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.*;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;



public class Main {
    
    private void solve() throws Exception {
        int n = in.nextInt();
        String s1 = in.nextToken();
        String s2 = in.nextToken();
        int g = lcm(s1.length(), s2.length());
        int whole = n / g;
        int part = n % g;
        int c1=0, c2=0;
        c1 = calc(g, s1, s2) * whole;
        c2 = calc(g, s2, s1) * whole;
        for(int j=0;j<part; ++j) {
            c1 += beat(s2.charAt(j % s2.length()), s1.charAt(j % s1.length()));
            c2 += beat(s1.charAt(j % s1.length()), s2.charAt(j % s2.length()));
            
        }
        out.println(c1 + " " + c2);
    }
    
    
    

    private int calc(int g, String s1, String s2) {
        int res = 0;
        for(int i = 0; i < g; ++i) {
            res += beat(s2.charAt(i % s2.length()), s1.charAt(i % s1.length()));
        }
        return res;
    }




    private int beat(char a, char b) {
        return a=='R' && b =='S' || a=='S' && b=='P' || a=='P' && b=='R' ? 1  : 0; 
    }




    private int lcm(int a, int b) {
        return a*b / gcd(a, b);
    }

    private int gcd(int a, int b) {
        return a==0 ? b : gcd(b % a, a);
    }




    private void run() {
        try {
            long start = System.currentTimeMillis();
            in = new FastScanner("input.txt", "output.txt");
            solve();
            out.flush();
            System.err.print("running time = " + (System.currentTimeMillis() - start) * 1e-3);
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
    
    
    public static void main(String[] args) {
        Main main = new Main();
        main.run();
    }
    FastScanner in;
    static PrintWriter out;
    static class FastScanner {
        public BufferedReader reader;
        private StringTokenizer tokenizer;
        public FastScanner(String input, String output) {
            try {
                reader = new BufferedReader(new FileReader(new File(input)));
                out = new PrintWriter(new File(output));
                tokenizer = null;
            } catch (Exception e) {
                reader = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
                tokenizer = null;
            }
        }
        public String nextToken() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return tokenizer.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(nextToken());
        }
        long nextLong() {
            return Long.parseLong(nextToken());
        }
    }
}