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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Solver {

    public static void main(String[] Args) throws NumberFormatException,
            IOException {
        new Solver().Run();

    }

    PrintWriter pw;
    StringTokenizer Stok;
    BufferedReader br;

    public String nextToken() throws IOException {
        while (Stok == null || !Stok.hasMoreTokens()) {
            Stok = new StringTokenizer(br.readLine());
        }
        return Stok.nextToken();
    }

    public int nextInt() throws NumberFormatException, IOException {
        return Integer.parseInt(nextToken());
    }

    public double nextDouble() throws NumberFormatException, IOException {
        return Double.parseDouble(nextToken());
    }

    public long nextLong() throws NumberFormatException, IOException {
        return Long.parseLong(nextToken());
    }

    public void Run() throws NumberFormatException, IOException {
        //br = new BufferedReader(new FileReader("input.txt"));
        //pw = new PrintWriter("output.txt");
        br = new BufferedReader(new InputStreamReader(System.in));
        pw = new PrintWriter(new OutputStreamWriter(System.out));
        long n = nextInt();
        String Nik = nextToken();
        String Pol = nextToken();
        int lNik = Nik.length();
        int lPol = Pol.length();
        long cNik = 0,cPol = 0;
        for (int i=0; i<lNik*lPol; i++)
        {
            if (Nik.charAt(i%lNik) == 'R')
                if (Pol.charAt(i%lPol) == 'S')
                    cPol++;
                    else{
                        if (Pol.charAt(i%lPol) == 'P')
                            cNik++;}
            else 
                if (Nik.charAt(i%lNik)=='S')
                    if (Pol.charAt(i%lPol)=='P')
                        cPol++;
                    else{
                        if (Pol.charAt(i%lPol)=='R')
                            cNik++;}
                else
                    if (Nik.charAt(i%lNik)=='P')
                        if (Pol.charAt(i%lPol)=='R')
                            cPol++;
                        else if (Pol.charAt(i%lPol)=='S')
                                cNik++; 
        }
        cNik = cNik*(n/(lNik*lPol));
        cPol = cPol*(n/(lNik*lPol));
        for (int i=0; i<n%(lNik*lPol); i++)
        {
            if (Nik.charAt(i%lNik) == 'R')
                if (Pol.charAt(i%lPol) == 'S')
                    cPol++;
                    else{
                        if (Pol.charAt(i%lPol) == 'P')
                            cNik++;}
            else 
                if (Nik.charAt(i%lNik)=='S')
                    if (Pol.charAt(i%lPol)=='P')
                        cPol++;
                    else{
                        if (Pol.charAt(i%lPol)=='R')
                            cNik++;}
                else
                    if (Nik.charAt(i%lNik)=='P')
                        if (Pol.charAt(i%lPol)=='R')
                            cPol++;
                        else if (Pol.charAt(i%lPol)=='S')
                                cNik++; 
        }
        pw.print(cNik);
        pw.print(' ');
        pw.print(cPol);
        pw.flush();
        pw.close();

    }

}

