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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;
import java.util.StringTokenizer;

public class H {
    public static void main(String[] args) {
        FastScanner scan=new FastScanner();
        n=scan.nextInt();
        pl=scan.nextInt();
        aud=scan.nextInt();

        ppl=new guy[n];
        playerpts=new long[n][pl];

        for(int i=0;i<n;i++) {
            ppl[i]=new guy(i,scan.nextLong());
        }
        Arrays.sort(ppl);

        for(int i=0;i<n;i++) {
            for(int j=0;j<pl;j++) {
                playerpts[i][j]=scan.nextLong();
            }
        }
        dp=new long[1<<pl][n];
        for(long[] d:dp) Arrays.fill(d,-1);
        System.out.println(go(0,0));
    }

    public static long go(int at, int mask) {
        if(at==n) {
            return 0L;
        }
        if(dp[mask][at]!=-1) return dp[mask][at];

        long res=0L;
        if(at+(pl-Integer.bitCount(mask))<n) {
            if(at+(pl-Integer.bitCount(mask))<n-aud) {
                //we must ignore him
                res=Math.max(res,go(at+1,mask));
            }

            else {
                //must be audience
                res=Math.max(res,ppl[at].apts+go(at+1,mask));
            }
        }
        for(int i=0;i<pl;i++) {
            if((mask&(1<<i))>0) continue;
            int newmask=mask|(1<<i);

            res=Math.max(res,playerpts[ppl[at].id][i]+go(at+1,newmask));
        }

        //if you are too close to the end to send away any more people, you must accept your current guy as an audience member
        //it never makes sense to accept audience members before this point because they're sorted

        //this is all assuming you are able to send people away at this point


        return dp[mask][at]=res;
    }
    static class guy implements Comparable<guy> {
        int id;
        long apts;

        guy(int id, long apts) {
            this.id=id;
            this.apts=apts;
        }

        @Override
        public int compareTo(guy o) {
            if(apts==o.apts) return id-o.id;
            return Long.compare(apts,o.apts);
        }
    }
    static guy[] ppl;
    static long[][] playerpts;
    static int n,pl,aud;
    static long[][] dp;

    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            try	{
                br = new BufferedReader(new InputStreamReader(System.in));
                st = new StringTokenizer(br.readLine());
            } catch (Exception e){e.printStackTrace();}
        }

        public String next() {
            if (st.hasMoreTokens())	return st.nextToken();
            try {st = new StringTokenizer(br.readLine());}
            catch (Exception e) {e.printStackTrace();}
            return st.nextToken();
        }

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

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

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

        public String nextLine() {
            String line = "";
            if(st.hasMoreTokens()) line = st.nextToken();
            else try {return br.readLine();}catch(IOException e){e.printStackTrace();}
            while(st.hasMoreTokens()) line += " "+st.nextToken();
            return line;
        }
    }
}
/*
3 1 1
100 1 3
1000
100
10
*/