Statement

You are given $n$ sets $S_1,S_2,\ldots,S_n$, where each element in the sets is an integer between $1$ and $m$.

You want to choose some of the sets (possibly none or all), such that every integer between $1$ and $m$ is included in at least one of the chosen sets.

You have to determine whether there exist at least three ways to choose the sets.

Input

The first line of each test case contains two integers $n$ and $m$ ($2 \leqslant n \leqslant 5\cdot 10^4$, $1\leqslant m \leqslant 10^5$) — the number of sets and the upper bound of the integers in the sets.

Then $n$ lines follow, the $i$-th line first containing an integer $l_i$ ($1\leqslant l_i\leqslant m$) — the size of set $S_i$.

Then $\ell_i$ integers $S_{i,1}, S_{i,2}, \ldots, S_{i, \ell_i}$ follow in the same line ($1\leqslant S_{i,1} < S_{i,2} < \cdots < S_{i, \ell_i}\leqslant m$) — the elements of set $S_i$.

Output

For each test case, print "YES" if there exist at least three ways to choose the sets. Otherwise, print "NO".

You can output the answer in any case (upper or lower). For example, the strings "yEs", "yes", "Yes", and "YES" will be recognized as positive responses.

Samples

3 2
2 1 2
1 1
1 2

YES

4 10
3 1 2 3
2 4 5
1 6
4 7 8 9 10

NO

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

NO

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

YES

5 10
4 1 2 3 4
5 1 2 5 6 7
5 2 6 7 8 9
4 6 7 8 9
2 9 10

YES

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

NO

Note

In the first test case, there are $5\geqslant 3$ possible ways to choose the sets:

• $S_1$ — both $1$ and $2$ are included in $S_1$;
• $S_1$ and $S_2$ — $1$ is included in $S_1$ and $S_2$, and $2$ is included in $S_1$;
• $S_1$ and $S_3$ — $1$ is included in $S_1$, and $2$ is included in $S_1$ and $S_3$;
• $S_2$ and $S_3$ — $1$ is included in $S_2$, and $2$ is included in $S_3$;
• $S_1$, $S_2$, and $S_3$ — $1$ is included in $S_1$ and $S_2$, and $2$ is included in $S_1$ and $S_3$.

Note that it is invalid to choose $S_2$ only because $2$ is not included in $S_2$.

In the second test case, the only way is to choose all the sets.

In the third test case, $5$ does not appear in any of the sets, so there is no way to choose the sets.

In the fourth test case, choosing any non-empty collection of the sets is valid, so the number of ways is $2^5-1=31\geqslant 3$.