Problem: Boy Valera likes strings. And even more he likes them, when they are identical. That's why in his spare time Valera plays the following game. He takes any two strings, consisting of lower case Latin letters, and tries to make them identical. According to the game rules, with each move Valera can change one arbitrary character Ai in one of the strings into arbitrary character Bi, but he has to pay for every move a particular sum of money, equal to Wi. He is allowed to make as many moves as he needs. Since Valera is a very economical boy and never wastes his money, he asked you, an experienced programmer, to help him answer the question: what minimum amount of money should Valera have to get identical strings. 

Input

The first input line contains two initial non-empty strings s and t, consisting of lower case Latin letters. The length of each string doesn't exceed 105. The following line contains integer n (0 ≤ n ≤ 500) — amount of possible changings. Then follow n lines, each containing characters Ai and Bi (lower case Latin letters) and integer Wi (0 ≤ Wi ≤ 100), saying that it's allowed to change character Ai into character Bi in any of the strings and spend sum of money Wi.

Output

If the answer exists, output the answer to the problem, and the resulting string. Otherwise output -1 in the only line. If the answer is not unique, output any.

Examples

Input

uayd
uxxd
3
a x 8
x y 13
d c 3


Output

21
uxyd


Input

a
b
3
a b 2
a b 3
b a 5


Output

2
b


Input

abc
ab
6
a b 4
a b 7
b a 8
c b 11
c a 3
a c 0


Output

-1

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;
import java.util.stream.*;

@SuppressWarnings("unchecked")
public class P33B {

  final static int SUB_ADD = 'a';
  final static int SIZE = 'z' - SUB_ADD + 1;
  final static int MAX = Integer.MAX_VALUE >> 2;

  public void run() throws Exception {
    String s = next(), t = next();
    if (s.length() != t.length()) {
      println(-1);
      return;
    }

    int [][] ab = new int [SIZE][SIZE];
    for (int [] a : ab) { Arrays.fill(a, MAX); }
    for (int n = nextInt(); n > 0; n--) {
      int a = next().charAt(0) - SUB_ADD, b = next().charAt(0) - SUB_ADD, v = nextInt();
      if (a != b) {
        ab[a][b] = Math.min(ab[a][b], v);
      }
    }

    for (boolean done = false; !done;) {
      done = true;
      for (int a = 0; a < SIZE; a++) {
        for (int b = 0; b < SIZE; b++) {
          if (ab[a][b] < MAX) {
            for (int c = 0; c < SIZE; c++) {
              if ((c != a) && (c != b) && ((ab[a][b] + ab[b][c]) < ab[a][c])) {
                ab[a][c] = ab[a][b] + ab[b][c];
                done = false;
              }
            }
          }
        }
      }
    }

    for (int a = 0; a < SIZE; ab[a][a] = 0, a++);

    int av = 0;
    StringBuilder as = new StringBuilder(s.length());
    for (int i = 0; i < s.length(); i++) {
      int a = s.charAt(i) - SUB_ADD, b = t.charAt(i) - SUB_ADD, c = 0, m = MAX;

      for (int j = 0; j < SIZE; j++) {
        if ((ab[a][j] + ab[b][j]) < m) {
          m = ab[a][j] + ab[b][j];
          c = j;
        }
      }

      if (m >= MAX) {
        println(-1);
        return;
      }

      av += m;
      as.append((char)(c + SUB_ADD));
    }

    println(av + "\n" + as);
  }

  public static void main(String... args) throws Exception {
    br = new BufferedReader(new InputStreamReader(System.in));
    pw = new PrintWriter(new BufferedOutputStream(System.out));
    new P33B().run();
    br.close();
    pw.close();
    System.err.println("\n[Time : " + (System.currentTimeMillis() - startTime) + " ms]");
  }

  static long startTime = System.currentTimeMillis();
  static BufferedReader br;
  static PrintWriter pw;
  StringTokenizer stok;

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

  void print(byte b) { print("" + b); }
  void print(int i) { print("" + i); }
  void print(long l) { print("" + l); }
  void print(double d) { print("" + d); }
  void print(char c) { print("" + c); }
  void print(Object o) {
    if (o instanceof int[]) { print(Arrays.toString((int [])o));
    } else if (o instanceof long[]) { print(Arrays.toString((long [])o));
    } else if (o instanceof char[]) { print(Arrays.toString((char [])o));
    } else if (o instanceof byte[]) { print(Arrays.toString((byte [])o));
    } else if (o instanceof short[]) { print(Arrays.toString((short [])o));
    } else if (o instanceof boolean[]) { print(Arrays.toString((boolean [])o));
    } else if (o instanceof float[]) { print(Arrays.toString((float [])o));
    } else if (o instanceof double[]) { print(Arrays.toString((double [])o));
    } else if (o instanceof Object[]) { print(Arrays.toString((Object [])o));
    } else { print("" + o); }
  }
  void print(String s) { pw.print(s); }
  void println() { println(""); }
  void println(byte b) { println("" + b); }
  void println(int i) { println("" + i); }
  void println(long l) { println("" + l); }
  void println(double d) { println("" + d); }
  void println(char c) { println("" + c); }
  void println(Object o) { print(o); println(); }
  void println(String s) { pw.println(s); }
  int nextInt() throws IOException { return Integer.parseInt(nextToken()); }
  long nextLong() throws IOException { return Long.parseLong(nextToken()); }
  double nextDouble() throws IOException { return Double.parseDouble(nextToken()); }
  char nextChar() throws IOException { return (char) (br.read()); }
  String next() throws IOException { return nextToken(); }
  String nextLine() throws IOException { return br.readLine(); }
  int [] readInt(int size) throws IOException {
    int [] array = new int [size];
    for (int i = 0; i < size; i++) { array[i] = nextInt(); }
    return array;
  }
  long [] readLong(int size) throws IOException {
    long [] array = new long [size];
    for (int i = 0; i < size; i++) { array[i] = nextLong(); }
    return array;
  }
  double [] readDouble(int size) throws IOException {
    double [] array = new double [size];
    for (int i = 0; i < size; i++) { array[i] = nextDouble(); }
    return array;
  }
  String [] readLines(int size) throws IOException {
    String [] array = new String [size];
    for (int i = 0; i < size; i++) { array[i] = nextLine(); }
    return array;
  }

  int gcd(int a, int b) {
    if (a == 0) return Math.abs(b); if (b == 0) return Math.abs(a);
    a = Math.abs(a); b = Math.abs(b);
    int az = Integer.numberOfTrailingZeros(a), bz = Integer.numberOfTrailingZeros(b);
    a >>>= az; b >>>= bz;
    while (a != b) {
      if (a > b) { a -= b; a >>>= Integer.numberOfTrailingZeros(a); }
            else { b -= a; b >>>= Integer.numberOfTrailingZeros(b); }
    }
    return (a << Math.min(az, bz));
  }

  long gcd(long a, long b) {
    if (a == 0) return Math.abs(b); if (b == 0) return Math.abs(a);
    a = Math.abs(a); b = Math.abs(b);
    int az = Long.numberOfTrailingZeros(a), bz = Long.numberOfTrailingZeros(b);
    a >>>= az; b >>>= bz;
    while (a != b) {
      if (a > b) { a -= b; a >>>= Long.numberOfTrailingZeros(a); }
            else { b -= a; b >>>= Long.numberOfTrailingZeros(b); }
    }
    return (a << Math.min(az, bz));
  }
}