Harry Potter and the Vector Spell

Harry Potter found one more strange spell in the Half Blood Prince's diary. The spell creates a binary vector of size $M$. Harry is not the best magician yet, so the spell does not work perfectly and every vector it creates has exactly 2 non-zero elements.

Harry used the spell $N$ times and stood all of the created vectors up as columns, which gives a matrix with $M$ rows and $N$ columns.

In the Magical Matrix Theory class the professor asked Harry to compute the rank of that matrix. Help him.

Operations in Magical Matrix Theory follow these rules.

The rank of a matrix $A$ is the largest number of linearly independent columns of $A$. The vectors in a set $T = \{\vec{v_1}, \vec{v_2}, \dots, \vec{v_k}\}$ are linearly independent when the equation $a_1\vec{v_1} + a_2\vec{v_2} + \dots + a_k\vec{v_k} = \vec{0}$, where $a_i \in \{0, 1\}$, holds only for $a_1 = a_2 = \dots = a_k = 0$.

The first line has two integers $M$ (the size of a vector) and $N$ (the number of vectors Harry created).

Each of the next $M$ lines has the format $k_i$, $c_1$, $c_2$, $\dots$, $c_{k_i}$. Here $k_i$ is the number of non-zero elements in row $i$, and the next $k_i$ numbers are the indices $c_j$ of the columns that are non-zero in that row ($1 \le c_j \le N$, $j = 1, \dots, k_i$).

• $1 \le N \le 10^5$
• $2 \le M \le 10^5$
• $0 \le k_i \le N$
• Every column has exactly 2 non-zero elements.

Print the rank of the matrix on the first line.

In the first example Harry created three vectors.

$\vec{v_1} = (1, 1, 0), \quad \vec{v_2} = (0, 1, 1), \quad \vec{v_3} = (1, 0, 1)$

The matrix is

$\begin{bmatrix} 1 & 0 & 1 \\ 1 & 1 & 0 \\ 0 & 1 & 1 \end{bmatrix}$

but $\vec{v_1} + \vec{v_2} + \vec{v_3} = \vec{0}$.