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.
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class main
{
	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;
	private PrintWriter pw;
	private long mod = 1000000000 + 7;
	
	private StringBuilder ans_sb;
	private ArrayList<Integer> primes;
	private long ans;
	private void soln()
	{
		int h1 = nextInt();
		int a1 = nextInt();
		int c1 = nextInt();
		int h2 = nextInt();
		int a2 = nextInt();
		ArrayList<String> l = new ArrayList<>();
		int k = 0;
		while(true) {
			k++;
			if(h1<=a2 && (h2-a1)>0) {
				h1 += c1;
				l.add("HEAL");
			}else {
				h2 -= a1;
				l.add("STRIKE");
			}
			if(h2<=0) {
				break;
			}
			h1 -= a2;
		}
		pw.println(k);
		for(String x:l) {
			pw.println(x);
		}
	}

public class Segment
	{
		private Node[] tree;
		private boolean[] lazy;
		private int size;
		private int n;

		private class Node
		{
			private int l;
			private int r;
			private long ans;
			private long ans2;
		}

		public Segment(int n)
		{
			// this.base=arr;
			int x = (int) (Math.ceil(Math.log(n) / Math.log(2)));
			size = 2 * (int) Math.pow(2, x) - 1;
			tree = new Node[size];
			lazy = new boolean[size];
			this.n = n;
			//this.set = set1;
			//build(0, 0, n - 1);
		}

		public void build(int id, int l, int r)
		{
			if (l == r)
			{
				tree[id] = new Node();
				tree[id].l = l;
				tree[id].r = r;
				return;
			}
			int mid = (l + r) / 2;
			build(2 * id + 1, l, mid);
			build(2 * id + 2, mid + 1, r);
			tree[id] = merge(tree[2*id+1], tree[2*id+2], l, r);
			//System.out.println(l+" "+r+" "+tree[id].l+" "+tree[id].r+" "+tree[id].ans);
		}
		public Node merge(Node n1, Node n2, int l, int r) {
			Node ret = new Node();
			if(n1 == null && n2 == null)
				return null;
			else if(n1 == null) {
				ret.ans = n2.ans;
			}
			
			else if(n2 == null) {
				ret.ans = n1.ans;
			}
			else {
				
				ret.ans = n1.ans + n2.ans;
				
			}
			
			return ret;
		}
		public long query(int l, int r)
		{
			Node ret = queryUtil(l, r, 0, 0, n - 1);
			if(ret == null) {
				return 0;
			}
			else
				return ret.ans;
		}

		private Node queryUtil(int x, int y, int id, int l, int r)
		{
			if (l > y || x > r)
				return null;
			if (x <= l && r <= y)
			{
				return tree[id];
			}
			int mid = l + (r - l) / 2;
			// shift(id);
			Node q1 = queryUtil(x, y, 2 * id + 1, l, mid);
			Node q2 = queryUtil(x, y, 2 * id + 2, mid + 1, r);

			return merge(q1, q2, Math.max(l,x), Math.min(r, y));
		}
		
		public void update(int x, int y, int c) {
			update1(x, y, c, 0, 0, n-1);
		}
		
		private void update1(int x, int y, int colour, int id, int l, int r)
		{
			//System.out.println(l+" "+r+" "+x);
			if (x > r || y < l)
				return;
			if (x <= l && r <= y)
			{
				if(colour!=-1) {
					tree[id] = new Node();
					tree[id].ans = 1;
				}else
					tree[id] = null;
				return;
			}
			int mid = l + (r - l) / 2;
			// shift(id);
			if(y<=mid)
				update1(x, y, colour, 2 * id + 1, l, mid);
			else if(x>mid)
				update1(x, y, colour, 2 * id + 2, mid + 1, r);
			else {
				update1(x, y, colour, 2 * id + 1, l, mid);
				update1(x, y, colour, 2 * id + 2, mid + 1, r);
			}
			tree[id] = merge(tree[2*id+1], tree[2*id+2], l, r);
			
		}
		public void print(int l ,int r,int id) {
			if(l==r) {
				if(tree[id] != null)
					System.out.println(l+" "+r+" "+tree[id].l+" "+tree[id].r+" "+tree[id].ans+" "+tree[id].ans2);
				return;
			}
			int mid = l + (r - l)/2;
			print(l,mid,2*id+1);
			print(mid+1,r,2*id+2);
			if(tree[id] != null)
				System.out.println(l+" "+r+" "+tree[id].l+" "+tree[id].r+" "+tree[id].ans+" "+tree[id].ans2);
		}
		public void shift(int id)
		{

		}
	}

	private class Node implements Comparable<Node>{
		int node, dist;

		@Override
		public int compareTo(Node arg0)
		{
			if(this.dist != arg0.dist)
				return this.dist - arg0.dist;
			return this.node - arg0.node;
		}
		public Node(int a, int b) {
			node = a;
			dist = b;
		}
		public boolean equals(Object o){
			if(o instanceof Node){
				Node c = (Node)o;
				return this.node == c.node && this.dist == c.dist;
			}
			return false;
		}
		public String toString() {
			return this.node+", "+this.dist;
		}
	}
	
	private void debug(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
	
	private long pow(long a, long b, long c)
	{
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}

	private long gcd(long n, long l)
	{
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}
	public static void main(String[] args) throws Exception
	{
		new Thread(null, new Runnable()
		{
			@Override
			public void run()
			{
				new main().solve();
			}
		}, "1", 1 << 26).start();
	}
	public StringBuilder solve(){
		InputReader(System.in);
		/*try { 
			InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\in.txt"));
		} catch(FileNotFoundException e) {}
		*/
		pw = new PrintWriter(System.out);
		ans_sb = new StringBuilder();
		soln();
		
		pw.close();
		//System.out.println(ans_sb);
		return ans_sb;
	}
	public void InputReader(InputStream stream1)
	{
		stream = stream1;
	}

	private boolean isWhitespace(int c)
	{
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private boolean isEndOfLine(int c)
	{
		return c == '\n' || c == '\r' || c == -1;
	}

	private int read()
	{
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars)
		{
			curChar = 0;
			try
			{
				numChars = stream.read(buf);
			} catch (IOException e)
			{
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private int nextInt()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-')
		{
			sgn = -1;
			c = read();
		}
		int res = 0;
		do
		{
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private long nextLong()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-')
		{
			sgn = -1;
			c = read();
		}
		long res = 0;
		do
		{
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private String nextToken()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do
		{
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private String nextLine()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do
		{
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}

	private int[] nextIntArray(int n)
	{
		int[] arr = new int[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextInt();
		}
		return arr;
	}

	private long[] nextLongArray(int n)
	{
		long[] arr = new long[n];
		for (int i = 0; i < n; i++)
		{
			arr[i] = nextLong();
		}
		return arr;
	}

	private void pArray(int[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private void pArray(long[] arr)
	{
		for (int i = 0; i < arr.length; i++)
		{
			System.out.print(arr[i] + " ");
		}
		System.out.println();
		return;
	}

	private boolean isSpaceChar(int c)
	{
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	private char nextChar()
	{
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1 = (char) c;
		while (!isSpaceChar(c))
			c = read();
		return c1;
	}

	private interface SpaceCharFilter
	{
		public boolean isSpaceChar(int ch);
	}
}