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.

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from __future__ import print_function
import os
import sys
Debug = True
Conda = False
UseFileIO = True
UseLibrary = False
Archive = False
EdX = False
BOJ = False
ReadTarget = None
WriteTarget = None

def AddImports(libraryNames):
    for libname in libraryNames:
        if (type(libname) == type(tuple())):
            short = libname[1]
            libname = libname[0]
        else:
            short = None
        try:
            lib = __import__(libname)
        except ImportError:
            pass
        else:
            if short:
                globals()[short] = lib
            else:
                globals()[libname] = lib
    return True
libnames = ['fileinput', 'codecs', 'operator', 'functools', 'math', 'io', 'platform', 'collections', 'mmap', 'logging', 'logging.handlers']
AddImports(libnames)
IntellisenseHint = False
if IntellisenseHint:
    import fileinput
    import codecs
    import operator
    import functools
    import math
    import io
    import platform
    import collections
    import mmap
    import logging
    import logging.handlers
    import defs

def readSequence(elementType=None, inputLine=None, seperator=None, strip=True):
    global readTarget
    if (inputLine == None):
        inputLine = readTarget.readline()
    if strip:
        inputLine = inputLine.strip()
    if isinstance(inputLine, bytes):
        inputLine = inputLine.decode('utf-8')
    if (elementType == None):
        return [x for x in inputLine.split(seperator)]
    return [elementType(x) for x in inputLine.split(seperator)]
rl = RobertsSpaceIndustries = readSequence

def ToSpaceSeperatedString(targetList):
    return ' '.join(map(str, targetList))

def convert_to_bytes(arg):
    if isinstance(arg, bytes):
        return arg
    elif isinstance(arg, str):
        return arg.encode('utf-8')
    elif hasattr(arg, '__iter__'):
        return ' '.join(map(convert_to_bytes, arg))
    else:
        return str(arg).encode('utf-8')

class edx_in:

    def __init__(self, target=None):
        self.target = target

    def create_lineTokenizer(self):
        if self.mm:
            for line in iter(self.mm.readline, ''):
                (yield line)
        else:
            for line in iter(self.stream.readline, ''):
                (yield line)

    def __enter__(self):
        if (self.target and UseFileIO):
            self.isFileEmpty = (os.stat(self.target).st_size == 0)
            if self.isFileEmpty:
                return self
            self.stream = open(self.target, 'rb', 1)
            self.mm = mmap.mmap(self.stream.fileno(), 0, access=mmap.ACCESS_READ)
        else:
            self.mm = None
            self.isFileEmpty = True
            self.stream = sys.stdin
        self.lines = self.create_lineTokenizer()
        self.lineTokens = None
        return self

    def __exit__(self, type, value, traceback):
        if (not self.isFileEmpty):
            if self.mm:
                self.mm.close()
            self.stream.close()

    def next_line(self):
        ret = None
        try:
            ret = ' '.join(self.lineTokens)
            self.lineTokens.close()
            if (ret == ''):
                raise ValueError()
            return ret
        except:
            pass
        if hasattr(self.lines, 'next'):
            ret = self.lines.next()
        if hasattr(self.lines, '__next__'):
            ret = self.lines.__next__()
        return ret

    def next_int(self):
        return int(self.next_token())

    def next_float(self):
        return float(self.next_token())

    def next_str(self, encoding=None):
        if encoding:
            return self.next_token().decode(encoding)
        else:
            return self.next_token()

    def getLineTokens(self, line):
        for token in iter(line.split()):
            (yield token)

    def nextNToken(self, rep=0):
        ans = []
        while (rep > 0):
            ans.append(self.next_token())
            rep -= 1
        return ans

    def next_token(self):
        try:
            if hasattr(self.lineTokens, 'next'):
                ret = self.lineTokens.next()
            if hasattr(self.lineTokens, '__next__'):
                ret = self.lineTokens.__next__()
            return ret
        except:
            self.lineTokens = self.getLineTokens(self.next_line())
            return self.next_token()

class edx_out:

    def __init__(self, target=None):
        self.target = target

    def __enter__(self):
        self.is_cpython = (platform.python_implementation() == 'CPython')
        if (self.target and UseFileIO):
            if self.is_cpython:
                self.stream = open(self.target, 'wb', 1)
            else:
                self.stream = io.BytesIO()
        else:
            self.stream = sys.stdout
        return self

    def __exit__(self, type, value, traceback):
        if (self.target and UseFileIO):
            if self.is_cpython:
                self.stream.close()
            else:
                outf = open(self.target, 'wb', 1)
                outf.write(self.stream.getvalue())
                outf.close()
                self.stream.close()
        else:
            pass

    def write(self, arg):
        self.stream.write(convert_to_bytes(arg))

    def writeln(self, arg):
        self.write(arg)
        self.write('\n')

    def test(this, expression):
        frame = sys._getframe(1)
        exp = expression
        ans = repr(eval(exp, frame.f_globals, frame.f_locals))
        this.debug(((('test : ' + exp) + ' = ') + ans))
        pass

def solve():
    solve903a()
    solve903b()
    solve903c()
    solve903d()

def solve903a():
    pass

def solve903b():
    steplist = []
    (h1, a1, c1) = (ri(), ri(), ri())
    (h2, a2) = (ri(), ri())
    curhp = h1
    enemyhp = h2
    strikeTimes = ((h2 // a1) if ((h2 % a1) == 0) else ((h2 // a1) + 1))
    healTimes = int(math.ceil((float(((((a2 * strikeTimes) - a2) - h1) + 0.001)) / float((c1 - a2)))))
    debug(healTimes, strikeTimes)
    for i in range(healTimes):
        steplist.append('HEAL')
    for i in range(strikeTimes):
        steplist.append('STRIKE')
    put(len(steplist))
    for step in steplist:
        put(step)
    pass

def solve903c():
    pass

def solve903d():
    pass
reader = None
writer = None
try:
    logger1 = logging.getLogger('log1')
    debug = (lambda *x: logger1.log(logging.DEBUG, convert_to_bytes(x)))
    PutLevel = 100
    logging.PUT = PutLevel
    logging.addLevelName(PutLevel, 'PUT')
    logger1.setLevel(logging.PUT)
    formatter = logging.Formatter()
except:
    pass
with edx_in(ReadTarget) as Reader:
    with edx_out(WriteTarget) as Writer:
        try:
            outHandler = logging.StreamHandler(Writer.stream)
            outHandler.setFormatter(formatter)
            logger1.addHandler(outHandler)
            put = (lambda *args: logger1.log(logging.PUT, convert_to_bytes(args)))
            info = (lambda *args: logger1.log(logging.INFO, convert_to_bytes(args)))
            critical = (lambda *args: logger1.log(logging.CRITICAL, convert_to_bytes(args)))
        except:
            debug = Writer.writeln
            put = Writer.writeln
            info = Writer.writeln
            critical = Writer.writeln

        def nop(*arg):
            pass
        debug = nop
        test = nop
        info = nop
        reader = Reader
        writer = Writer
        ri = reader.next_int
        rs = reader.next_str
        rt = reader.next_token
        rf = reader.next_float
        rl = reader.next_line
        wl = writer.writeln
        solve()
