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.math.*;
import java.util.*;

public class Solution implements Runnable {

	void solve() throws Exception {
		int n = nextInt();
		char[] a = nextToken().toCharArray();
		char[] b = nextToken().toCharArray();
		int cycleLen = a.length * b.length;
		int cntA = 0, cntB = 0;
		for (int i = 0; i < cycleLen; ++i) {
			int cur = getWin(getMove(a, i), getMove(b, i));
			if (cur < 0) {
				++cntA;
			} else if (cur > 0) {
				++cntB;
			}
		}
		cntA *= n / cycleLen;
		cntB *= n / cycleLen;
		int upto = n / cycleLen * cycleLen;
		for (int i = upto; i < n; ++i) {
			int cur = getWin(getMove(a, i), getMove(b, i));
			if (cur < 0) {
				++cntA;
			} else if (cur > 0) {
				++cntB;
			}
		}
		out.print(cntA + " " + cntB);
	}
	
	private char getMove(char[] a, int x) {
		return a[x % a.length];
	}

	int getWin(char a, char b) {
		String t = "RPS";
		if (a == b) {
			return 0;
		} else if (t.indexOf("" + a) == (t.indexOf("" + b) + 1) % 3) {
			return 1;
		} else {
			return -1;
		}
	}
	
	public void run() {
		try {
			solve();
		} catch (Exception e) {
			NOO(e);
		} finally {
			out.close();
		}
	}
	
	long nextLong() {
		return Long.parseLong(nextToken());
	}
	
	double nextDouble() {
		return Double.parseDouble(nextToken());
	}
	
	int nextInt() {
		return Integer.parseInt(nextToken());
	}
	
	String nextToken() {
		while (!stringTokenizer.hasMoreTokens()) {
			String line = null;
			try {
				line = in.readLine();
			} catch (IOException e) {
				NOO(e);
			}
			if (line == null) {
				return null;
			}
			stringTokenizer = new StringTokenizer(line);
		}
		return stringTokenizer.nextToken();
	}
	
	BufferedReader in;
	PrintWriter out;
	StringTokenizer stringTokenizer;
	
	void NOO(Exception e) {
		e.printStackTrace();
		System.exit(42);
	}
	
	public Solution(String name) {
		try {
			in = new BufferedReader(new FileReader("input.txt"));
			out = new PrintWriter(new FileWriter("output.txt"));
			stringTokenizer = new StringTokenizer("");
		} catch (Exception e) {
			NOO(e);
		}
	}
	
	public Solution() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter(System.out);
			stringTokenizer = new StringTokenizer("");
		} catch (Exception e) {
			NOO(e);
		}
	}
	
	public static void main(String[] args) {
		Locale.setDefault(Locale.US);
		new Solution().run();
	}
}
