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.Scanner;

public class CF173A{
    private static int gcd(int a, int b){
        if (b==0) return a;
        return gcd(b, a%b);
    }

    private static int atob(char a, char b){
        if (a==b) return 0;
        if (a=='R'){
            if (b=='S') return 1;
            else return -1;
        } else if (a=='S'){
            if (b=='P') return 1;
            else return -1;
        } else {
            if (b=='R') return 1;
            else return -1;
        }
    }

    public static void main(String[] args){
        Scanner scn = new Scanner(System.in);
        while (scn.hasNext()){
            int n = scn.nextInt();
            scn.nextLine();
            String a = scn.nextLine();
            String b = scn.nextLine();
            int la = a.length();
            int lb = b.length();
            int lcm = la*lb/gcd(la, lb);
            int cnta = 0, cntb = 0;
            int idxa = 0, idxb = 0;
            int rmda = 0, rmdb = 0, rmd = n%lcm;
            for (int i=0; i<lcm; i++){
                int result = atob(a.charAt(idxa), b.charAt(idxb));
                if (i == rmd){
                    rmda = cnta;
                    rmdb = cntb;
                }
                if (result == 1){
                    cnta++;
                } else if (result == -1){
                    cntb++;
                }
                idxa++;
                if (idxa == la) idxa = 0;
                idxb++;
                if (idxb == lb) idxb = 0;
            }
            cnta = cnta*(n/lcm)+rmda;
            cntb = cntb*(n/lcm)+rmdb;
            System.out.printf("%d %d%n", cntb, cnta);
        }
    }
}