Nikephoros and Polycarpus play rock-paper-scissors. The loser gets pinched (not too severely!).

Let us remind you the rules of this game. Rock-paper-scissors is played by two players. In each round the players choose one of three items independently from each other. They show the items with their hands: a rock, scissors or paper. The winner is determined by the following rules: the rock beats the scissors, the scissors beat the paper and the paper beats the rock. If the players choose the same item, the round finishes with a draw.

Nikephoros and Polycarpus have played n rounds. In each round the winner gave the loser a friendly pinch and the loser ended up with a fresh and new red spot on his body. If the round finished in a draw, the players did nothing and just played on.

Nikephoros turned out to have worked out the following strategy: before the game began, he chose some sequence of items A = (a1, a2, ..., am), and then he cyclically showed the items from this sequence, starting from the first one. Cyclically means that Nikephoros shows signs in the following order: a1, a2, ..., am, a1, a2, ..., am, a1, ... and so on. Polycarpus had a similar strategy, only he had his own sequence of items B = (b1, b2, ..., bk).

Determine the number of red spots on both players after they've played n rounds of the game. You can consider that when the game began, the boys had no red spots on them.

Input

The first line contains integer n (1 ≤ n ≤ 2·109) — the number of the game's rounds.

The second line contains sequence A as a string of m characters and the third line contains sequence B as a string of k characters (1 ≤ m, k ≤ 1000). The given lines only contain characters "R", "S" and "P". Character "R" stands for the rock, character "S" represents the scissors and "P" represents the paper.

Output

Print two space-separated integers: the numbers of red spots Nikephoros and Polycarpus have.

Examples

Input

7
RPS
RSPP


Output

3 2

Input

5
RRRRRRRR
R


Output

0 0

Note

In the first sample the game went like this:

  * R - R. Draw. 
  * P - S. Nikephoros loses. 
  * S - P. Polycarpus loses. 
  * R - P. Nikephoros loses. 
  * P - R. Polycarpus loses. 
  * S - S. Draw. 
  * R - P. Nikephoros loses. 



Thus, in total Nikephoros has 3 losses (and 3 red spots), and Polycarpus only has 2.
import java.io.InputStream;
import java.io.OutputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.PrintWriter;
import java.io.FileInputStream;
import java.io.FileOutputStream;
import java.io.File;
import java.io.FileNotFoundException;
import java.util.StringTokenizer;

public class Task {

	private static final boolean readFromFile = false;
	
	public static void main(String args[]){
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		FileOutputStream fileOutputStream;
		FileInputStream fileInputStream;
		if (readFromFile){
			try{
				fileInputStream = new FileInputStream(new File("input.txt"));
				fileOutputStream = new FileOutputStream(new File("output.txt"));
			}catch (FileNotFoundException e){
				throw new RuntimeException(e);
			}
		}
		PrintWriter out = new PrintWriter((readFromFile)?fileOutputStream:outputStream);
		InputReader in = new InputReader((readFromFile)?fileInputStream:inputStream);
		
		Solver s = new Solver(in,out);
		s.solve();
		
		out.close();
	}
}

class Solver{
	InputReader in;
	PrintWriter out;
	
	private int nod(int a, int b){
		while (a>0 && b>0)
			if (a>b)
				a %= b;
			else
				b %= a;
		return a+b;
	}
	
	public void solve(){
		int n=in.nextInt();
		String ss=in.nextLine(),
			   tt=in.nextLine();
		StringBuilder s = new StringBuilder(ss),
			   t = new StringBuilder(tt);	
				
		int k = s.length()*t.length()/nod(s.length(),t.length());
		while (s.length()<k) s.append(ss);
		while (t.length()<k) t.append(tt);
		int countRound = n/k,
			countAfterRound = n%k;
		int ansRound1=0,
			ansRound2=0;
		for (int i=0;i<s.length();i++){
			char c1 = s.charAt(i),
				 c2 = t.charAt(i);
			if (c1==c2)
				continue;
			else
			if (c1=='R' && c2=='S' || c1=='S' && c2=='P' || c1=='P' && c2=='R')
				ansRound2++;
			else
				ansRound1++;
		}
		int ans1 = ansRound1*countRound,
		    ans2 = ansRound2*countRound;
		for (int i=0;i<countAfterRound;i++){
			char c1 = s.charAt(i),
				 c2 = t.charAt(i);
			if (c1==c2)
				continue;
			else
			if (c1=='R' && c2=='S' || c1=='S' && c2=='P' || c1=='P' && c2=='R')
				ans2++;
			else
				ans1++;
		}
		out.println(ans1 + " " + ans2);
		
	}

		
	Solver(InputReader in, PrintWriter out){
		this.in=in;
		this.out=out;
	}
}

class InputReader{
	private BufferedReader buf;
	private StringTokenizer tok;
	
	InputReader(InputStream in){
		tok = null;
		buf = new BufferedReader(new InputStreamReader(in));
	}
	
	InputReader(FileInputStream in){
		tok = null;
		buf = new BufferedReader(new InputStreamReader(in));
	}
	
	public String next(){
		while (tok==null || !tok.hasMoreTokens()){
			try{
				tok = new StringTokenizer(buf.readLine());
			}catch (IOException e){
				throw new RuntimeException(e);
			}
		}
		return tok.nextToken();
	}
	
	public int nextInt(){
		return Integer.parseInt(next());
	}
	
	public long nextLong(){
		return Long.parseLong(next());
	}
	
	public double nextDouble(){
		return Double.parseDouble(next());
	}
	
	public float nextFloat(){
		return Float.parseFloat(next());
	}
	
	public String nextLine(){
		try{
			return buf.readLine();
		}catch (IOException e){
			return null;
		}
	}
}