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 A {

    private static int gcd(int x, int y) {
        if (x < y) {
            if (y % x == 0) {
                return y;
            }
            return x * y;
        } else {
            if (x > y) {
                if (x % y == 0) {
                    return x;
                }
                return x * y;
            } else {
                return x;
            }
        }
    }

    public static void get() {
        int n = 0;
        Scanner s = new Scanner(System.in);
        n = s.nextInt();
        char[] nike = s.next().toCharArray();
        char[] poly = s.next().toCharArray();

        int gcd = gcd(nike.length, poly.length);
        int count = n / gcd;
        int mod = n % gcd;
        int atModN = 0, atModP = 0;
        int nCounter = 0;
        int pCounter = 0;
        for (int i = 0; i < gcd; i++) {
            if (i == mod) {
                atModN = nCounter;
                atModP = pCounter;
                if (gcd > n) {
                    break;
                }
            }
            char c1 = nike[i % nike.length];
            char c2 = poly[i % poly.length];
            if (c1 == c2) {
                continue;
            }
            if ((c1 == 'R' && c2 == 'S') || (c1 == 'S' && c2 == 'P')
                    || (c1 == 'P' && c2 == 'R')) {
                pCounter++;
            } else {
                nCounter++;
            }

        }

        nCounter = nCounter * count + atModN;
        pCounter = pCounter * count + atModP;

        System.out.println(nCounter + " " + pCounter);

    }

    public static void main(String[] args) {

        get();

    }

}
