403182: GYM101061 K Army

When HIAST CPC 2016 was finally over, Feras found himself taking the last place !!

He went home exhausted from all the hard problems he had tried to solve in the contest. In order to take his mind off the problems for a while, he decided to play a PC game. Yes, he decided to play his favorite game Army (Army is an advanced version of the well known game Red Alert).

Rules for Army are quite simple. On the battlefield you have the following 3 concepts:

1. N soldiers numbered from 1 to N.
2. M places numbered from 1 to M.
3. W type of weapons numbered from 1 to W.

Each one of your soldiers may guard exactly one place, and each place may be guarded by exactly one soldier. In order for a soldier to guard a certain place, he needs to have exactly one weapon. Your job is to cover as many places as possible. However, it's not that simple.

On one hand, your soldiers are a bit moody. For the i^th soldier you are given two lists:

1. The first list is for places consisting of Y_i places. It means that the i^th soldier prefers exactly Y_i places. Therefore, the i^th soldier will only guard one of the places mentioned in his places list.
2. The second list is for weapons consisting of Z_i weapons. It means that the i^th soldier prefers exactly Z_i weapons. Therefore, the i^th soldier will only guard one of the places that has one of the weapons mentioned in his weapons list.

On the other hand, for each place you are given a list consisting of C_k weapons indicating the weapons available at the k^th place. Therefore, if you assign soldier x to guard place y, then he can only have one of the weapons available at place y. Please note that it's possible that many places have the same kind of weapons. i.e. 2 places may have the same kind of weapons.

Place y is called "guarded" if there is a soldier x standing on place y and carrying a weapon z, such that:

1. Weapon z is one of the weapons available at place y.
2. Weapon z is one of the weapons preferred by soldier x.
3. Place y is one of the places preferred by soldier x.

Feras is exhausted from HIAST CPC, and he felt frustrated because he couldn't find the perfect distribution for soldiers in order to guard as many places as possible, so he asked for your help. Can you help poor Feras to feel better about him self? Help him calculate the maximum number of places that could be guarded.

The first line of input contains a single integer T, indicating the number of test cases.

The second line of input consists of three integers (1 ≤ N ≤ 100), (1 ≤ M ≤ 100) and (1 ≤ W ≤ 100), indicating the number of soldiers, the number of places and the number of weapons, respectively.

Then N lines follow. The i^th line of them describes the places which the i^th soldier prefers. Each line starts with an integer Y_i denoting the number of the places, followed by Y_i distinct integers (1 ≤ y_i ≤ M) separated by spaces indicating the list of places which the i^th soldier prefers.

N lines follow. The i^th line of them describes the weapons which the i^th soldier prefers. Each line starts with an integer Z_i denoting the number of the weapons, followed by Z_i distinct integers (1 ≤ z_i ≤ W) separated by spaces indicating the list of weapons which the i^th soldier prefers.

M lines follow. The k^th line of them describes the weapons available at the k^th place. Each line starts with an integer C_k denoting the number of the weapons, followed by C_k distinct integers (1 ≤ c_k ≤ W) separated by spaces indicating the list of the weapons available at the k^th place.

For each test case print a single line containing the maximum number of places that can be guarded.

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

3
0