You are going out for a walk, when you suddenly encounter N monsters. Each monster has a parameter called health, and the health of the i-th monster is hi at the moment of encounter. A monster will vanish immediately when its health drops to 0 or below.
Fortunately, you are a skilled magician, capable of causing explosions that damage monsters. In one explosion, you can damage monsters as follows:
At least how many explosions do you need to cause in order to vanish all the monsters?
Input is given from Standard Input in the following format:
N A B h1 h2 : hN
Print the minimum number of explosions that needs to be caused in order to vanish all the monsters.
4 5 3 8 7 4 2
You can vanish all the monsters in two explosion, as follows:
2 10 4 20 20
You need to cause two explosions centered at each monster, for a total of four.
5 2 1 900000000 900000000 1000000000 1000000000 1000000000