Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. String Problem

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBoy 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 *A*_{i} in one of the strings into arbitrary character *B*_{i}, but he has to pay for every move a particular sum of money, equal to *W*_{i}. 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 10^{5}. The following line contains integer *n* (0 ≤ *n* ≤ 500) — amount of possible changings. Then follow *n* lines, each containing characters *A*_{i} and *B*_{i} (lower case Latin letters) and integer *W*_{i} (0 ≤ *W*_{i} ≤ 100), saying that it's allowed to change character *A*_{i} into character *B*_{i} in any of the strings and spend sum of money *W*_{i}.

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

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jun/21/2019 01:21:39 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|