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 Shishki {
    public static void main(String[] args) {
        solve();
    }

    public static void solve() {
        BufferedReader br = null;
        InputStreamReader is = null;
        is = new InputStreamReader(System.in);
        br = new BufferedReader(is);
        try {
            
            Game game = new Game();
            int gamesNumber = Integer.valueOf(br.readLine());
            game.firstAlgo = br.readLine();
            game.secondAlgo = br.readLine();
            game.firstSize = game.firstAlgo.length();
            game.secondSize = game.secondAlgo.length();
            int nok = getNOK(game.firstSize, game.secondSize);
            if (gamesNumber < nok) {
                for (int index = 0; index < gamesNumber; ++index) {
                    game.round(index);
                }
            } else {
                int first;
                int second;
                int pause = gamesNumber % nok;
                for (int index = 0; index < pause; ++index) {
                    game.round(index);
                }
                first = game.firstShishki;
                second = game.secondShiski;
                for (int index = pause; index < nok; ++index) {
                    game.round(index);
                }
                int number = gamesNumber / nok;
                game.firstShishki = number * game.firstShishki + first;
                game.secondShiski = number * game.secondShiski + second;
            }
            System.out.println(game.firstShishki + " " + game.secondShiski);
        } catch (Exception e) {
            e.printStackTrace();
        }
        if (is != null)
            try {
                is.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        if (br != null)
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
    }
    
    static int getNod(int num1, int num2) {
        int n = num1 % num2;
        num1 = num2;
        num2 = n;
        if (n > 0) 
            return getNod(num1, num2);
        else 
            return num1;
    }
    
    static int getNOK(int num1, int num2) {
        return num1 * num2 / getNod(num1, num2);
    }
    
    
}
class Game {
    int firstShishki = 0;
    int secondShiski = 0;
    String firstAlgo;
    String secondAlgo;
    int firstSize;
    int secondSize;
    int lastGame;
    void round(int round) {
        int first = round % firstSize;
        int second = round % secondSize;
        if (firstAlgo.charAt(first) == 'R') {
            if (secondAlgo.charAt(second) == 'P') {
                ++firstShishki;
            } else if (secondAlgo.charAt(second) == 'S')
                ++secondShiski;
        } else if (firstAlgo.charAt(first) == 'P') {
            if (secondAlgo.charAt(second) == 'S') {
                ++firstShishki;
            } else if (secondAlgo.charAt(second) == 'R')
                ++secondShiski;
        } else if (firstAlgo.charAt(first) == 'S') {
            if (secondAlgo.charAt(second) == 'R') {
                ++firstShishki;
            } else if (secondAlgo.charAt(second) == 'P')
                ++secondShiski;
        }
    }
}
