Data Structures Are Really the Best

After learning about stacks, Chanwoo fell in love with the data structures course.

Having resolved to devote himself to the data structures course alone, Chanwoo piled the textbooks of his other $N$ courses carelessly in a corner of his room as $M$ stacks. But as the midterm exam approached, he could no longer study only data structures, so he decided to tidy up the abandoned textbooks of his other courses and arrange them in numerical order.

The $N$ textbooks are numbered from $1$ to $N$. Chanwoo can take only the textbook at the top of each stack, and since he must lay them out in the order he takes them, he has to take textbook $1$, then $2$, ..., then $N - 1$, then $N$ to arrange them in numerical order. Chanwoo says he will give up studying for the midterm if he cannot arrange the textbooks correctly. Write a program that tells him whether he can arrange them in numerical order.

The first line gives the number of textbooks $N$ and the number of textbook stacks $M$.

From the second line, $2\times M$ lines give information about each stack.

For the $i$-th stack, the first line gives the number of textbooks $k_{i}$ in the stack, and the second line gives $k_{i}$ integers separated by spaces.

Each integer is a textbook number, given starting from the textbook at the bottom.

Each integer from $1$ to $N$ appears exactly once as a textbook number.

Print Yes if the textbooks can be taken in the correct order, and No otherwise.

• $1 \leq M \leq N \leq 200\,000$
• $1 \leq k_i$
• The sum of all $k_{i}$ is always $N$.