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.OutputStream;
import java.io.IOException;
import java.io.PrintWriter;
import java.util.NoSuchElementException;
import java.io.InputStream;

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

class TaskA {
    String S = "RPS";
    public void solve(int testNumber, MyScanner in, PrintWriter out) {
        int A=0,B=0;
        int N=in.nextInt();
        String a=in.next(),b=in.next();
        for(int i=0;i<N;i++){
            int ai = i%a.length();
            int bi = i%b.length();
            if(i>0 && ai==0 && bi==0){
                int k = N/i;
                A = A*k;
                B = B*k;
                i = i*k;
            }
            if(i==N)break;
            if(a.charAt(ai)==b.charAt(bi));
            else if(S.indexOf(a.charAt(ai)) == (S.indexOf(b.charAt(bi)) + 1) % 3){
                B++;
            }else{
                A++;
            }
        }
        out.println(A+" "+B);
    }
}

class MyScanner {
    private final InputStream in;
    public MyScanner(InputStream in){
        this.in = in;
    }

    char[] buf = new char[2000000];
    int strLen;
    public String next() {
        try {
            strLen = 0;
            int c;
            do{
                c = in.read();
                if(c==-1)throw new NoSuchElementException();
            }while(Character.isWhitespace(c));
            do {
                buf[strLen++] = (char)c;
                c = in.read();
            } while (c!=-1 && !Character.isWhitespace(c));
            return new String(buf,0,strLen);
        } catch (IOException e) {
            throw new NoSuchElementException();
        }
    }

    public int nextInt(){
        try{
            int c=in.read();
            if(c==-1) return c;
            while(c!='-'&&(c<'0'||'9'<c)){
                c=in.read();
                if(c==-1) return c;
            }
            if(c=='-') return -nextInt();
            int res=0;
            do{
                res*=10;
                res+=c-'0';
                c=in.read();
            }while('0'<=c&&c<='9');
            return res;
        }catch(Exception e){
            return -1;
        }
    }


    }
