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.security.SecureRandom;
import java.util.*;
import java.math.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
    
    
	
	int gcd(int a, int b) {
		if (a == 0)
			return b;
		if (a < b) {
			int t = a;
			a = b;
			b = t;
		}
		return gcd(a % b, b);
	}
	
	public void solve() throws Exception {
		
		long n = sc.nextLong();
		char a[] = sc.nextToken().toCharArray();
		char b[] = sc.nextToken().toCharArray();
		
		int sz1 = a.length;
		int sz2 = b.length;
		
		long m = sz1 * sz2 / gcd(sz1, sz2);
		
		int c11 = 0, c12 = 0;
		int c21 = 0, c22 = 0;
		
		for (int i = 0, l = 0, r = 0;i < m; ++ i, l = (l + 1) % sz1, r = (r + 1) % sz2) {
			if (a[l] == 'R' && b[r] == 'S' || a[l] == 'S' && b[r] == 'P' || a[l] == 'P' && b[r] == 'R')
				c11 ++;
			if (b[r] == 'R' && a[l] == 'S' || b[r] == 'S' && a[l] == 'P' || b[r] == 'P' && a[l] == 'R')
				c21 ++;
		}
		
		for (int i = 0, l = 0, r = 0;i < n % m; ++ i, l = (l + 1) % sz1, r = (r + 1) % sz2) {
			if (a[l] == 'R' && b[r] == 'S' || a[l] == 'S' && b[r] == 'P' || a[l] == 'P' && b[r] == 'R')
				c12 ++;
			if (b[r] == 'R' && a[l] == 'S' || b[r] == 'S' && a[l] == 'P' || b[r] == 'P' && a[l] == 'R')
				c22 ++;
		}
		
		out.println((c21 * (n / m) + c22) + " " + (c11 * (n / m) + c12));		
    }
    
    
    
    
    /*--------------------------------------------------------------*/
    
    static String filename = "";
    static boolean fromFile = false;
    
    BufferedReader in;
    PrintWriter out;
    FastScanner sc;
    
    public static void main(String[] args) {
        new Thread(null, new Solution(), "", 1 << 25).start();
    }
   
    public void run() {
        try {
            init();
            solve();
        } catch (Exception e) {
            throw new RuntimeException(e);
        } finally {
            out.close();
        }
    }
    
    void init() throws Exception {
    	if (fromFile) {
    		in = new BufferedReader(new FileReader(filename+".in"));
        	out = new PrintWriter(new FileWriter(filename+".out"));
    	} else {
    		in = new BufferedReader(new InputStreamReader(System.in));
        	out = new PrintWriter(System.out);
    	}
        sc = new FastScanner(in);
    }
}

class FastScanner {
    
    BufferedReader reader;
    StringTokenizer strTok;
    
    public FastScanner(BufferedReader reader) {
        this.reader = reader;
    }
    
    public String nextToken() throws IOException {
        while (strTok == null || !strTok.hasMoreTokens()) {
            strTok = new StringTokenizer(reader.readLine());
        }
        
        return strTok.nextToken();
    }
    
    public int nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }
    
    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }
    
    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }
    
    public BigInteger nextBigInteger() throws IOException {
    	return new BigInteger(nextToken());
    }
    
    public BigDecimal nextBigDecimal() throws IOException {
    	return new BigDecimal(nextToken());
    }
}