Problem: When Kefa came to the restaurant and sat at a table, the waiter immediately brought him the menu. There were n dishes. Kefa knows that he needs exactly m dishes. But at that, he doesn't want to order the same dish twice to taste as many dishes as possible. 

Kefa knows that the i-th dish gives him ai units of satisfaction. But some dishes do not go well together and some dishes go very well together. Kefa set to himself k rules of eating food of the following type — if he eats dish x exactly before dish y (there should be no other dishes between x and y), then his satisfaction level raises by c. 

Of course, our parrot wants to get some maximal possible satisfaction from going to the restaurant. Help him in this hard task!

Input

The first line of the input contains three space-separated numbers, n, m and k (1 ≤ m ≤ n ≤ 18, 0 ≤ k ≤ n * (n - 1)) — the number of dishes on the menu, the number of portions Kefa needs to eat to get full and the number of eating rules.

The second line contains n space-separated numbers ai, (0 ≤ ai ≤ 109) — the satisfaction he gets from the i-th dish.

Next k lines contain the rules. The i-th rule is described by the three numbers xi, yi and ci (1 ≤ xi, yi ≤ n, 0 ≤ ci ≤ 109). That means that if you eat dish xi right before dish yi, then the Kefa's satisfaction increases by ci. It is guaranteed that there are no such pairs of indexes i and j (1 ≤ i < j ≤ k), that xi = xj and yi = yj.

Output

In the single line of the output print the maximum satisfaction that Kefa can get from going to the restaurant.

Examples

Input

2 2 1
1 1
2 1 1


Output

3


Input

4 3 2
1 2 3 4
2 1 5
3 4 2


Output

12

Note

In the first sample it is best to first eat the second dish, then the first one. Then we get one unit of satisfaction for each dish and plus one more for the rule.

In the second test the fitting sequences of choice are 4 2 1 or 2 1 4. In both cases we get satisfaction 7 for dishes and also, if we fulfill rule 1, we get an additional satisfaction 5.

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.PrintWriter;
import java.util.Arrays;

public class CF2_321D {
  
  static Reader sc = new Reader();
  static PrintWriter out = new PrintWriter(System.out);
  
  static int n;
  static int m;
  static long[] sat;
  static long[][] bonus;
  
  static long[][] dp; // [Mask of eaten before][Number of last eaten] 
  
  static long get(int mask, int last) {
    if (dp[mask][last] != -1) {
      return dp[mask][last];
    }
    if (mask == 0) {
      dp[mask][last] = sat[last];
      return sat[last];
    }
    
    for (int i = 0; i < n; i++) {
      if ((mask & (1 << i)) != 0) {
        // Find best submask with current as last
        long sub = get(mask ^ (1 << i), i);
        // Add last
        dp[mask][last] = Math.max(dp[mask][last], sub + bonus[i][last] + sat[last]);
      }
    }
    
    return dp[mask][last];
  }
  
  public static void main(String[] args) throws IOException {
    n = sc.nextInt();
    m = sc.nextInt();
    int k = sc.nextInt();
    
    sat = new long[n];
    
    for (int i = 0; i < n; i++) {
      sat[i] = sc.nextLong();
    }
    
    bonus = new long[n][n];
    for (int i = 0; i < k; i++) {
      bonus[sc.nextInt() - 1][sc.nextInt() - 1] = sc.nextLong();
    }
    
    dp =  new long[1 << n][n];
    
    for (int i = 0; i < 1 << n; i++) {
      Arrays.fill(dp[i], -1);
    }
    
    long best = 0;
    
    for (int mask = 0; mask < (1 << n); mask++) {
      for (int last = 0; last < n; last++) {
        if (Integer.bitCount(mask) == m - 1 && ( (mask & (1 <<last)) == 0) ) {
          best = Math.max(best, get(mask,last));
        }
      }
    }
    
    out.println(best);
    out.close();
  }
  
  static class Reader {
    boolean consume = false; final private int BUFFER_SIZE = 1 << 12;private byte[] buffer;private int bufferPointer, bytesRead;private boolean reachedEnd = false;public Reader() {buffer = new byte[BUFFER_SIZE];bufferPointer = 0;bytesRead = 0;}
    public boolean hasNext() {return !reachedEnd;} private void fillBuffer() throws IOException {bytesRead = System.in.read(buffer, bufferPointer = 0, BUFFER_SIZE);if (bytesRead == -1) {buffer[0] = -1;reachedEnd = true;}}
    private void consumeSpaces() throws IOException {while (read() <= ' ' && reachedEnd == false);bufferPointer--;} private byte read() throws IOException {if (bufferPointer == bytesRead) {fillBuffer();}return buffer[bufferPointer++];}
    public String next() throws IOException {StringBuilder sb = new StringBuilder();consumeSpaces();byte c = read();do {sb.append((char) c);} while ((c = read()) > ' ');if (consume) {consumeSpaces();};if (sb.length() == 0) {return null;}return sb.toString();}
    public String nextLine() throws IOException {StringBuilder sb = new StringBuilder();byte c;boolean read = false;while ((c = read()) != -1) {if (c == '\n') {read = true;break;}if (c >= ' ')sb.append((char) c);}if (!read) {return null;}return sb.toString();}
    public int nextInt() throws IOException {consumeSpaces();int ret = 0;      byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}
    public long nextLong() throws IOException {consumeSpaces();long ret = 0;byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10L + c - '0';} while ((c = read()) >= '0' && c <= '9');if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}
    public double nextDouble() throws IOException {consumeSpaces();double ret = 0;double div = 1;byte c = read();boolean neg = (c == '-');if (neg) {c = read();}do {ret = ret * 10 + c - '0';} while ((c = read()) >= '0' && c <= '9');if (c == '.') {while ((c = read()) >= '0' && c <= '9') {ret += (c - '0') / (div *= 10);}}if (consume) {consumeSpaces();}if (neg) {return -ret;}return ret;}    public int[] nextIntArray(int n) throws IOException {int[] a = new int[n];for (int i = 0; i < n; i++) {a[i] = nextInt();}return a;}
    public int[][] nextIntMatrix(int n, int m) throws IOException {int[][] grid = new int[n][m];for (int i = 0; i < n; i++) {grid[i] = nextIntArray(m);}return grid;}
    public char[][] nextCharacterMatrix(int n) throws IOException {char[][] a = new char[n][];for (int i = 0; i < n; i++) {a[i] = next().toCharArray();}return a;}
    public void close() throws IOException {if (System.in == null) {return;} else {System.in.close();}}
  }
  
  static void print(int[] A) {for (int i = 0; i < A.length; i++) {if (i != 0) {out.print(' ');}out.print(A[i]);}out.println();}
  static <T> void print(Iterable<T> A) {int i = 0;for (T act : A) {if (i != 0) {out.print(' ');}out.print(act);i++;}out.println();}
  static void printPlus1(Iterable<Number> A) {int i = 0;for (Number act : A) {if (i != 0) {out.print(' ');}out.print(act.longValue() + 1L);i++;}out.println();  }
  static void debug(Object... o) {System.err.println(Arrays.deepToString(o));}
  
  /*
  long s = System.currentTimeMillis();
  debug(System.currentTimeMillis() - s + "ms");
   */
}