Luigi's Tavern

Time Limit : 8 sec, Memory Limit : 65536 KB

Problem D: Luigi's Tavern

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 NW, NC 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.

Input

The input consists of multiple datasets. Each dataset has the following format:

The first line of the input contains 7 non-negative integers H, W, C, M, NW, NC, 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.

The last dataset is followed by a line containing seven negative integers. This line is not a part of any dataset and should not be processed.

Output

For each dataset, you should output the maximum number of parties possible.

Sample Input

2 1 1 1 1 1 1
1 1
1 1
1 1
1 1 1 1 0 0 0
1 1
1 1
1 1
1 0 1 0 1 0 1
0
1 1 0 1 0 1 0
0
0
1 1 0 1 0 1 0
1 1
0
-1 -1 -1 -1 -1 -1 -1

Output for the Sample Input

2
1
1
0
1

Source: ACM-ICPC Japan Alumni Group Summer Camp 2009 , Day 3, Tokyo, Japan, 2009-09-20
http://acm-icpc.aitea.net/