Harry Potter has found another strange spell in Half-blood Prince diary, that could generate a different binary vector of size M. As he is not the best magician, this spell does not work perfectly so he could generate only vectors where exactly 2 elements are non zero. Harry has used this spell N times and he has constructed a matrix of M rows and N columns, where all generated vectors are columns.</p>

Now Harry has a class of Magical Matrix Theory, where the professor asked him to calculate the rank of such a matrix. You are here to help him!

Operations in Magical Matrix Theory satisfied next rules:

The rank of a matrix A corresponds to the maximal number of linearly independent columns of A. The vectors in a set (T = {\vec{v_1}, \vec{v_2}, \dots, \vec{v_k}}) are said to be linearly independent if the equation (a_1\vec{v_1} + a_2\vec{v_2} + \dots + a_k\vec{v_k} = \vec{0}), where (a_i = {0, 1}) for (i = 1, \dots, k) can only be satisfied by (a_i = 0) for (i = 1, \dots, k).

입력 형식

On the first line two integers - M (size of vectors) and N (number of vectors generated by Harry). Each of the next M lines has the format: k_i, c₁, c₂, ..., c_ki, where ki is the number of non-zero elements in row i. The next ki numbers are column indexes (1 ≤ cj ≤ N, j = 1, ..., ki), which are non-zero in this row. For more details, see exampels.</p></sub>

• 1 ≤ N ≤ 10⁵
• 2 ≤ M ≤ 10⁵
• 0 ≤ k_i ≤ N

## 출력 형식 ## 예제 입력 1 3 3 2 1 3 2 1 2 2 2 3 ## 예제 출력 1 2 ## 예제 입력 2 4 3 3 1 2 3 1 1 1 2 1 3 ## 예제 출력 2 3 ## 힌트

In first example, Harry has generated 3 vectors:

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

and 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}).