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 h₂ health points and an attack power of a₂. Knowing that, Vova has decided to buy a lot of strong healing potions and to prepare for battle.

Vova's character has h₁ health points and an attack power of a₁. Also he has a large supply of healing potions, each of which increases his current amount of health points by c₁ when Vova drinks a potion. All potions are identical to each other. It is guaranteed that c₁ > a₂.

The battle consists of multiple phases. In the beginning of each phase, Vova can either attack the monster (thus reducing its health by a₁) or drink a healing potion (it increases Vova's health by c₁; Vova's health can exceed h₁). Then, if the battle is not over yet, the Modcrab attacks Vova, reducing his health by a₂. 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.

Input

The first line contains three integers h₁, a₁, c₁ (1 ≤ h₁, a₁ ≤ 100, 2 ≤ c₁ ≤ 100) — Vova's health, Vova's attack power and the healing power of a potion.

The second line contains two integers h₂, a₂ (1 ≤ h₂ ≤ 100, 1 ≤ a₂ < c₁) — the Modcrab's health and his attack power.

Output

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.

Note

In the first example Vova's character must heal before or after his first attack. Otherwise his health will drop to zero in 2 phases while he needs 3 strikes to win.

In the second example no healing needed, two strikes are enough to get monster to zero health and win with 6 health left.

The Modcrab

Examples