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.


-----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.

Difficulty: interview

Starter code:

Solutions:
h1, a1, c1 = list(map(int, input().split()))
h2, a2 = list(map(int, input().split()))
d = []
while h2 > 0:
	if h2 <= a1:
		h2 -= a1
		d.append('STRIKE')
	else:
		if h1 <= a2:
			d.append('HEAL')
			h1 += c1
		else:
			d.append('STRIKE')
			h2 -= a1
	h1 -= a2
print(len(d))
for i in d:
	print(i)


h1, a1, c = list(map(int, input().split()))
h2, a2 = list(map(int, input().split()))

turn = 0
l = list()

while ((h1 > 0) and (h2 > 0)):
    if (turn % 2 == 0):
        if (h1 > a2) or (h2 <= a1):
            l.append('STRIKE')
            h2 -= a1
        else:
            l.append('HEAL')
            h1 += c
    else:
        h1 -= a2

    turn += 1

print(len(l))
print('\n'.join(l))


my_health, my_attack, my_potion = [int(x) for x in input().split()]
boss_health, boss_attack = [int(x) for x in input().split()]

actions = []

while boss_health > 0:
    if my_health <= boss_attack and boss_health > my_attack:
        actions.append('HEAL')
        my_health += my_potion
    else:
        actions.append('STRIKE')
        boss_health -= my_attack
        if boss_health <= 0:
            break
    my_health -= boss_attack

print(len(actions))
print('\n'.join(actions))


h1, a1, c1 = list(map(int, input().split()))
h2, a2 = list(map(int, input().split()))
an = []
while h2 > 0:
    if h2 - a1 <= 0:
        an.append('STRIKE')
        break
    if h1 <= a2:
        h1 += c1
        an.append('HEAL')
    else:
        h2 -= a1
        an.append('STRIKE')
    h1 -= a2
print(len(an))
for i in an:
    print(i)


h1, a1, c1 = map(int, input().split())
h2, a2 = map(int, input().split())
coms = []
while h2 > 0:
    if h2 <= a1:
        coms.append('STRIKE')
        h2 -= a1
    elif h1 <= a2:
        coms.append('HEAL')
        h1 += c1
    else:
        coms.append('STRIKE')
        h2 -= a1
    h1 -= a2
print(len(coms))
print(*coms, sep='\n')

h1, a1, c1 = map(int, input().split())
h2,a2 = map(int, input().split())
cache = []
while h2>0:
  if h2<= a1:
    h2-=a1
    cache.append('STRIKE')
  elif h1<=a2:
    h1+=c1
    cache.append('HEAL')
  else:
    h2-=a1
    cache.append('STRIKE')
  h1-=a2
print(len(cache))
for i in range(len(cache)):
  print(cache[i])

h1, a1, c1 = map(int, input().split())
h2, a2 = map(int, input().split())

a = []

while True:
	if h2 <= a1 or h1 > a2:
		h2 -= a1 
		a += ["STRIKE"]
	else:
		h1 += c1
		a += ["HEAL"]

	if h2 <= 0:
		break
	h1 -= a2
print(len(a))
for x in a:
	print(x)

h1, a1, c1 = [int(i) for i in input().split()]
h2, a2 = [int(i) for i in input().split()]
n = 0
a = []
while h2 > 0:
    if h2 <= a1:
        a.append('STRIKE')
        h2 -= a1
    else:
        if h1 > a2:
            a.append('STRIKE')
            h2 -= a1
        else:
            a.append('HEAL')
            h1 += c1
        if h2 > 0:
            h1 -= a2
    n += 1
print(n)
for i in a:
    print(i)


h1, a1, c1 = list(map(int, input().strip().split()))
h2, a2 = list(map(int, input().strip().split()))
answer = []
count = 0
while h2 > 0:
    if a1 >= h2:
        answer.append("STRIKE")
        h2 -= a1
    elif a2 >= h1:
        answer.append("HEAL")
        h1 += c1
        h1 -= a2
    else:
        answer.append("STRIKE")
        h2 -= a1
        h1 -= a2
    count += 1

print(count)
for i in answer:
    print(i)

h1,a1,c1=[int(i) for i in input().split(" ")]
h2,a2=[int(i) for i in input().split(" ")]

ans=[]
while h2>0:
    if h2<=a1:
        ans.append(1)
        h2-=a1
        break
    if h2>0 and h1>a2:
        ans.append(1)
        h2-=a1
        if h2>0:
            h1-=a2
        if h2<=0:
            break
    elif h2>0 and h1<=a2:
        ans.append(0)
        h1+=c1
        h1-=a2
print(len(ans))
for i in range(len(ans)):
    if ans[i]==1:
        print('STRIKE')
    else:
        print('HEAL')


def ii():
    return int(input())
def mi():
    return map(int, input().split())
def li():
    return list(mi())

h1, a1, c1 = mi()
h2, a2 = mi()
ans = []
while h2 > 0:
    h1 -= a2
    if h1 > 0 or h2 <= a1:
        ans += ['STRIKE']
        h2 -= a1
    else:
        ans += ['HEAL']
        h1 += c1
print(len(ans))
print(*ans, sep='\n')

h1, a1, c1 = list(map(int, input().split()))
h2, a2 = list(map(int, input().split()))
a = []
t = 0
while h1 > 0 and h2 > 0:
    t += 1
    if h1 > a2 or h2 <= a1:
        h2 -= a1
        a.append('STRIKE')
    else:
        h1 += c1
        a.append('HEAL')
    h1 -= a2
print(t)
for i in range(len(a)):
    print(a[i])


h1,a1,c1=map(int,input().split())
h2,a2=map(int,input().split())
a=list()
n=0
while h2>0:
    n+=1
    if (h1<(a2+1)) and (h2>a1):
        a.append('HEAL')
        h1+=c1
    else:
        a.append('STRIKE')
        h2-=a1
    h1-=a2
print(n)
for i in a:
    print(i)

h1, a1, c1 = list(map(int, input().split()))
h2, a2 = list(map(int, input().split()))

n = 0
l = []
while(h2 > 0):
	n += 1
	if (h2 - a1 <=0):
		l.append(1)
		break
	if h1 - a2 <=0:
		l.append(0)
		h1 += c1
		h1 -= a2
		continue
	else:
		l.append(1)
		h1 -= a2
		h2 -= a1

print(n)
for i in l:
	if i == 0:
		print("HEAL")
	else:
		print("STRIKE")					


h1, a1, c1 = map(int, input().split())
h2, a2 = map(int, input().split())
ans = 0
ad = []
while 1:
    #print(h1)
    ans += 1
    if h1 <= a2 and h2 > a1:
        h1 += c1
        ad.append('HEAL')
    else:
        h2 -= a1
        ad.append('STRIKE')
    if h2 <= 0:
        break
    h1 -= a2
print(ans)
for d in ad:
    print(d)

import sys
h1, a1, c1 = map(int, input().split())
h2, a2 = map(int, input().split())
ans = []
while h2 > 0:
    if h1 - a2 <= 0 and h2 - a1 > 0:
        ans.append("HEAL")
        h1 += c1
    else:
        ans.append("STRIKE")
        h2 -= a1
    h1 -= a2
print(len(ans))
for i in range(len(ans)):
    print(ans[i])

h1, a1, c1 = list(map(int, input().split()))
h2, a2 = list(map(int, input().split()))
res = []

while h2 > 0:
    if h1 <= a2 and h2 > a1:
        h1 += c1
        res.append('HEAL')
        h1 -= a2
    else:
        h2 -= a1
        res.append('STRIKE')
        h1 -= a2

print(len(res))
print('\n'.join(res))


read=lambda: list(map(int,input().split()))
h1,a1,c1=read()
h2,a2=read()
ans=1
a=[]
ap=a.append
while h2>a1:
    ans+=1
    if h1>a2:
        h2-=a1
        ap('STRIKE')
    else:
        h1+=c1
        ap('HEAL')
    h1-=a2
ap('STRIKE')
print(ans)
print('\n'.join(a))

h,a,c=list(map(int,input().split()))
h2,a2=list(map(int,input().split()))
count=1
S=[]
while(h2>a):
    count+=1
    if(h>a2):
        S.append('STRIKE')
        
        h2-=a
    else:
        S.append('HEAL')
        h+=c
    h-=a2
S.append('STRIKE')
print(count)
for i in S:
    print(i)


pht, pa, phl = map(int, input().split())
bht, ba = map(int, input().split())

st = []
while bht > 0:
	if pht <= ba and bht > pa:
		st += ['HEAL']
		pht += phl
	else:
		bht -= pa
		st += ['STRIKE']
	pht -= ba

print(len(st))
print('\n'.join(st))

h1, a1, c1 = list(map(int, input().split()))
h2, a2 = list(map(int, input().split()))

ans = list()
while True:
    if h1 <= a2 and h2 > a1:
        ans.append('HEAL')
        h1 += c1
    else:
        ans.append('STRIKE')
        h2 -= a1
        if h2 <= 0:
            break

    h1 -= a2

print(len(ans))
print('\n'.join(ans))


h1, a1, c1 = [int(i) for i in input().split()]
h2, a2 = [int(i) for i in input().split()]
k = (h2 + a1 - 1) // a1
#print(k)
e = []
while k > 0:
    #print(k, h1, a2)
    if k == 1:
        e.append("STRIKE")
        break
    if h1 <= a2:
        e.append("HEAL")
        h1 += c1
    else:
        e.append("STRIKE")
        k -= 1
    h1 -= a2
print(len(e))
for el in e:
    print(el)


h1,a1,c1=map(int,input().split())
h2,a2=map(int,input().split())
k=0
if h2%a1==0:
    n=h2//a1-1
else:
    n=h2//a1
while k<=(n*a2-h1)/(c1-a2):
    k+=1
print(k+n+1)
for i in range(k):
    print('HEAL')
for i in range(n+1):
    print('STRIKE')

h1, a1, c1 = [int(x) for x in input().split()]
h2, a2 = [int(x) for x in input().split()]

n_rounds = 0
things_to_do = []

while(h2 > 0):
	n_rounds += 1
	if h2 <= a1 or h1 > a2:
		things_to_do.append('STRIKE')
		h2 -= a1
		h1 -= a2
	else:
		things_to_do.append('HEAL')
		h1 += c1
		h1 -= a2

print(n_rounds)
for i in things_to_do:
	print(i)


h1,a1,c1 = list(map(int,input().split()))
h2,a2 = list(map(int,input().split()))
actions = [0]*10000
j = 0

while h2 >= 0:
    if h2 <= a1:
        actions[j] = 1
        j += 1
        break
    if h1 <= a2:
        actions[j] = 2
        j += 1
        h1 += c1 - a2
        continue
    actions[j] = 1
    j += 1
    h1 -= a2
    h2 -= a1

print(j)
for i in range(j):
    if actions[i] == 1:
        print("STRIKE")
    elif actions[i] == 2:
        print("HEAL")