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.InputStreamReader;
import java.util.StringTokenizer;

public class Solution {
    //<editor-fold desc="input parse" defaultstate="collapsed">

    private static StringTokenizer st;
    private static BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

    private static long nextLong() {
        return Long.parseLong(st.nextToken());
    }

    private static int nextInt() {
        return Integer.parseInt(st.nextToken());
    }

    private static double nextDouble() {
        return Double.parseDouble(st.nextToken());
    }

    private static short nextShort() {
        return Short.parseShort(st.nextToken());
    }

    private static byte nextByte() {
        return Byte.parseByte(st.nextToken());
    }

    private static void initTokenizer() throws Exception {
        st = new StringTokenizer(reader.readLine());
    }

    //</editor-fold>

    private static int nod(int a, int b) {
        if (b == 0) return a;
        return nod(b, a % b);
    }

    private static int nok(int a, int b) {
        return a / nod(a, b) * b;
    }

    private static char[] first, second;

    private static int[] count(int length) {
        int c1 = 0;
        int c2 = 0;

        for (int i = 0; i < length; i++) {
            char fi = first[i % first.length];
            char se = second[i % second.length];

            switch (fi) {
                case 'R': {
                    if (se == 'P') c1++;
                    else if (se == 'S') c2++;

                    break;
                }
                case 'P': {
                    if (se == 'R') c2++;
                    else if (se == 'S') c1++;

                    break;
                }
                case 'S': {
                    if (se == 'P') c2++;
                    else if (se == 'R') c1++;

                    break;
                }
            }
        }

        return new int[] { c1, c2 };
    }

    public static void main(String[] args) throws Exception {
        initTokenizer();

        int rounds = nextInt();

        first = reader.readLine().trim().toCharArray();
        second = reader.readLine().trim().toCharArray();

        int period = nok(first.length, second.length);

        int[] cper = count(period);

        int full  = rounds / period;
        int piece = rounds % period;

        int c1 = cper[0] * full;
        int c2 = cper[1] * full;

        cper = count(piece);

        c1 += cper[0];
        c2 += cper[1];

        System.out.print(c1 + " " + c2);
    }
}