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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.StringTokenizer;

public class Solver {

    StringTokenizer st;
    BufferedReader in;
    PrintWriter out;

    public static void main(String[] args) throws NumberFormatException, IOException {
        Solver solver = new Solver();
        solver.open();
        solver.solve();
        solver.close();
    }

    public void open() throws IOException {
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
    }

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

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

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

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

    public class player{
        int count = 0;
        char[] seq = null;
        int length = 0;
        int current = 0;
        
        public player(String s){
            this.seq = s.toCharArray();
            this.length = seq.length;
        }
        
        public char getStep(){
            char result = seq[current++];
            if (current>=length) current = 0;
            return result;
        }
    }
    
    public int who(char c1,char c2){
        int result = 0;
        if (c1=='R' && c2=='S') result = -1;
        else if (c1=='R' && c2=='P') result = 1;
        else if (c1=='S' && c2=='R') result = 1;
        else if (c1=='S' && c2=='P') result = -1;
        else if (c1=='P' && c2=='R') result = -1;
        else if (c1=='P' && c2=='S') result = 1;
        return result;
    }
    
    public void solve() throws NumberFormatException, IOException {
        int n = nextInt();
        char[] Nick = (in.readLine().toCharArray());
        char[] Poly = (in.readLine().toCharArray());
        
        int l1 = Nick.length;
        int l2 = Poly.length;
        int x = 0;
        int y = 0;
        int i1 = 0;
        int i2 = 0;
        
        int bar = l1*l2;
        
        for (int i=0;i<bar;i++){
            char c1 = Nick[i1++];
            if (i1>=l1) i1 = 0;
            char c2 = Poly[i2++];
            if (i2>=l2) i2 = 0;
            
            if (c1=='R' && c2=='S') y++;
            else if (c1=='R' && c2=='P') x++;
            else if (c1=='S' && c2=='R') x++;
            else if (c1=='S' && c2=='P') y++;
            else if (c1=='P' && c2=='R') y++;
            else if (c1=='P' && c2=='S') x++;
        }
        
        int coef = n/bar;
        x*=coef;
        y*=coef;
        
        n %= bar;
        for (int i=0;i<n;i++){
            char c1 = Nick[i1++];
            if (i1>=l1) i1 = 0;
            char c2 = Poly[i2++];
            if (i2>=l2) i2 = 0;
            
            if (c1=='R' && c2=='S') y++;
            else if (c1=='R' && c2=='P') x++;
            else if (c1=='S' && c2=='R') x++;
            else if (c1=='S' && c2=='P') y++;
            else if (c1=='P' && c2=='R') y++;
            else if (c1=='P' && c2=='S') x++;
        }
        
        out.println(x+" "+y);
    }

    public void close() {
        out.flush();
        out.close();
    }

}