Irhas is in charge of managing a herd of cows, and he is stressed out since many of them don't seem to be eating as much they should. He has ~n~ cows and ~m~ feeding troughs, and each cow will visit a subset of feeding troughs throughout the day. Irhas has bought some GoPros and wants to make sure he records every single interaction between a cow and a feeding trough.

If he puts a GoPro on a cow, it will capture every interaction between itself and all the troughs it visits. If he puts a GoPro on a feeding trough, it will capture its interactions with every cow that visits it. How many GoPros does Irhas need at minimum to cover every single cow/feeding trough interaction? These cameras are expensive and he wants to spend as little as possible.

It is possible for no cows to visit a trough, or a cow to visit no troughs, we regard these as having no interactions, and don't need to monitor them with cameras.

Input

The first line contains two integers ~n~ and ~m~ ~(1 \leq n,m \leq 10^5)~, the number of cows and the number of troughs, labelled ~1\dots n~ and ~1\dots m~ respectively.

The next ~2n~ lines come in pairs, detailing the troughs each cow will visit. The first line of each pair contains a single number ~T_i~ ~(0 \leq T_i \leq m)~, the number of troughs the ~i~th cow will visit throughout the day. The next line contains ~T_i~ space-separated integers ~t_j~ ~(1 \leq t_j \leq m)~, each trough that this cow will visit.

The trough numbers are unique in each line. The total number of cow/trough interactions (i.e., the sum of all ~T_i~s) will not exceed ~5\times 10^5~.

Output

Output the minimum number of cameras Irhas needs to buy to make sure every interaction between a cow and a trough is recorded. Irhas can either place the cameras on cows or on troughs, following the rules above.

Example

Input 1

3 3
2
1 2
1
3
1
3

Output 1

2

In this case, it is optimal to place a camera on cow ~1~, and on trough ~3~. This will ensure that all interactions are covered.

Input 2

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

Output 2

3

Here it is optimal to place cameras on cow ~1~, and troughs ~2~ and ~3~.