The Modcrab (简单模拟)

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 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.

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.

code：

#include <iostream>
#include <cstdio>
#include <cstring>
using namespace std;
int main(){
    int h1,a1,c1;
    int h2,a2;
    cin >> h1 >> a1 >> c1;
    cin >> h2 >> a2;
    int attack = h2 / a1;
    int heal = 0;
    if(attack * a1 < h2) attack++;
    int be_attacked = attack - 1;
    int need = be_attacked * a2 - h1;
    if(need >= 0){
        int add = c1 - a2;
        heal = need / add;
        if(heal * add <= need) heal++;
    }
    printf("%d\n",heal+attack);
    while(heal--){
        printf("HEAL\n");
    }
    while(attack--){
        printf("STRIKE\n");
    }
    return 0;
}