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.*;
import java.util.*;

public class A
{
	String line;
	StringTokenizer inputParser;
	BufferedReader is;
	FileInputStream fstream;
	DataInputStream in;
	String FInput="";
	
	void openInput(String file)
	{

		if(file==null)is = new BufferedReader(new InputStreamReader(System.in));//stdin
		else
		{
			try{
		
				
			fstream = new FileInputStream(file);
			in = new DataInputStream(fstream);
			is = new BufferedReader(new InputStreamReader(in));
			}catch(Exception e)
			{
				System.err.println(e);
			}
		}

	}
	
	void readNextLine()
	{
		try {
			line = is.readLine();
			inputParser = new StringTokenizer(line, " ");
			//System.err.println("Input: " + line);
		} catch (IOException e) {
			System.err.println("Unexpected IO ERROR: " + e);
		}	
		catch (NullPointerException e)
		{
			line=null;
			
		}
		
	}
	
	int NextInt()
	{
		String n = inputParser.nextToken();
		int val = Integer.parseInt(n);
		
		//System.out.println("I read this number: " + val);
		return val;
	}
	
	long NextLong()
	{
		String n = inputParser.nextToken();
		long val = Long.parseLong(n);
		
		//System.out.println("I read this number: " + val);
		return val;
	}
	
	String NextString()
	{
		String n = inputParser.nextToken();
		return n;
	}
	
	void closeInput()
	{
		try {
			is.close();
		} catch (IOException e) {
			System.err.println("Unexpected IO ERROR: " + e);
		}
			
	}
	
	
	public static void main(String [] argv)
	{
		String filePath=null;
		if(argv.length>0)filePath=argv[0];
		new A(filePath);
	}
	
	public void readFInput()
	{
		for(;;)
		{
			try
			{
				readNextLine();
				FInput+=line+" ";
			}
			catch(Exception e)
			{
				break;
			}
		}
		inputParser = new StringTokenizer(FInput, " ");
	}
	 
	public A(String inputFile)
	{
		openInput(inputFile);
		
		readNextLine();
		long n=NextLong();
		
    	
		readNextLine();
		String s1=line;
		
		readNextLine();
		String s2=line;
		
		int L1=s1.length();
		int L2=s2.length();
		long r1=0,r2=0;
		int G=L1*L2;
		for(int i=0; i<G; i++)
		{
			r1+=get(s1.charAt(i%L1), s2.charAt(i%L2));
			r2+=get(s2.charAt(i%L2), s1.charAt(i%L1));
		}
		r1*=n/G;
		r2*=n/G;
		for(int i=0; i<n%G; i++)
		{
			r1+=get(s1.charAt(i%L1), s2.charAt(i%L2));
			r2+=get(s2.charAt(i%L2), s1.charAt(i%L1));
		}
		System.out.print(r1+" "+r2);
        closeInput();		
	}

	private long get(char a, char b) {
		if(a=='R'&&b=='P')return 1;
		if(a=='P'&&b=='S')return 1;
		if(a=='S'&&b=='R')return 1;
		return 0;
	}
	

}
