Problem: Alice, the president of club FCB, wants to build a team for the new volleyball tournament. The team should consist of p players playing in p different positions. She also recognizes the importance of audience support, so she wants to select k people as part of the audience.

There are n people in Byteland. Alice needs to select exactly p players, one for each position, and exactly k members of the audience from this pool of n people. Her ultimate goal is to maximize the total strength of the club.

The i-th of the n persons has an integer a_{i} associated with him — the strength he adds to the club if he is selected as a member of the audience.

For each person i and for each position j, Alice knows s_{i, j} — the strength added by the i-th person to the club if he is selected to play in the j-th position.

Each person can be selected at most once as a player or a member of the audience. You have to choose exactly one player for each position.

Since Alice is busy, she needs you to help her find the maximum possible strength of the club that can be achieved by an optimal choice of players and the audience.

Input

The first line contains 3 integers n,p,k (2 ≤ n ≤ 10^{5}, 1 ≤ p ≤ 7, 1 ≤ k, p+k ≤ n).

The second line contains n integers a_{1},a_{2},…,a_{n}. (1 ≤ a_{i} ≤ 10^{9}).

The i-th of the next n lines contains p integers s_{i, 1}, s_{i, 2}, ..., s_{i, p}. (1 ≤ s_{i,j} ≤ 10^{9})

Output

Print a single integer {res} — the maximum possible strength of the club.

Examples

Input


4 1 2
1 16 10 3
18
19
13
15


Output


44


Input


6 2 3
78 93 9 17 13 78
80 97
30 52
26 17
56 68
60 36
84 55


Output


377


Input


3 2 1
500 498 564
100002 3
422332 2
232323 1


Output


422899

Note

In the first sample, we can select person 1 to play in the 1-st position and persons 2 and 3 as audience members. Then the total strength of the club will be equal to a_{2}+a_{3}+s_{1,1}.

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.util.Arrays;
import java.util.Comparator;
import java.util.Locale;
import java.util.StringTokenizer;

public class Solution2 implements Runnable {
	
	public static final int MAXA = 1000000000;
	public static final int MAXP = 7;
	public static final long INF = 1L * MAXA * MAXP + 1;
	
	private PrintStream out;
	private BufferedReader in;
	private StringTokenizer st;
	
	public void solve() throws IOException {
		long time0 = System.currentTimeMillis();
		
		int n = nextInt();
		int p = nextInt();
		int k = nextInt();
		int[] a = new int[n];
		for (int i = 0; i < n; i++) {
			a[i] = nextInt();
		}
		int[][] s = new int[n][p];
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < p; j++) {
				s[i][j] = nextInt();
			}
		}
		long answer = solve(n, p, k, a, s);
		out.println(answer);
		
		System.err.println("time: " + (System.currentTimeMillis() - time0));
	}
	
	private long solve(int n, int p, int k, int[] a, int[][] s) {
		long result = 0;
		sortPower(n, a, s);
		long sum = 0;
		for (int i = n - k - p; i < n; i++) {
			sum += a[i];
		}
		long[] ansleft = solve(0, n - k - p, p, 0, a, s);
		long[] ansright = solve(n - k, n, p, 1, a, s);
		int allMask = (1 << p) - 1;
		for (int p0 = 0; p0 <= p; p0++) {
			int p1 = p - p0;
			long[] answer0 = solve(n - k - p, n - k - p1, p, 0, a, s);
			long[] answer1 = solve(n - k - p1, n - k, p, 1, a, s);
			answer0 = combine(ansleft, answer0, p);
			answer1 = combine(ansright, answer1, p);
			filter(answer0, p0);
			filter(answer1, p1);
			long[] answerComb = combine(answer0, answer1, p);
			if (answerComb[allMask] != -INF) {
				long answer = answerComb[allMask] + sum;
				if (result < answer) {
					result = answer;
				}
			}
			sum -= a[n - k - p1];
		}
		return result;
	}

	private void filter(long[] answer, int p) {
		for (int mask = 0; mask < answer.length; mask++) {
			if (ones(mask) != p) {
				answer[mask] = -INF;
			}
		}
	}

	private long[] combine(long[] answer0, long[] answer1, int p) {
		long[] result = new long[1 << p];
		Arrays.fill(result, -INF);
		for (int mask0 = 0; mask0 < answer0.length; mask0++) {
			if (answer0[mask0] != -INF) {
				for (int mask1 = 0; mask1 < answer1.length; mask1++) {
					if (answer1[mask1] != -INF) {
						if ((mask0 & mask1) == 0) {
							if (result[mask0 | mask1] < answer0[mask0] + answer1[mask1]) {
								result[mask0 | mask1] = answer0[mask0] + answer1[mask1];
							}
						}
					}
				}
			}
		}
		return result;
	}

	private int ones(int mask) {
		int result = 0;
		while (mask > 0) {
			result++;
			mask = mask & (mask - 1);
		}
		return result;
	}

	private long[] solve(int from, int to, int p, int amult, int[] a, int[][] s) {
		long[] ans = new long[1 << p];
		Arrays.fill(ans, -INF);
		ans[0] = 0;
		for (int i = from; i < to; i++) {
			for (int mask = ans.length - 1; mask >= 0; mask--) {
				if (ans[mask] != -INF) {
					for (int j = 0; j < p; j++) {
						if ((mask & (1 << j)) == 0) {
							long pret = ans[mask] + s[i][j] - amult * a[i];
							int nmask = mask | (1 << j);
							if (ans[nmask] < pret) {
								ans[nmask] = pret;
							}
						}
					}
				}
			}
		}
		return ans;
	}

	private void sortPower(int n, int[] a, int[][] s) {
		Integer[] id = new Integer[n];
		for (int i = 0; i < n; i++) {
			id[i] = i;
		}
		Arrays.sort(id, new Comparator<Integer>() {
			@Override
			public int compare(Integer id0, Integer id1) {
				return Integer.compare(a[id0], a[id1]);
			}
		});
		int[] abuf = new int[n];
		int[][] sbuf = new int[n][];
		for (int i = 0; i < n; i++) {
			abuf[i] = a[id[i]];
			sbuf[i] = s[id[i]];
		}
		for (int i = 0; i < n; i++) {
			a[i] = abuf[i];
			s[i] = sbuf[i];
		}
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}
	
	public long nextLong() throws IOException {
		return Long.parseLong(next());
	}
	
	public int nextInt() throws IOException {
		return Integer.parseInt(next());
	}
	
	public String next() throws IOException {
		while (!st.hasMoreTokens()) {
			String line = in.readLine();
			if (line == null) {
				return null;
			}
			st = new StringTokenizer(line);
		}
		return st.nextToken();
	}
	
	@Override
	public void run() {
		try {
			solve();
			out.close();
		} catch (Throwable e) {
			throw new RuntimeException(e);
		}
	}
	
	public Solution2(String name) throws IOException {
		Locale.setDefault(Locale.US);
		if (name == null) {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintStream(new BufferedOutputStream(System.out));
		} else {
			in = new BufferedReader(new InputStreamReader(new FileInputStream(name + ".in")));
			out = new PrintStream(new BufferedOutputStream(new FileOutputStream(name + ".out")));
		}
		st = new StringTokenizer("");
	}
	
	public static void main(String[] args) throws IOException {
		new Thread(new Solution2(null)).start();
	}
}