Two sequences of integers A: A₁ A₂ ... A_n and B: B₁ B₂ ... B_m and a set of rewriting rules of the form "x₁ x₂ ... x_k → y" are given. The following transformations on each of the sequences are allowed an arbitrary number of times in an arbitrary order independently.</p>

• Rotate: Moving the first element of a sequence to the last. That is, transforming a sequence c₁ c₂ ... c_p to c₂ ... c_p c₁.
• Rewrite: With a rewriting rule "x₁ x₂ ... x_k → y", transforming a sequence c₁ c₂ ... c_i x₁ x₂ ... x_k d₁ d₂ ... d_j to c₁ c₂ ... c_i y d₁ d₂ ... d_j.

Your task is to determine whether it is possible to transform the two sequences A and B into the same sequence. If possible, compute the length of the longest of the sequences after such a transformation.

입력 형식

The input consists of multiple datasets. Each dataset has the following form.</p>

n m r
A1 A2 ... An
B1 B2 ... Bm
R1
...
Rr

The first line of a dataset consists of three positive integers n, m, and r, where n (n ≤ 25) is the length of the sequence A, m (m ≤ 25) is the length of the sequence B, and r (r ≤ 60) is the number of rewriting rules. The second line contains n integers representing the n elements of A. The third line contains m integers representing the m elements of B. Each of the last r lines describes a rewriting rule in the following form.

k x1 x2 ... xk y

The first k is an integer (2 ≤ k ≤ 10), which is the length of the left-hand side of the rule. It is followed by k integers x₁ x₂ ... x_k, representing the left-hand side of the rule. Finally comes an integer y, representing the right-hand side.

All of A₁, .., A_n, B₁, ..., B_m, x₁, ..., x_k, and y are in the range between 1 and 30, inclusive.

A line "0 0 0" denotes the end of the input.

출력 형식

For each dataset, if it is possible to transform A and B to the same sequence, print the length of the longest of the sequences after such a transformation. Print -1 if it is impossible.

예제 입력

3 3 3
1 2 3
4 5 6
2 1 2 5
2 6 4 3
2 5 3 1
3 3 2
1 1 1
2 2 1
2 1 1 2
2 2 2 1
7 1 2
1 1 2 1 4 1 2
4
3 1 4 1 4
3 2 4 2 4
16 14 5
2 1 2 2 1 3 2 1 3 2 2 1 1 3 1 2
2 1 3 1 1 2 3 1 2 2 2 2 1 3
2 3 1 3
3 2 2 2 1
3 2 2 1 2
3 1 2 2 2
4 2 1 2 2 2
0 0 0

예제 출력

2
-1
1
9