A lock contains \(n\) wheels where each wheel contains \(k_i\) numbers in a specific order. You have \(m\) sets and each set contains \(c_i\) wheels. At each move, you select a set and turn all of its wheels one unit up.

For example, this is the wheel \(s_1, s_2 , s_3, s_4\) and after one move, it becomes \(s_2, s_3, s_4, s_1\).

Your task is to unlock the lock.

Input format

The first line contains \(n\) denoting the number of the wheels and \(m\) denoting the number of the sets.
For the next \(n\) lines, each line contains \(k_i\) denoting the size of the \(i^{th}\) wheel and \(k_i\) numbers (\(s_1, s_2, s_3 \dots s_{k_i}\)) denoting the numbers of the \(i^{th}\) wheel.
Note: In each wheel, the initial state of the wheel is \(s_1\).
Each of the next \(m\) lines contains \(c_i\) denoting the size of the \(i^{th}\) set and \(c_i\) numbers (\(a_1, a_2, a_3 \dots a_{c_i}\)) denoting the wheels of the \(i^{th}\) list.
The last line contains \(n\) numbers showing the password of the lock.

Output format

The first line contain the \(ans \) denoting the number of moves. Each of the next \(m\) lines contains \(u_i\) denoting the number of the moves with the \(i^{th}\) set.

Constraints

\(1 \leq n \leq 10 \space 000\)

\(1 \leq m \leq 100 \space 000\)

\(1 \leq k_i \leq 40 \space 000\)

\(1 \leq s_i, p_i \leq 10^9\)

\(1 \leq c_i, a_i \leq n\)

\(\displaystyle\sum_{i=1}^{n} k_i \leq 40 \space 000\)

\(\displaystyle\sum_{i=1}^{m} c_i \leq 400 \space 000\)

Note: For each input, at least one solution exist.