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G - Replace

Score : $600$ points

Problem Statement

You are given two strings $S$ and $T$ consisting of lowercase English letters.

Takahashi starts with the string $S$. He can perform $K$ kinds of operations any number of times in any order.
The $i$-th operation is the following:

Pay a cost of $1$. Then, if the current string contains the character $C_i$, choose one of its occurrences and replace it with the string $A_i$. Otherwise, do nothing.

Find the minimum total cost needed to make the string equal $T$. If it is impossible to do so, print $-1$.

Constraints

• $1\leq |S|\leq |T|\leq 50$
• $1\leq K\leq 50$
• $C_i$ is a, b,$\ldots$, or z.
• $1\leq |A_i|\leq 50$
• $S$, $T$, and $A_i$ are strings consisting of lowercase English letters.
• $C_i\neq A_i$, regarding $C_i$ as a string of length $1$.
• All pairs $(C_i,A_i)$ are distinct.

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Input

Input is given from Standard Input in the following format:

$S$

$T$

$K$

$C_1$ $A_1$

$C_2$ $A_2$

$\vdots$

$C_K$ $A_K$

Output

Print the minimum total cost needed to make the string equal $T$. If it is impossible to do so, print $-1$.

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ab
cbca
3
a b
b ca
a efg

4

Starting with $S=$ab, Takahashi can make $T=$cbca in four operations as follows:

• Replace the $1$-st character a in ab with b (Operation of the $1$-st kind). The string is now bb.
• Replace the $2$-nd character b in bb with ca (Operation of the $2$-nd kind). The string is now bca.
• Replace the $1$-st character b in bca with ca (Operation of the $2$-nd kind). The string is now caca.
• Replace the $2$-nd character a in caca with b (Operation of the $1$-st kind). The string is now cbca.

Each operation incurs a cost of $1$, for a total of $4$, which is the minimum possible.

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a
aaaaa
2
a aa
a aaa

2

Two operations a $\to$ aaa $\to$ aaaaa incur a cost of $2$, which is the minimum possible.

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a
z
1
a abc

-1

No sequence of operations makes $T=$z from $S=$a.