A11564 | The Modcrab

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 he attacks the Modcrab.

The strategy must be valid: Vova's character must not be defeated before slaying the Modcrab, and the monster's health must be $0$ or lower after Vova's last action.

If there are multiple optimal solutions, print any of them.