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 {
    static final int BIG = 1000000000;

    public void solve() throws IOException {
        int n = nextInt();
        String a = nextToken();
        String b = nextToken();
        int ansa = 0;
        int ansb = 0;
        int lcm = a.length() * b.length() / gcd(a.length(), b.length());
        for (int i = 0; i < lcm; i++) {
            char x = a.charAt(i % a.length());
            char y = b.charAt(i % b.length());
            if (x == y) continue;
            if (x == 'R' && y == 'S') ansb++;
            if (y == 'R' && x == 'S') ansa++;
            if (x == 'S' && y == 'P') ansb++;
            if (y == 'S' && x == 'P') ansa++;
            if (x == 'P' && y == 'R') ansb++;
            if (y == 'P' && x == 'R') ansa++;
        }
        ansa *= n / lcm;
        ansb *= n / lcm;
        for (int i = 0; i < n % lcm; i++) {
            char x = a.charAt(i % a.length());
            char y = b.charAt(i % b.length());
            if (x == y) continue;
            if (x == 'R' && y == 'S') ansb++;
            if (y == 'R' && x == 'S') ansa++;
            if (x == 'S' && y == 'P') ansb++;
            if (y == 'S' && x == 'P') ansa++;
            if (x == 'P' && y == 'R') ansb++;
            if (y == 'P' && x == 'R') ansa++;
        }
        writer.println(ansa + " " + ansb);
    }
    
    int gcd(int a, int b) {
        if (b == 0) return a;
        return gcd(b, a % b);
    }

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

    BufferedReader reader;

    StringTokenizer tokenizer;

    PrintWriter writer;

    public void run() {
        try {
            long tbegin = System.currentTimeMillis();
            reader = new BufferedReader(new InputStreamReader(System.in));
            //reader = new BufferedReader(new InputStreamReader(new FileInputStream("fselect.inp")));
            tokenizer = null;
            writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(
                    System.out)));
            //writer = new PrintWriter(new FileOutputStream("fselect.out"));
            solve();
            //System.out.println(System.currentTimeMillis() - tbegin + "ms...");
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }

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

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

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

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

}
