Vasya plays the LionAge II. He was bored of playing with a stupid computer, so he installed this popular MMORPG, to fight with his friends. Vasya came up with the name of his character — non-empty string s, consisting of a lowercase Latin letters. However, in order not to put up a front of friends, Vasya has decided to change no more than k letters of the character name so that the new name sounded as good as possible. Euphony of the line is defined as follows: for each pair of adjacent letters x and y (x immediately precedes y) the bonus c(x, y) is added to the result. Your task is to determine what the greatest Euphony can be obtained by changing at most k letters in the name of the Vasya's character.

Input

The first line contains character's name s and an integer number k (0 ≤ k ≤ 100). The length of the nonempty string s does not exceed 100. The second line contains an integer number n (0 ≤ n ≤ 676) — amount of pairs of letters, giving bonus to the euphony. The next n lines contain description of these pairs «x y c», which means that sequence xy gives bonus c (x, y — lowercase Latin letters,  - 1000 ≤ c ≤ 1000). It is guaranteed that no pair x y mentioned twice in the input data.

Output

Output the only number — maximum possible euphony оf the new character's name.

Examples

Input

winner 4
4
s e 7
o s 8
l o 13
o o 8


Output

36

Input

abcdef 1
5
a b -10
b c 5
c d 5
d e 5
e f 5


Output

20

Note

In the first example the most euphony name will be looser. It is easy to calculate that its euphony is 36.
import java.io.*;
import java.math.*;
import java.util.*;
import static java.lang.Math.*;
public class C {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    String line;
    StringTokenizer st;
    StringBuilder buf = new StringBuilder();
    public C() throws Exception {
        line = br.readLine();
        st = new StringTokenizer(line);
        String name = st.nextToken();
        int l = Integer.parseInt(st.nextToken());

        int[][] g = new int[26][26];

        int m = Integer.parseInt(br.readLine());

        for (int i=0;i<m;i++) {
            line = br.readLine();
            st = new StringTokenizer(line);
            int x = st.nextToken().charAt(0)-'a';
            int y = st.nextToken().charAt(0)-'a';
            int c = Integer.parseInt(st.nextToken());
            g[x][y] = c;
        }

        int[][][] dp = new int[name.length()][101][676];
        for (int i=0;i<name.length();i++) {
            for (int j=0;j<=l;j++)  {
                for (int k=0;k<676;k++) {
                    dp[i][j][k] = -1<<28;
                }
            }
        }

        for (int i=0;i<26;i++) {
            int d = 1;
            if(name.charAt(0)-'a'==i)
                d = 0;
            dp[0][d][i] = 0;
        }

        // debug(dp[0][1]['e'-'a']);

        for (int i=1;i<name.length();i++) {
            for (int p=0;p<26;p++) {
                for (int c=0;c<26;c++) {
                    int d = 1;
                    if(name.charAt(i)-'a'==c) 
                        d = 0;
                    for (int j=d;j<=l;j++) {
                        dp[i][j][c] = max(dp[i][j][c], dp[i-1][j-d][p]+g[p][c]);
                    }
                }
            }
        }

        int ans = -1<<26;
        for (int j=0;j<=l;j++) {
            for (int c=0;c<26;c++) {
                ans = max(ans, dp[name.length()-1][j][c]);
            }
        }

        
        buf.append(ans).append('\n');

        System.out.print(buf);
    }

    public static void main(String[] args) throws Exception { // {{{
        new C();
    } // }}}
    public static void debug(Object... arr) { // {{{
        System.err.println(Arrays.deepToString(arr));
    } // }}}
}
