Supporting everyone

Alice is attending a sport event with many national teams, and one thing is important to her: supporting every country.

There are $N$ countries represented. She has two ways to support a country: either have the flag drawn on her, or have a pin with the name of the country. Alice has a list containing, for each country, the colours needed to make its flag. There are $M$ colours that may appear across all flags, and in Alice's list each colour is an integer between $1$ and $M$.

Each crayon and pin costs $1$. Her budget is tight. Can you help her find the minimum she can spend to support everyone?

The first line contains two space-separated numbers $N$ and $M$. Then follow $2N$ lines, grouped in pairs. The $(2i-1)$th line contains a single integer $k_i$, the number of colours in the flag of the $i$th country. The $2i$th line contains $k_i$ space-separated numbers $c_{i,1}, c_{i,2}, \dots, c_{i,k_i}$, the colours in the flag of the $i$th country.

The output should contain a single line with a single number: the minimum amount Alice spends on crayons and pins to represent every country.

• $1 \le N \le 1\,000$
• $1 \le M \le 100$
• $1 \le k_i \le M$ for all $i \le N$
• $1 \le c_{i,j} \le M$ for all $i \le N$ and $j \le k_i$
• For all $i \le N$, the $k_i$ colour numbers $c_{i,j}$ are pairwise distinct.