Vova is again playing some computer game, now an RPG. In the game Vova's character received a quest: to slay the fearsome monster called Modcrab. After two hours of playing the game Vova has tracked the monster and analyzed its tactics. The Modcrab has h 2 health points and an attack power of a 2 . Knowing that, Vova has decided to buy a lot of strong healing potions and to prepare for battle. Vova's character has h 1 health points and an attack power of a 1 . Also he has a large supply of healing potions, each of which increases his current amount of health points by c 1 when Vova drinks a potion. All potions are identical to each other. It is guaranteed that c 1 > a 2 . The battle consists of multiple phases. In the beginning of each phase, Vova can either attack the monster (thus reducing its health by a 1 ) or drink a healing potion (it increases Vova's health by c 1 ; Vova's health can exceed h 1 ). Then, if the battle is not over yet , the Modcrab attacks Vova, reducing his health by a 2 . The battle ends when Vova's (or Modcrab's) health drops to 0 or lower. It is possible that the battle ends in a middle of a phase after Vova's attack. Of course, Vova wants to win the fight. But also he wants to do it as fast as possible. So he wants to make up a strategy that will allow him to win the fight after the minimum possible number of phases. Help Vova to make up a strategy! You may assume that Vova never runs out of healing potions, and that he can always win. The first line contains three integers h 1 , a 1 , c 1 ( 1 ≤ h 1 , a 1 ≤ 100 , 2 ≤ c 1 ≤ 100 ) — Vova's health, Vova's attack power and the healing power of a potion. The second line contains two integers h 2 , a 2 ( 1 ≤ h 2 ≤ 100 , 1 ≤ a 2 < c 1 ) — the Modcrab's health and his attack power. In the first line print one integer n denoting the minimum number of phases required to win the battle. Then print n lines. i -th line must be equal to HEAL if Vova drinks a potion in i -th phase, or STRIKE if