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.*;
import java.math.*;

public class Codeforces implements Runnable {
	BufferedReader in;
	PrintWriter out;
	StringTokenizer st;
	Random rnd;
	
	int getResult(char a, char b) {
		if(a == 'R') {
			if(b == 'S') {
				return 1;
			} else if(b == 'P') {
				return -1;
			} else {
				return 0;
			}
		} else if(a == 'P') {
			if(b == 'R') {
				return 1;
			} else if(b == 'S') {
				return -1;
			} else {
				return 0;
			}
		} else {
			if(b == 'P') {
				return 1;
			} else if(b == 'R') {
				return -1;
			} else {
				return 0;
			}
		}
	}
	
	void solve() throws IOException {
		int rounds = nextInt();
		
		String a = nextToken(), b = nextToken();
		int n = a.length(), m = b.length(), total = n * m;
		
		int[] firstWin = new int[total];
		int[] secondWin = new int[total];
		
		for(int i = 0; i < total; i++) {
			int curRes = getResult(a.charAt(i % n), b.charAt(i % m));
			
			int firstAdd = 0, secondAdd = 0;
			
			if(curRes == 1) {
				firstAdd = 1;
			} else if(curRes == -1) {
				secondAdd = 1;
			}
			
			int firstBefore = (i > 0) ? firstWin[i - 1] : 0;
			int secondBefore = (i > 0) ? secondWin[i - 1] : 0;
			
			firstWin[i] = firstBefore + firstAdd;
			secondWin[i] = secondBefore + secondAdd;
		}
		
		//out.println(Arrays.toString(firstWin));
		//out.println(Arrays.toString(secondWin));
		
		int resFirst = 0, resSecond = 0;
		
		int fullCycles = rounds / total;
		int remain = rounds % total;
		
		resFirst += firstWin[total - 1] * fullCycles;
		resSecond += secondWin[total - 1] * fullCycles;
		
		if(remain > 0) {
			resFirst += firstWin[remain - 1];
			resSecond += secondWin[remain - 1];
		}
		
		
		out.println(resSecond + " " + resFirst);
		
	}

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

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

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(42);
		}
	}

	String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null) {
				return null;
			}

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

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

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

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