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Problem G
Splay the Spire

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Atli is wasting his time by playing computer games, as usual. Currently he is playing the game Splay the Sire. He is currently figuring out how to defeat an enemy while only having a few cards left. The battle proceeds with Atli playing a card from his hand, then the enemy damages Atli by a fixed amount and this is then repeated. First one to lose all of their hit points loses. If both Atli and the enemy reach $0$ hit points at the same time that counts as a loss for Atli, only a clear victory will satisfy him. The problem is that each card can only be played once, when he is out of cards he will have no means to damage the enemy and thus will eventually lose. In addition to this he can not skip his turn while he still has cards in his hand. He is wondering whether the cards he has left are enough to defeat the enemy. Both Atli and the enemy have some number of initial life points and the enemy has some base damage which he inflicts on Atli each time they attack. In addition to this, both Atli and the enemy have a strength value which starts at $0$ which they add to their damage. This value can be negative but if the damage comes out negative it is rounded up to $0$ . What follows is a table of all cards Atli might have.

Name	Effect
Lay into	Damage an enemy by $1$ $4$ times
Power up	Increase own strength value by $2$
Whack	Damage the enemy by $6$
Haymaker	Damage the enemy by $10$ and damage self by $3$ (Self damage is not affected by either player’s strength)
Surpass limits	Double own strength value
Dirty tactics	Lower the enemy’s strength value by $2$
Bandages	Increase own life points by $8$
Xzodiac	Win instantly if own strength value is more than twice of your own current health points

Input

The first line of the input contains three positive integers $h_{A}, h_{E}, d$ satisfying $1 \leq h_{A}, h_{E}, d \leq 10^{9}$ . $h_{A}$ is the number of life points Atli starts with, $h_{E}$ is the number of life points the enemy starts with and $d$ is the enemy’s base damage. The second line of the input contains one positive integer $n$ satisfying $1 \leq n \leq 8$ , the number of cards Atli has. Finally there are $n$ lines, each containing the name of a card Atli has in his hand, there will only be names from the table above.

Output

If Atli can not win, print ‘Engin vinningsleid!’. Otherwise first print the number of cards Atli will play on its own line. Then print that many lines, each with the name of one card, in the same order as Atli plays them. Do not print any cards that would be played after he has already won. If there is more than one way to win, any one of them will suffice.

Sample Input 1	Sample Output 1
10 10 1 2 Lay into Power up	2 Power up Lay into

Sample Input 2	Sample Output 2
8 27 3 7 Bandages Power up Whack Power up Dirty tactics Haymaker Power up	7 Bandages Power up Power up Dirty tactics Power up Whack Haymaker

Sample Input 3	Sample Output 3
7 1000000 1 6 Power up Bandages Power up Whack Surpass limits Xzodiac	5 Power up Power up Whack Surpass limits Xzodiac

Sample Input 4	Sample Output 4
1 100 1 4 Whack Whack Lay into Power up	Engin vinningsleid!

Problem GSplay the Spire

Input

Output

Problem G
Splay the Spire