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.