To Be Or Not To Be

That's a question. Now Happy (Xi Yangyang) has been caught by Wolffy (Hui Tailang). As Wolffy is busy preparing the big meal, a good idea comes to Happy. He proposes a game that only Wolffy had won, he can eat Happy. Wolffy always believes he is the cleverest one, so they reach a consensus. And they both agree with Wolnie (Hong Tailang) when the referee. A theater will be beat to die by Wolnie's pan.


The game is defined as follow.

There are multiple test cases.

In each case there are R (R < 10) rounds of the game, R is an odd number to guarantee that there must be a winner in the end.

In each round: There is a pile of n (10 <= n <= 200) Special-cards and m (1 <= m <= 100) piles of Point-card on the table. The Point-card piles are ordered from 1 to m. Wolffy and Happy take turns to get one card from the top of Special-cards pile. Wolffy always takes first in the game. When all the Special-cards have been taken, the round is over and the one with more cards in the hands gains one point. If there is a tie, Wolffy gains one point.(Wolffty and Happy both have 0 point before the game).

There are 5 kinds of Special-cards besides the Point-card in the game.

0) Point-card: a card with a point X (1 <= X <= 2000000).

1) Challenge-card: no matter who takes this card, they both take one card with the maximum point from their own hands. After a comparison, if Happy's card has a larger point, He takes all the Wolffy's in-hands cards, vice versa; If there is a tie no more operation.

2) Loss-card: the one who takes this card, He must throw a card with the maximum point.

3) Add-card: a card with P point, the one who gets this card will make the card with maximum point P point larger, i.e. if a Point-card with X point is the maximum, its point will change to X + P. An Add-card can only work on one Point-card.

4) Exchange-card: a card with Q point. The one who gets this card must change one maximum-point card's point to Q.

5) Take-card: a card with a integer K, indicates one can get the all the cards of Kth Point-card pile. In one round no two Take-card have the same K.

You can assume that when one gets the Loss-card, Add-card, Exchange-card, He has at least one card in the hands, when one gets a Challenge-card, they both have at least one card in the hands.

Input

For each test case, the first line of input is an integer R, indicates the number of rounds:

Line 2: two integers n indicates the number of Special-cards, m indicates the number of Point-card piles.

Line 3: a line of m integers. The ith number Pi (1 <= Pi <= 10000)indicates the number cards of ith Point-card pile.

For the next m lines, ith line contains Pi numbers indicate every Point-card's point of ith Point-card pile.

The next n lines, in each line, there are five kinds of input, indicate Special-cards by the order of "from top to bottom".

1) T K: indicates one gets a Take-card, and He can get Kth Point-card pile(1 <= K <= m).

2) C: indicates one gets a Challenge card.

3) L: indicates one gets a Loss card.

4) A P: indicates one gets an Add card with P point (1 <= P <= 30).

5) E Q: indicates one gets an Exchange card with Q point (1 <= Q <= 2000000).

For each round you should print A:B in a line. A indicate the number of left cards of Wolffy, B indicates the number of left cards of Happy. At the end of game, if Wolffy gains more points, print "Hahaha...I win!!", else print "I will be back!!".

3
5 3
3 3 3
10 11 2
7 4 12
4 2 9
T 1
T 2
A 7
T 3
C
6 3
2 2 2
1 4
5 2
4 2
T 2
T 1
L
A 2
T 3
C
5 3
2 2 2
1 3
4 2
5 2
T 2
T 1
E 3
A 1
L

9:0
0:5
1:2
I will be back!!

2009 Multi-University Training Contest 13 - Host by HIT