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.*;
import java.util.*;

public class D {

	static int[] a;
	static int[][] s;
	static int n, p;
	static long INF = (long) 1e18;
	static Integer[] indices;
	static long[][][] memo1;
	static long[][] memo2;

//	static long dp(int idx, int msk, int skip) {
//		if (idx == n) {
//			return msk == 0 && skip == 0 ? 0 : -INF;
//		}
//		if (memo1[skip][msk][idx] != -1)
//			return memo1[skip][msk][idx];
//		int tmpIdx = indices[idx];
//		long ans = dp(idx + 1, msk, skip) + a[tmpIdx];
//		if (skip > 0)
//			ans = dp(idx + 1, msk, skip - 1);
//		for (int pos = 0; pos < p; pos++) {
//			if ((msk & 1 << pos) == 0)
//				continue;
//			ans = Math.max(ans, dp(idx + 1, msk & ~(1 << pos), skip) + s[tmpIdx][pos]);
//		}
//		return memo1[skip][msk][idx] = ans;
//
//	}
	static int[] log;

	static void dp(int start) {

		for (int skip = 0; skip <= p; skip++)
			for (int msk = 0; msk < 1 << p; msk++)
				memo1[n & 1][skip][msk] = msk == 0 && skip == 0 ? 0 : -INF;
		for (int idx = n - 1; idx >= start; idx--) {
			int curr = idx & 1;
			int tmpIdx = indices[idx];
			long currA = a[tmpIdx];
			for (int skip = 0; skip <= p; skip++)
				for (int msk = 0; msk < 1 << p; msk++) {
					long ans = memo1[curr ^ 1][skip][msk] + currA;
					if (skip > 0)
						ans = Math.max(ans, memo1[curr ^ 1][skip - 1][msk]);
					int tmpMsk = msk;
					while (tmpMsk > 0) {
						int pos = tmpMsk & -tmpMsk;
						tmpMsk -= pos;
						pos = log[pos];
						ans = Math.max(ans, memo1[curr ^ 1][skip][msk & ~(1 << pos)] + s[tmpIdx][pos]);

					}

					memo1[curr][skip][msk] = ans;
				}
		}

	}

	static long dp2(int idx, int msk, int end) {
		if (idx == end)
			return msk == 0 ? 0 : -INF;
		if (memo2[msk][idx] != -1)
			return memo2[msk][idx];
		int tmpIdx = indices[idx];

		long ans = dp2(idx + 1, msk, end);
		int tmpMsk = msk;
		while (tmpMsk > 0) {
			int pos = tmpMsk & -tmpMsk;
			tmpMsk -= pos;
			pos = log[pos];
			ans = Math.max(ans, dp2(idx + 1, msk & ~(1 << pos), end) + s[tmpIdx][pos]);

		}

		return memo2[msk][idx] = ans;

	}

	public static void main(String[] args) throws IOException {
		Scanner sc = new Scanner();
		PrintWriter out = new PrintWriter(System.out);
		n = sc.nextInt();
		p = sc.nextInt();
		int k = sc.nextInt();
		memo2 = new long[1 << p][n];
		for (long[] x : memo2)
			Arrays.fill(x, -1);
		memo1 = new long[2][p + 1][1 << p];
		log = new int[1 << p];
		for (int i = 0; i < p; i++)
			log[1 << i] = i;
		indices = new Integer[n];
		a = new int[n];
		s = new int[n][p];
		for (int i = 0; i < n; i++) {
			a[i] = sc.nextInt();
			indices[i] = i;
		}
		for (int i = 0; i < n; i++)
			for (int j = 0; j < p; j++)
				s[i][j] = sc.nextInt();
		Arrays.sort(indices, Comparator.comparingInt(i -> a[i]));
		int suffix = n - p - k;
		long ans = -INF;
		int all = 1 << p;

		all--;
		dp(suffix);

		for (int msk = 0; msk < 1 << p; msk++) {
			int skip = p - Integer.bitCount(msk);
			ans = Math.max(ans, memo1[suffix & 1][skip][msk] + dp2(0, all ^ msk, suffix));
		}
		out.println(ans);
		out.close();

	}

	static class Scanner {
		BufferedReader br;
		StringTokenizer st;

		Scanner() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

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

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

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

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

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

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

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

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

	}

	static void sort(int[] a) {
		shuffle(a);
		Arrays.sort(a);
	}

	static void shuffle(int[] a) {
		int n = a.length;
		Random rand = new Random();
		for (int i = 0; i < n; i++) {
			int tmpIdx = rand.nextInt(n);
			int tmp = a[i];
			a[i] = a[tmpIdx];
			a[tmpIdx] = tmp;
		}
	}

}