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문제

Luigi's Tavern is a thriving tavern in the Kingdom of Nahaila. The owner of the tavern Luigi supports to organize a party, because the main customers of the tavern are adventurers. Each adventurer has a job: hero, warrior, cleric or mage.

Any party should meet the following conditions:

  • A party should have a hero.
  • The warrior and the hero in a party should get along with each other.
  • The cleric and the warrior in a party should get along with each other.
  • The mage and the cleric in a party should get along with each other.
  • It is recommended that a party has a warrior, a cleric, and a mage, but it is allowed that at most NWNC and Nm parties does not have a warrior, a cleric, and a mage respectively.
  • A party without a cleric should have a warrior and a mage.

Now, the tavern has H heroes, W warriors, C clerics and M mages. Your job is to write a program to find the maximum number of parties they can form.

입력

The first line of the input contains 7 non-negative integers HWCMNWNC, and NM, each of which is less than or equals to 50. The i-th of the following W lines contains the list of heroes who will be getting along with the warrior i. The list begins with a non-negative integer ni , less than or equals to H. Then the rest of the line should contain ni positive integers, each of which indicates the ID of a hero getting along with the warrior i.

After these lists, the following C lines contain the lists of warriors getting along with the clerics in the same manner. The j-th line contains a list of warriors who will be getting along with the cleric j. Then the last M lines of the input contain the lists of clerics getting along with the mages, of course in the same manner. The k-th line contains a list of clerics who will be getting along with the mage k.

출력

You should output the maximum number of parties possible.

예제 입력 1

2 1 1 1 1 1 1
1 1
1 1
1 1

예제 출력 1

2

예제 입력 2

1 1 1 1 0 0 0
1 1
1 1
1 1

예제 출력 2

1

예제 입력 3

1 0 1 0 1 0 1
0

예제 출력 3

1

예제 입력 4

1 1 0 1 0 1 0
0
0

예제 출력 4

0

예제 입력 5

1 1 0 1 0 1 0
1 1
0

예제 출력 5

1