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;

/**
 * Created by IntelliJ IDEA.
 * User: Linkov Mikl
 * Date: 04.04.12
 * Time: 23:52
 * To change this template use File | Settings | File Templates.
 */
public class ProblemFirst {
    public static void main(String [] args) {
        Scanner scanner = new Scanner(System.in);

        int roundCount = scanner.nextInt();
        scanner.nextLine();
        String polyString = scanner.nextLine();
        String kolString = scanner.nextLine();
        int m = polyString.length() * kolString.length();
        int [] var1 = new int[m];
        int [] var2 = new int[m];
        for (int i = 0; i < m; i++) {
            if (polyString.charAt(i % polyString.length()) == 'R') {
                var1[i] = 0;
            }
            if (polyString.charAt(i % polyString.length()) == 'S') {
                var1[i] = 1;
            }
            if (polyString.charAt(i % polyString.length()) == 'P') {
                var1[i] = 2;
            }
        }

        for (int i = 0; i < m; i++) {
            if (kolString.charAt(i % kolString.length()) == 'R') {
                var2[i] = 0;
            }
            if (kolString.charAt(i % kolString.length()) == 'S') {
                var2[i] = 1;
            }
            if (kolString.charAt(i % kolString.length()) == 'P') {
                var2[i] = 2;
            }
        }

        if (m >= roundCount) {
            int polyCount = 0;
            int kolCount = 0;
            for (int i = 0; i < roundCount; i++) {
                if ((var1[i] == 0) && (var2[i] == 1)) {
                    polyCount++;
                }
                if ((var1[i] == 1) && (var2[i] == 2)) {
                    polyCount++;
                }
                if ((var1[i] == 2) && (var2[i] == 0)) {
                    polyCount++;
                }

                if ((var2[i] == 0) && (var1[i] == 1)) {
                    kolCount++;
                }
                if ((var2[i] == 1) && (var1[i] == 2)) {
                    kolCount++;
                }
                if ((var2[i] == 2) && (var1[i] == 0)) {
                    kolCount++;
                }
            }
            System.out.println(kolCount + " " + polyCount);
            return;
        }

        int polyCount = 0;
        int kolCount = 0;

        for (int i = 0; i < m; i++) {
            if ((var1[i] == 0) && (var2[i] == 1)) {
                polyCount++;
            }
            if ((var1[i] == 1) && (var2[i] == 2)) {
                polyCount++;
            }
            if ((var1[i] == 2) && (var2[i] == 0)) {
                polyCount++;
            }

            if ((var2[i] == 0) && (var1[i] == 1)) {
                kolCount++;
            }
            if ((var2[i] == 1) && (var1[i] == 2)) {
                kolCount++;
            }
            if ((var2[i] == 2) && (var1[i] == 0)) {
                kolCount++;
            }
        }

        int allPoly = 0;
        int allKol = 0;

        allKol = (roundCount) / m * kolCount;
        allPoly =(roundCount) / m * polyCount;

        roundCount %= m;

        polyCount = 0;
        kolCount = 0;

        for (int i = 0; i < roundCount; i++) {
            if ((var1[i] == 0) && (var2[i] == 1)) {
                polyCount++;
            }
            if ((var1[i] == 1) && (var2[i] == 2)) {
                polyCount++;
            }
            if ((var1[i] == 2) && (var2[i] == 0)) {
                polyCount++;
            }

            if ((var2[i] == 0) && (var1[i] == 1)) {
                kolCount++;
            }
            if ((var2[i] == 1) && (var1[i] == 2)) {
                kolCount++;
            }
            if ((var2[i] == 2) && (var1[i] == 0)) {
                kolCount++;
            }
        }

        allKol += kolCount;
        allPoly += polyCount;

        System.out.println(allKol + " " + allPoly);
        return;
    }
}
