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 taskA {

	BufferedReader br;
	PrintWriter out;
	StringTokenizer st;

	public String nextToken() throws IOException {
		while ((st == null) || (!st.hasMoreTokens()))
			st = new StringTokenizer(br.readLine());
		return st.nextToken();
	}

	public int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	public double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}

	public long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	int get(char a, char b) {
		if ((a == 'S') && (b == 'P'))
			return 1;
		if ((a == 'P') && (b == 'R'))
			return 1;
		if ((a == 'R') && (b == 'S'))
			return 1;
		return 0;
	}

	public void solve() throws IOException {
		int n = nextInt();
		String a = nextToken();
		String b = nextToken();
		int x = 0;
		int y = 0;
		boolean[][] was = new boolean[a.length()][b.length()];
		ArrayList<Integer> ans1 = new ArrayList<Integer>();
		ArrayList<Integer> ans2 = new ArrayList<Integer>();
		ans1.add(0);
		ans2.add(0);
		while (!was[x][y]) {
			was[x][y] = true;
			if ((a.charAt(x) != b.charAt(y))) {
				ans1.add(ans1.get(ans1.size() - 1)
						+ get(a.charAt(x), b.charAt(y)));
				ans2.add(ans2.get(ans2.size() - 1) + 1
						- get(a.charAt(x), b.charAt(y)));
			} else {
				ans1.add(ans1.get(ans1.size() - 1));
				ans2.add(ans2.get(ans2.size() - 1));
			}
			x = (x + 1) % a.length();
			y = (y + 1) % b.length();
		}
		out.print(ans2.get(ans1.size() - 1) * (n / (ans2.size() - 1))
				+ ans2.get(n % (ans2.size() - 1)));
		out.print(' ');
		out.print(ans1.get(ans1.size() - 1) * (n / (ans1.size() - 1))
				+ ans1.get(n % (ans1.size() - 1)));

	}

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

			//br = new BufferedReader(new FileReader("taskA.in"));
			//out = new PrintWriter("taskA.out");

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}

	public static void main(String[] args) {
		new taskA().run();
	}
}