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B. The Modcrab

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVova 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.

Input

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.

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.

Examples

Input

10 6 100

17 5

Output

4

STRIKE

HEAL

STRIKE

STRIKE

Input

11 6 100

12 5

Output

2

STRIKE

STRIKE

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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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