Subject Pairing

Every February, 10th-grade students at the school select their optional subjects for the next academic year.

Each of the $N$ students (numbered from $0$ to $N - 1$) submits a list of subjects they would like to attend. Students must choose at least one and at most five subjects from a total of $M$ available subjects. The subjects are numbered from $1$ to $M$ (inclusive).

Your task is to help the schedule creator determine which pairs of subjects can be held simultaneously. A pair of subjects $(i, j)$ can be scheduled at the same time if no student has chosen both subjects. Note that the pair $(i, j)$ is considered the same as $(j, i)$.

Input data

The first line contains two integers $N$ and $M$.

Each of the next $N$ lines contains an integer $K_i$, indicating the number of subjects chosen by student $i$, followed by $K_i$ integers $S_{i,j}$, denoting the chosen subjects.

Output data

In the first line you need to write an integer $P$, indicating the number of pairs.

In each of the next $P$ lines you should write two integers, denoting a pair of subjects that can be held simultaneously. You can write the pairs in arbitrary order.

Constraints and clarifications

• $1 \le N \le 100 \ 000$.
• $1 \le M \le 1 \ 000$.
• $1 \le K_i \le 5$ for each $i=0\ldots N-1$.
• $1 \le S_{i, j} \le M$ for each $i=0\ldots N-1$ and $j=0\ldots K_{i}-1$.

Example 1

stdin

4 5
4 1 2 3 4
1 2
2 1 5
3 2 3 1

stdout

3
2 5
3 5
5 4

Explanation

In the first sample case:

• Subjects $(1, 2)$ are selected by students: $0, 3$.
• Subjects $(1, 3)$ are selected by students: $0, 3$.
• Subjects $(1, 4)$ is selected by student: $0$.
• Subjects $(1, 5)$ is selected by student: $2$.
• Subjects $(2, 3)$ are selected by students: $0, 3$.
• Subjects $(2, 4)$ is selected by student: $0$.
• Subjects $(3, 4)$ is selected by student: $0$.

Any other pair of subjects can be held at the same time.

Example 2

stdin

5 8
4 1 2 4 6
4 3 5 7 8
5 4 7 8 2 3
4 2 7 1 4
2 3 4

stdout

9
1 5
6 5
1 3
8 1
2 5
3 6
5 4
6 7
6 8