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.*;
import java.util.*;

public class Main {

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw = new PrintWriter(System.out);
		n = sc.nextInt();
		m = sc.nextInt();
		k = sc.nextInt();
		arr = sc.nextIntArr(n);
		rule = new long[n + 1][n];
		memo = sc.nextInt2DArr(n + 1, 1 << n, -1);
		for (int i = 0; i < k; i++) {
			rule[sc.nextInt() - 1][sc.nextInt() - 1] = sc.nextInt();
		}

		System.out.println(dp(n, 0, m));
		pw.close();
	}

	static int n, m, k;
	static int[] arr;
	static long[][] rule;
	static long memo[][];

	static long dp(int idx, int mask, int remainm) {

		if (remainm == 0) {

			return 0;
		}
		if (memo[idx][mask] != -1)
			return memo[idx][mask];

		long ans = 0;
		for (int i = 0; i < n; i++) {
			if ((mask & (1 << i)) == 0) {
				ans = max(ans, rule[idx][i] + arr[i] + dp(i, mask | (1 << i), remainm - 1));
			}
		}
		return memo[idx][mask] = ans;
	}

	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}

		public Scanner(String file) throws FileNotFoundException {
			br = new BufferedReader(new FileReader(file));
		}

		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

		public String nextLine() throws IOException {
			return br.readLine();
		}

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

		public boolean ready() throws IOException {
			return br.ready();
		}

		public int[] nextIntArr(int n) throws IOException {
			int arr[] = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public int[] nextIntArr(int n, int f) throws IOException {
			int arr[] = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = f;
			}
			return arr;
		}

		public int[][] nextInt2DArr(int n, int m) throws IOException {
			int arr[][] = new int[n][m];
			for (int i = 0; i < n; i++) {
				for (int k = 0; k < m; k++) {
					arr[i][k] = nextInt();
				}
			}
			return arr;
		}

		public long[][] nextInt2DArr(int n, int m, int f) throws IOException {
			long arr[][] = new long[n][m];
			for (int i = 0; i < n; i++) {
				for (int k = 0; k < m; k++) {
					arr[i][k] = f;
				}
			}
			return arr;
		}

		public String[] nextStringArr(int n) throws IOException {
			String arr[] = new String[n];
			for (int i = 0; i < n; i++) {
				arr[i] = next();
			}
			return arr;
		}

		public char[] nextCharArr(int n) throws IOException {
			char arr[] = new char[n];
			for (int i = 0; i < n; i++) {
				arr[i] = next().charAt(0);
			}
			return arr;
		}

	}

	public static long max(long a, long b) {
		return a > b ? a : b;
	}

	public static int min(int a, int b) {
		return a < b ? a : b;
	}
}