Problem Statement

315-san's job is to paste images into Excel and run batch files exactly as instructed.
This job is monotonous and tedious, and 315-san had always wanted to do more advanced work.
One day, 315-san realized that this job can be represented by at most $N$ operation sequences $S$.
The operation sequence $S_i$ is a sequence of length $d_i$, and each term of this sequence corresponds one-to-one to an operation of an input device, such as a key.
Since 315-san enjoys competitive programming, 315-san decided to create a macro that automatically completes the work no matter what work is assigned.

A macro is defined as an integer sequence $A$ consisting of integers between $0$ and $2000$, inclusive.
First, define a sequence $M$ of length $N$ whose terms are all $0$.
Next, for $n=0, 1, 2, \dots, $, perform the following operations in order.

• Find all $j$ such that $A_{(n \mod |A|) + 1} = S_{j, (M_j \mod |S_j|) + 1}$.
• Then, for all of those $j$, add $1$ to $M_j$.

• There exists an $n$ such that $n$ is a multiple of $|A|$ $-1$, that is, at the moment exactly the end of the macro has been read, all the work is in the accomplished state.

Input

$N$
$d_1 \ S_{1,1} \ \cdots \ S_{1, d_1}$
$\vdots$
$d_N \ S_{N, 1} \ \cdots \ S_{N, d_N}$

• $1 \leq N \leq 2000$
• $1 \leq d_i \leq 2000$
• $0 \leq S_{i, j} < \sum_{i=1}^{N} d_i \leq 2000$
• All inputs are integers.

Output

If no macro $A$ satisfying the condition exists, print 0 on the first line.
Otherwise, first print the length of the macro $|A| \leq 2000$ on the first line.
Then, print the terms of $A$ separated by spaces on the second line.
In either case, print a newline at the end.

Sample

1
3 1 2 1

3
1 2 1

3
3 1 1 2
1 1
5 3 1 1 1 2

4
3 1 1 2

2
2 1 2
2 2 1

0