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.util.List;
import java.io.InputStreamReader;
import java.io.IOException;
import java.util.Arrays;
import java.util.ArrayList;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author lwc626
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        MyInputReader in = new MyInputReader(inputStream);
        MyOutputWriter out = new MyOutputWriter(outputStream);
        TaskA solver = new TaskA();
        solver.solve(1, in, out);
        out.close();
    }
}

class TaskA {
    public void solve(int testNumber, MyInputReader in, MyOutputWriter out) {
        int n = in.nextInt() ;
        char[] A = in.next().toCharArray() ;
        char[] B = in.next().toCharArray() ;
        int na = A.length , nb = B.length ;
        //System.out.println( na + " " + nb );
        int pa = na * nb / (int)IntegerUtils.gcd( na , nb )  ;
        //System.out.println( na * nb  + " " +pa);

        int ra = 0 ,rb = 0 ;
        for( int i = 0 ; i < pa ; i ++ ){
            int d = win( A[i%na] , B[ i % nb ] );
            if(  d == 1 )
                ra ++ ;
            else if( d == -1 )
                rb ++ ;
        }

        ra = n / pa * ra ;
        rb = n / pa * rb ;

        for( int i = 0 ; i < n % pa ; i ++ ){
            int d = win( A[i%na] , B[ i % nb ] );
            if(  d == 1 )
                ra ++ ;
            else if( d == -1 )
                rb ++ ;
        }
        out.printLine( rb , ra );
    }

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

class MyInputReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public MyInputReader(InputStream stream) {
        reader = new BufferedReader(new InputStreamReader(stream));
        tokenizer = null;
    }

    public String next() {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }
    
    }

class MyOutputWriter {
    private final PrintWriter writer;

    public MyOutputWriter(OutputStream outputStream) {
        writer = new PrintWriter(outputStream);
    }

    public MyOutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object...objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0)
                writer.print(' ');
            writer.print(objects[i]);
        }
    }

    public void printLine(Object...objects) {
        print(objects);
        writer.println();
    }

    public void close() {
        writer.close();
    }

}

class IntegerUtils {

    public static long gcd(long a, long b) {
        while (b != 0) {
            a = a % b;
            long t = a ; a = b ; b = t;
        }
        return a;
    }

    }

