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.PrintWriter;
import java.util.Scanner;

/**
 * Created by IntelliJ IDEA.
 * User: komarov
 * Date: 4/6/12
 * Time: 7:00 PM
 * To change this template use File | Settings | File Templates.
 */
public class A {

    int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }
    
    int get(char a, char b) {
        if (a == b)
            return 0;
        if (a == 'R' && b == 'S')
            return 1;
        if (a == 'S' && b == 'P')
            return 1;
        if (a == 'P' && b == 'R')
            return 1;
        return -1;
    }
    
    void solve() {
        int rounds = in.nextInt();
        String s1 = in.next();
        String s2 = in.next();
        int n = s1.length();
        int m = s2.length();
        int k = n * m / gcd(n, m);
        
        int[] outcome = new int[k];
        
        for (int i = 0; i < k; i++) {
            outcome[i] = get(s1.charAt(i % n), s2.charAt(i % m));
        }

        int sum1 = 0;
        int sum2 = 0;
        for (int i = 0; i < k; i++) {
            sum1 += outcome[i] > 0 ? 1 : 0;
            sum2 += outcome[i] < 0 ? 1 : 0;
        }

        int a1 = rounds / k * sum1;
        int a2 = rounds / k * sum2;

        for (int i = 0; i < rounds % k; i++) {
            a1 += outcome[i] > 0 ? 1 : 0;
            a2 += outcome[i] < 0 ? 1 : 0;
        }

        
        out.print(a2 + " " + a1);

    }

    static Scanner in;
    static PrintWriter out;
    
    public static void main(String[] args) {
        in = new Scanner(System.in);
        out = new PrintWriter(System.out);
        new A().solve();
        out.close();
    }
    
}
