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 ProblemA {

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

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        char[] a = sc.next().toCharArray();
        int m = a.length;
        char[] b = sc.next().toCharArray();
        int k = b.length;
        long polycounter = 0;
        long nikcounter = 0;
        long addpolycounter = 0;
        long addnikcounter = 0;
        int nok = m * k / gcd(m, k);
        for (int i = 0; i < Math.min(nok, n); i++) {
            if (n > nok && i == n % nok) {
                addpolycounter = polycounter;
                addnikcounter = nikcounter;
            }
            char nik = a[i % m];
            char poly = b[i % k];
            if (nik == poly)
                continue;
            switch (nik) {
            case 'P': {
                if (poly == 'R') {
                    polycounter++;
                } else if (poly == 'S') {
                    nikcounter++;
                }
                break;
            }
            case 'R': {
                if (poly == 'S') {
                    polycounter++;
                } else if (poly == 'P') {
                    nikcounter++;
                }
                break;
            }
            case 'S': {
                if (poly == 'P') {
                    polycounter++;
                } else if (poly == 'R') {
                    nikcounter++;
                }
                break;
            }
            }
        }
        polycounter *= n / nok == 0 ? 1 : n / nok;
        polycounter += addpolycounter;
        nikcounter *= n / nok == 0 ? 1 : n / nok;
        nikcounter += addnikcounter;
        System.out.println(nikcounter + " " + polycounter);
    }
}