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;
import java.text.DecimalFormat;
import java.util.Date;
import java.util.StringTokenizer;

public class Main {

	/**
	 * @param args
	 * @throws IOException
	 * @throws NumberFormatException
	 */
	public static void main(String[] args) throws NumberFormatException, IOException {
		new Main().run();
	}

	private StringTokenizer input;
	private BufferedReader reader;
	
	private void run() throws NumberFormatException, IOException {
		openInput(null);

		long start = new Date().getTime();
		
		long l = nextLong();
		char[] a = next().toCharArray();
		char[] b = next().toCharArray();
		
		int ai = 0;
		int bi = 0;
		
		int an = 0;
		int bn = 0;
		long i = 0;
		long period = a.length * b.length;
		while (i < l) {
			switch (a[ai] - b[bi]) {
			case 0:
				break;
			case -1:
				bn++;
				break;
			case 2:
				an++;
				break;
			case 1:
				an++;
				break;
			case 3:
				bn++;
				break;
			case -2:
				bn++;
				break;
			case -3:
				an++;
				break;
			}
			
			ai++;
			if (ai == a.length) {
				ai = 0;
			}
			bi++;
			if (bi == b.length) {
				bi = 0;
			}
			i++;
			if (i == period) {
				an *= l / period;
				bn *= l / period;
				i = l - l % period;
				period = -1;
			}
		}
		
		System.out.println(an + " " + bn);
		
		closeInput();
	}
	
	private void openInput(String fileName) {
		reader = new BufferedReader(new InputStreamReader(System.in));
	}
	
	private void closeInput() {
		try {
			reader.close();
		} catch (IOException e) {
			e.printStackTrace();
		}
	}
	
	private String next() throws IOException {
		while (input == null || !input.hasMoreTokens()) {
			input = new StringTokenizer(reader.readLine());
		}
		return input.nextToken();
	}
	
	@SuppressWarnings("unused")
	private long nextLong() throws NumberFormatException, IOException {
		return Long.parseLong(next());
	}
	
	@SuppressWarnings("unused")
	private int nextInt() throws NumberFormatException, IOException {
		return Integer.parseInt(next());
	}
	
	@SuppressWarnings("unused")
	private double nextDouble() throws NumberFormatException, IOException {
		return Double.parseDouble(next());
	}

}
