102721: [AtCoder]ABC272 B - Everyone is Friends

Problem Statement

There are $N$ people numbered $1,2,\ldots,N$.

$M$ parties were held. $k_i$ people attended the $i$-th $(1\leq i \leq M)$ party, and they were People $x_{i,1},x_{i,2},\ldots,x_{i,k_i}$.

Determine if every two people attended the same party at least once.

Constraints

• $2\leq N \leq 100$
• $1\leq M \leq 100$
• $2\leq k_i \leq N$
• $1\leq x_{i,1}<x_{i,2}<\ldots < x_{i,k_i}\leq N$
• All values in the input are integers.

Input

The input is given from Standard Input in the following format:

$N$ $M$
$k_1$ $x_{1,1}$ $x_{1,2}$ $\ldots$ $x_{1,k_1}$
$\vdots$
$k_M$ $x_{M,1}$ $x_{M,2}$ $\ldots$ $x_{M,k_M}$

Output

Print Yes if every two people attended the same party at least once; print No otherwise.

Sample Input 1

3 3
2 1 2
2 2 3
2 1 3

Sample Output 1

Yes

Both Person $1$ and Person $2$ attended the $1$-st party.

Both Person $2$ and Person $3$ attended the $2$-nd party.

Both Person $1$ and Person $3$ attended the $3$-rd party.

Therefore, every two people attended the same party at least once, so the answer is Yes.

Sample Input 2

4 2
3 1 2 4
3 2 3 4

Sample Output 2

No

Person $1$ and Person $3$ did not attend the same party, so the answer is No.