < K; j++) {
                    if (dist[i][j] > dist[i][k] + dist[k][j]) {
                        dist[i][j] = dist[i][k] + dist[k][j];
                    }
                }
            }
        }
        out.println("Yes");
        for (int i = 0; i < K; i++) {
            for (int j = 0; j < K; j++) {
                if (dist[i][j] == INF) {
                    dist[i][j] = -1;
                }
                out.print(dist[i][j] + " ");
            }
            out.println();
        }
    }

    void dfs(int v) {
        color[v] = tot;
        was[v] = true;
        for (int to : g[v]) {
            if (!was[to]) {
                dfs(to);
            }
        }
    }

    void merge(int a, int b) {
        a = get(a);
        b = get(b);
        if (a != b) {
            p[a] = b;
        }
    }

    int get(int a) {
//        if (p[a] == a) {
//            return a;
//        }
        while (p[a] != a) {
            p[a] = p[p[a]];
            a = p[a];
        }
//        return p[a] = get(p[a]);
        return a;
    }

    boolean isSorted(ArrayList<Integer> al) {
        int size = al.size();
        for (int i = 1; i < size - 2; i++) {
            if (al.get(i) > al.get(i + 1)) {
                return false;
            }
        }
        return true;
    }

    /**
     * SHUFFLE: shuffle the array 'a' of size 'N'
     */
    private void shuffle(int[] a, int N) {
        for (int i = 0; i < N; i++) {
            int r = i + (int) ((N - i) * Math.random());
            int t = a[i];
            a[i] = a[r];
            a[r] = t;
        }
    }

    /**
     * TEMPLATE-STUFF: main method, run method - ( fileIO and stdIO ) and
     * various methods for input like nextInt, nextLong, nextToken and
     * nextDouble with some declarations.
     */
    /**
     * For solution to the problem ... see the solve method
     */
    public static void main(String[] args) {
        new Main().run();
    }

    public void run() {
        try {
            in = new BufferedReader(new FileReader("D-large.in"));
            out = new PrintWriter(new BufferedWriter(new FileWriter("Main.out")));
            tok = null;
            solve();
            in.close();
            out.close();
            System.exit(0);
        } catch (IOException e) {//(FileNotFoundException e) {
            try {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(new OutputStreamWriter(System.out));
                tok = null;
                solve();
                in.close();
                out.close();
                System.exit(0);
            } catch (IOException ex) {
                System.out.println(ex.getMessage());
                System.exit(0);
            }
        }
    }

    private String nextToken() throws IOException {
        while (tok == null || !tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    private int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    private long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    private double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    BufferedReader in;
    StringTokenizer tok;
    PrintWriter out;
}