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 implements Runnable {
    private MyScanner in;
    private PrintWriter out;
    
    private int[][] win;

    private void solve() {
        int n = in.nextInt();
        char[] a = in.next().toCharArray();
        int m = a.length;
        char[] b = in.next().toCharArray();
        int k = b.length;
        win = new int[200][200];
        win['S']['P'] = 1;
        win['R']['S'] = 1;
        win['P']['R'] = 1;
        int full = m * k;
        int[] awin = new int[full + 1], bwin = new int[full + 1];
        for (int i = 0, p1 = 0, p2 = 0; i < full; ++i, ++p1, ++p2) {
            if (p1 == m) {
                p1 = 0;
            }
            if (p2 == k) {
                p2 = 0;
            }
            awin[i + 1] = awin[i] + win[a[p1]][b[p2]];
            bwin[i + 1] = bwin[i] + win[b[p2]][a[p1]];
        }
        int fullRounds = n / full, left = n % full;
        out.println((bwin[full] * fullRounds + bwin[left]) + " " + (awin[full] * fullRounds + awin[left]));
    }

    @Override
    public void run() {
        in = new MyScanner();
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

    public static void main(String[] args) {
        new A().run();
    }

    static class MyScanner {
        private BufferedReader br;
        private StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                    return null;
                }
            }
            return st.nextToken();
        }

        public String nextLine() {
            try {
                st = null;
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                return null;
            }
        }

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

        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public boolean hasNext() {
            if (st != null && st.hasMoreTokens()) {
                return true;
            }
            try {
                while (br.ready()) {
                    st = new StringTokenizer(br.readLine());
                    if (st != null && st.hasMoreTokens()) {
                        return true;
                    }
                }
            } catch (IOException e) {
                e.printStackTrace();
            }
            return false;
        }
    }
}