Find the Double Class

$M$ members of Cycom are all taking the same courses this year, and the number of courses they take is $N$. Even for the same course there are several sections, and only people in the same section attend the lecture together. Surprisingly, all $M$ members are in different sections, so no pair of them attends even one class together.

To escape loneliness, the Cycom members decide to create $K$ imaginary friends. Each friend will take the same set of courses as the Cycom members, and their sections can be chosen freely. The goal is to make every person attend every course together with an imaginary friend.

$K$ can be chosen freely, but an imaginary friend must not outnumber real humans, so $K \le M$ must hold. Also, for each Cycom member, there must not exist an imaginary friend whose course section numbers all match exactly.

The first line gives the number of courses $N$ and the number of members $M$.

From the second line to the $M+1$-th line, the $i+1$-th line gives the integers $A_{i, 1}, A_{i,2}, \cdots, A_{i, N}$. $A_{i, j}$ is the section number of course $j$ taken by member $i$.

The first line prints the number of imaginary friends $K$.

From the second line to the $K+1$-th line, the $i+1$-th line prints the integers $B_{i,1}, B_{i,2}, \cdots, B_{i,N}$. $B_{i,j}$ is the section number of course $j$ taken by imaginary friend $i$.

• $2 \le N \le 1000$
• $2 \le M \le 1000$
• For all $1 \le i \le N$ and $1 \le x < y \le M$, $A_{x,i} \neq A_{y,i}$. (In other words, the Cycom members have no overlapping sections in any course.)
• $1 \le A_{i,j} \le M$
• $0 \le K \le M$
• $1 \le B_{i,j} \le M$
• For all $1 \le i \le M$ and $1 \le j \le K$, there must exist at least one $x$ with $1 \le x \le N$ such that $A_{i, x} \neq B_{j, x}$. (In other words, for each Cycom member, there must not exist an imaginary friend whose course section numbers all match exactly.)
• For all $1 \le i \le M$ and $1 \le j \le N$, there must exist at least one $x$ with $1 \le x \le K$ such that $A_{i, j} = B_{x, j}$. (In other words, each Cycom member must be able to attend every course together with at least one imaginary friend.)