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 Crc_A {

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        long n = in.nextLong();
        char[] a = in.next().toCharArray();
        char[] b = in.next().toCharArray();
        long ans1 = 0, ans2 = 0;
        long m = a.length * b.length;

        long x = n / m;
        int next1 = 0;
        int next2 = 0;
        for (int i = 0; i < m; i++) {
            int q = check(a[next1 % a.length], b[next2 % b.length]);
            next1++;
            next2++;
            if (q == -1)
                ans2++;
            else if (q == 1)
                ans1++;
        }
        ans1 *= x;
        ans2 *= x;
        next1 = 0;
        next2 = 0;
        for (int i = 0; i < n % m; i++) {
            int q = check(a[next1 % a.length], b[next2 % b.length]);
            next1++;
            next2++;
            if (q == -1)
                ans2++;
            else if (q == 1)
                ans1++;
        }
        System.out.println(ans1 + " " + ans2);

    }

    // R , S , P
    public static int check(char x, char y) {
        if (x == y)
            return 0;
        if (x == 'R' && y == 'S') {
            return -1;
        }
        if (y == 'R' && x == 'S') {
            return 1;
        }
        if (x == 'S' && y == 'P') {
            return -1;
        }
        if (x == 'P' && y == 'S') {
            return 1;
        }

        if (x == 'P' && y == 'R') {
            return -1;
        }
        if (x == 'R' && y == 'P') {
            return 1;
        }

        return 0;
    }

}
