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.*;
import java.util.*;

public class Main implements Runnable {

	public void _main() throws IOException {
		int n = nextInt();
		String s1 = next();
		String s2 = next();
		int len = lcm(s1.length(), s2.length());
		int r1 = 0;
		int r2 = 0;
		for (int i = 0; i < len; i++) {
			int c1 = "RPS".indexOf(s1.charAt(i % s1.length()));
			int c2 = "RPS".indexOf(s2.charAt(i % s2.length()));
			if ((c1 + 1) % 3 == c2) {
				++r1;
			}
			if ((c2 + 1) % 3 == c1) {
				++r2;
			}
		}
		r1 *= n / len;
		r2 *= n / len;
		n %= len;
		for (int i = 0; i < n; i++) {
			int c1 = "RPS".indexOf(s1.charAt(i % s1.length()));
			int c2 = "RPS".indexOf(s2.charAt(i % s2.length()));
			if ((c1 + 1) % 3 == c2) {
				++r1;
			}
			if ((c2 + 1) % 3 == c1) {
				++r2;
			}
		}
		out.println(r1 + " " + r2);
	}

	private int lcm(int a, int b) {
		return (a / gcd(a, b)) * b;
	}


	private int gcd(int a, int b) {
		return b == 0 ? a : gcd(b, a % b);
	}




	private BufferedReader in;
	private PrintWriter out;
	private StringTokenizer st;

	private String next() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String rl = in.readLine();
			if (rl == null)
				return null;
			st = new StringTokenizer(rl);
		}
		return st.nextToken();
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(next());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(next());
	}

	private double nextDouble() throws IOException {
		return Double.parseDouble(next());
	}

	public static void main(String[] args) {
		Locale.setDefault(Locale.UK);
		new Thread(new Main()).start();
	}

	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);

			_main();

			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(202);
		}
	}

}
