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.StringTokenizer;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import static java.lang.System.*;
import java.math.BigInteger;
import java.util.List;
import java.util.ArrayList;
import java.util.Scanner;
import java.util.Arrays;

public class rockpaperscissor {

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static Scanner sc = new Scanner(System.in);

    public static String getString() {
        try {
            return br.readLine();
        } catch (Exception e) {
        }
        return "";
    }

    public static Integer getInt() {
        try {
            return Integer.parseInt(br.readLine());
        } catch (Exception e) {
        }
        return 0;
    }

    public static Integer[] getIntArr() {
        try {
            String temp[] = br.readLine().split(" ");
            Integer temp2[] = new Integer[temp.length];
            for (int i = 0; i < temp.length; i++) {
                temp2[i] = Integer.parseInt(temp[i]);
            }
            return temp2;
        } catch (Exception e) {
        }
        return null;
    }

    public static int getMax(Integer[] ar) {
        int t = ar[0];
        for (int i = 0; i < ar.length; i++) {
            if (ar[i] > t) {
                t = ar[i];
            }
        }
        return t;
    }

    public static void printList(List<Integer> a) {
        System.out.println(a.toString().replace("[", "").replace("]", "").replace(",", ""));
    }

    public static void print(Object a) {
        out.println(a);
    }

    public static int nextInt() {
        return sc.nextInt();
    }

    public static double nextDouble() {
        return sc.nextDouble();
    }

    public static BigInteger getFact(long in) {
        BigInteger ot = new BigInteger("1");
        for (Integer i = 1; i <= in; i++) {
            ot = ot.multiply(new BigInteger(i.toString()));
        }
        return ot;
    }

    public static String gbase(int a, int base) {
        String out = "";
        int temp = a;
        while (temp > 0) {
            out = temp % base + out;
            temp /= base;
        }
        return out;
    }

    public static void main(String[] ar) {
        int n = getInt();
        char[] input = getString().toCharArray();
        char[] input2 = getString().toCharArray();
        int win = 0;
        int draw = 0;
        int kalah = 0;

        int kpk = kpk(input.length, input2.length);
        //System.out.println(kpk);
        int pengali = n / kpk;

        if (pengali > 0) {

            for (int i = 0, j = 0, k = 0; i < kpk; i++) {
                char a = input[j];
                char b = input2[k];
                if (a == b) {
                    draw++;
                    //print(a+" lwn "+b+" seri");
                } else if ((a == 'R' && b == 'S') || (a == 'P' && b == 'R') || (a == 'S' && b == 'P')) {
                    win++;
                    //print(a+" lwn "+b + " menang");
                } else {
                    //print(a+" lwn "+b + " kalah");
                    kalah++;
                }
                if (j < input.length - 1) {
                    j++;
                } else if (j == input.length - 1) {
                    j = 0;
                }
                if (k < input2.length - 1) {
                    k++;
                } else if (k == input2.length - 1) {
                    k = 0;
                }
            }
            win*=pengali;
            draw*=pengali;
            kalah*=pengali;
        }
        //System.out.println(kalah + " " + win);
        if (n % kpk > 0) {
            for (int i = 0, j = 0, k = 0; i < n % kpk; i++) {
                char a = input[j];
                char b = input2[k];

                if (a == b) {
                    draw++;
                    //print(a+" lwn "+b+" seri");
                } else if ((a == 'R' && b == 'S') || (a == 'P' && b == 'R') || (a == 'S' && b == 'P')) {
                    win++;
                    //print(a+" lwn "+b + " menang");
                } else {
                    kalah++;
                    //print(a+" lwn "+b + " kalah");
                }
                if (j < input.length - 1) {
                    j++;
                } else if (j == input.length - 1) {
                    j = 0;
                }
                if (k < input2.length - 1) {
                    k++;
                } else if (k == input2.length - 1) {
                    k = 0;
                }
            }
        }

        System.out.println(kalah + " " + win);
    }

    public static int kpk(int a, int b) {
        int min = Math.min(a, b);
        int max = Math.max(a, b);
        int out = 0;
        for (int i = min; i <= max*min; i += min) {
            if (i % max == 0) {
                out = i;
                break;
            }
        }
        return out;
    }
}
