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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.InputMismatchException;
import java.util.Scanner;
import java.util.StringTokenizer;

public class Tem 
{

    static long[][] dp;
    static long[] a;
    static long[][]g;
    static long ans=0;
    static int n,m,k;
    public static void main(String args[])
    {
        FasterScanner s=new FasterScanner();
        n=s.nextInt();
        m=s.nextInt();
        k=s.nextInt();
        dp=new long[n][1<<n];
        g=new long[n][n];
        a =new long[n];
        for(int i=0;i<n;i++)
            a[i]=s.nextLong();
        
        for(int i=0;i<k;i++)
        {
            int x=s.nextInt()-1;
            int y=s.nextInt()-1;
            g[x][y]=s.nextLong();
        }
        //System.out.println("Input taken");
        for(int i=0;i<n;i++)
            {
            dp[i][1<<i]=a[i];
            ans=Math.max(ans,a[i]);
            }
        
        for(int j=0;j<(1<<n);j++)
        {
            for(int n1=0;n1<n;n1++)
                {
                    
                int mask=j;
                //System.out.println(n1+" "+mask);
                long tmp=0;
                if((mask ^ (1<<n1))==0)
                    {
                    dp[n1][mask]=a[n1];
                    //System.out.println("only one hotel "+mask+" "+n1+" "+a[n1]);
                    if(m==1)
                        ans=Math.max(ans,a[n1]);
                    
                    continue;
                    }
                
                for(int i=0;i<32;i++)
                    {
                    tmp+=(mask>>i &(1))%2==1?1:0;
                    //System.out.println(i+" "+tmp+" "+(mask&(1<<i)));
                    }
                boolean b=false;
                if(tmp==1)
                    break;
                
                if(tmp==m)
                    b=true;
                
                
                //System.out.println("before calling "+n+" "+mask+" "+b+" "+tmp);
                tmp=0;
                mask=mask^(1<<n1);
                for(int i=0;i<n;i++)
                {
                    if((mask>>i&(1))%2==1)
                        tmp=Math.max(tmp, dp[i][mask]+g[n1][i]);
                }
                //System.out.println("after calling "+n+" "+mask+" "+b+" "+tmp);
                if(b)
                    {
                    //System.out.println("1");
                    ans=Math.max(ans, a[n1]+tmp);
                    }
                
                dp[n1][j]=a[n1]+tmp;
                //System.out.println(n1+" "+mask+" "+dp[n1][mask]);
                }
        }
//      for(int i=0;i<n;i++)
//          System.out.println(Arrays.toString(dp[i]));
        System.out.println(ans);
    }
    
    public static long gcd(long a, long b) 
    {

        if(a==b)
            return a;
        if(a==0)
            return b;
        if(b==0)
            return a;

        if(a>b)
            return gcd(b,a%b);
        else
            return gcd(a,b%a);
    }

    public static long modPow( long a, long b, long mod )
    {
        long res=1,pow=a;
        while( b>0 )
        {
            if( (b&1)==1 )
            {
                res = (pow*res)%mod;
            }
            pow = (pow*pow)%mod;
            b=b/2;
        }
        return res;
    }
    
    static class nck
    {
        public static long ncr[][];
        
        public nck(long z,long p)//z==maxvalue  p==mod
        {
            generateNCR(z, p);
        }
        
        private static void generateNCR( long z, long p )
        {
            ncr = new long[(int)z+1][(int)z+1];
            ncr[0][0] = 1;
            for(int i=1; i<=z; i++)
            {
                ncr[i][0] = 1;
                ncr[0][i] = 0;
            }
            for(int i=1; i<=z; i++)
            {
                for(int j=1; j<=z; j++)
                {
                    ncr[i][j] = (ncr[i-1][j] + ncr[i-1][j-1]) % p;
                }
            }
        }

        private static long lucas(long n, long k, long p) 
        {
        
            long ans = 1;
            
            while(n>0)
            {
                int N = (int)(n%p);
                int K = (int)(k%p);
                if(K>N)
                    return 0;
                ans *= (ncr[N][K] );
                n /= p;
                k /= p;
            }
            return ans % p;
        }
    }
    
    static class SegTree
    {
        static int seg[];
        static int dp[];
        int n;
        int d;
        public SegTree(int[] arr,int defaul)
        {
            this.dp=arr;
            n=dp.length;
            seg=new int[4*arr.length];
            build(1,0,n);
            this.d=defaul;
        }

        public void build(int id,int l,int r){
            if(r-l<2){
                seg[id]=dp[l];
                return;
            }
            int mid=(l+r)/2;
            build(2*id,l,mid);
            build(2*id+1,mid,r);
            seg[id]=merge(seg[2*id],seg[2*id+1]);
        }

        public int query(int l,int r)
        {
            return givemin(1,l,r,0,n);
        }

        public  int givemin(int id,int x,int y,int l,int r){
            if(x<=l && y>=r){
                return seg[id];
            }
            if(y<=l || r<=x){
                return d;
            }
            int mid=(l+r)/2;
            return merge(givemin(2*id, x, y, l, mid),givemin(2*id+1, x, y, mid, r));
        }

        public int upd(int id,int value)
        {
            return update(1,id,value,0,n);
        }
        public  int update(int id,int p,int value,int l,int r){
            if(r-l<2){
                dp[p]=value;
                seg[id]=value;
                return value;
            }
            int mid=(l+r)/2;
            if(p<mid){
                update(2*id, p, value, l, mid);
                seg[id]=merge(seg[2*id], seg[2*id+1]);
                return seg[id];
            }
            else{
                update(2*id+1, p, value, mid,r);
                seg[id]=merge(seg[2*id+1], seg[2*id]);
                return seg[id];

            }
        }

        public int merge(int l,int r)
        {

            //set initial value
            return l+r;
        }
    }


    static class UF {

        private int[] parent;  // parent[i] = parent of i
        private byte[] rank;   // rank[i] = rank of subtree rooted at i (never more than 31)
        private int count;   
        int[] seg;
        int max;
        // number of components
        public UF(int N) {
            if (N < 0) throw new IllegalArgumentException();
            count = N;
            parent = new int[N];
            rank = new byte[N];
            seg=new int[N];
            for (int i = 0; i < N; i++) {
                parent[i] = i;
                rank[i] = 0;
                seg[i]=1;
            }
            max=1;
        }

        public int find(int p) {
            if (p < 0 || p >= parent.length) throw new IndexOutOfBoundsException();
            while (p != parent[p]) {
                parent[p] = parent[parent[p]];    // path compression by halving
                p = parent[p];
            }
            return p;
        }
        public int count() {
            return count;
        }

        public boolean connected(int p, int q) {
            return find(p) == find(q);
        }

        public boolean union(int p, int q) {
            //    System.out.println("uf "+p+" "+q);
            int rootP = find(p);
            int rootQ = find(q);
            if (rootP == rootQ) return false;

            // make root of smaller rank point to root of larger rank
            if      (rank[rootP] < rank[rootQ])
            {
                parent[rootP] = rootQ;
                seg[rootQ]+=seg[rootP];
                max=Math.max(seg[rootQ],max);
            }
            else if (rank[rootP] > rank[rootQ])
            {
                parent[rootQ] = rootP;
                seg[rootP]+=seg[rootQ];
                max=Math.max(seg[rootP],max);
            }
            else {
                parent[rootQ] = rootP;
                rank[rootP]++;
                seg[rootP]+=seg[rootQ];
                max=Math.max(seg[rootP],max);
            }
            count--;
            return true;
        }

    }



    static class SparseTable
    {
        int[][] st;
        public SparseTable(int[] h){
            int n=h.length;
            int MAX_LOG=(int)Math.ceil(Math.log(n)/Math.log(2))+1;
            st=new int[n][MAX_LOG];
            for (int i = 0; i < n; i++)
                st[i][0] = h[i];
            for (int j = 1; (1 << j) <= n; j++)
            {
                for (int i = 0;( i + (1 << j) - 1 )< n; i++)
                {
                    st[i][j]=Math.max(st[i][j-1],st[i+(1<<(j-1))][j-1]);
                }
            }
        }
        public int query(int l,int r)
        {
            int x=(int )Math.floor((Math.log(r-l+1)/Math.log(2)));
            int ans=Math.max(st[l][x],st[r-(1<<x)+1][x]);
            return ans;
        }

    }

    public static class FasterScanner {
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = System.in.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

        public String nextString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

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

        public long[] nextLongArray(int n) {
            long[] arr = new long[n];
            for (int i = 0; i < n; i++) {
                arr[i] = nextLong();
            }
            return arr;
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }
    }

}