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.*;

public class cfArock {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int n = in.nextInt();
        String a = in.next();
        String b = in.next();
        int[] ret = new int[2];
        int[] cyc = new int[2];
        for (int k = 0; k < a.length() * b.length(); k++) {
            if (n % (a.length() * b.length()) == k) {ret[0]+=cyc[0]; ret[1]+=cyc[1];}
            int g = beats(a.charAt(k % a.length()),b.charAt(k % b.length()));
            if (g == 1) cyc[1]++;
            if (g == -1) cyc[0]++;
        }
        ret[0]+=n/(a.length() * b.length()) * cyc[0];
        ret[1]+=n/(a.length() * b.length()) * cyc[1];
        System.out.println(ret[0] + " " + ret[1]);
    }
    
    public static int beats(char l, char r) {
        if (l == 'R'){
            if (r == 'S') return 1;
            if (r == 'P') return -1;
        }
        if (l == 'P'){
            if (r == 'R') return 1;
            if (r == 'S') return -1;
        }
        if (l == 'S'){
            if (r == 'P') return 1;
            if (r == 'R') return -1;
        }
        return 0;
    }
}
