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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class A {
    public static int gcd(int x, int y) {
        if (y == 0)
            return x;
        else
            return gcd(y, x % y);
    }

    public static int lcm(int x, int y) {
        return x * y / gcd(x, y);
    }

    public static String sim(String s1, String s2, int g) {
        int a = 0;
        int b = 0;
        for (int i = 0; i < g; i++) {
            char c1 = s1.charAt(i % s1.length());
            char c2 = s2.charAt(i % s2.length());
            if (c1 == c2)
                continue;
            switch (c1) {
            case 'R':
                if (c2 == 'S')
                    a++;
                else
                    b++;
                break;
            case 'P':
                if (c2 == 'R')
                    a++;
                else
                    b++;
                break;
            case 'S':
                if (c2 == 'P')
                    a++;
                else
                    b++;
                break;
            }
        }
        return a + " " + b;
    }

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        String s1 = in.readLine();
        String s2 = in.readLine();
        int l = lcm(s1.length(), s2.length());
        int r = n / l;
        String[] S1 = sim(s1, s2, l).split(" ");
        String[] S2 = sim(s1, s2, n % l).split(" ");
        int a = Integer.parseInt(S1[0]) * r + Integer.parseInt(S2[0]);
        int b = Integer.parseInt(S1[1]) * r + Integer.parseInt(S2[1]);
        System.out.println(b + " " + a);
    }
}
