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.*;
import java.awt.geom.*;

import static java.lang.Math.*;

public class Solution implements Runnable {
	
	int gcd (int a, int b) {
		return b == 0 ? a : gcd (b, a % b);
	}
	
	int who (char a, char b) {
		if (a == 'R' && b == 'S') return 0;
		if (a == 'S' && b == 'R') return 1;
		
		if (a == 'S' && b == 'P') return 0;
		if (a == 'P' && b == 'S') return 1;
		
		if (a == 'P' && b == 'R') return 0;
		if (a == 'R' && b == 'P') return 1;
		
		return -1;
	}
	
	public void solve () throws Exception {
		int n = nextInt();
		String a = nextToken();
		String b = nextToken();
		int l1 = a.length();
		int l2 = b.length();
		int l3 = l1 * l2 / gcd (l1, l2);
		
		StringBuilder sb = new StringBuilder();
		for (int i = 0; i < l3 / l1; i++) {
			for (int j = 0; j < a.length(); j++) {
				sb.append(a.charAt(j));
			}
		}
		a = sb.toString();
		
		sb = new StringBuilder();
		for (int i = 0; i < l3 / l2; i++) {
			for (int j = 0; j < b.length(); j++) {
				sb.append(b.charAt(j));
			}
		}
		b = sb.toString();
		
		int ans [] = new int [2];
		for (int i = 0; i < l3; i++) {
			int v = who (a.charAt(i), b.charAt(i));
			if (v != -1) {
				ans [v]++;
			}
		}
		
		ans[0] *= n / l3;
		ans[1] *= n / l3;
		
		for (int i = 0; i < n % l3; i++) {
			int v = who (a.charAt(i), b.charAt(i));
			if (v != -1) {
				ans [v]++;
			}
		}
		
		out.println(ans[1]+" "+ans[0]);
	}
	
	final String fname = "";
	long stime = 0;
	
	BufferedReader in;
	PrintWriter out;
	StringTokenizer st;
	
	private String nextToken () throws Exception {
		while (st == null || !st.hasMoreTokens()) {
			st = new StringTokenizer(in.readLine());
		}
		return st.nextToken();
	}
	
	private int nextInt () throws Exception {
		return Integer.parseInt(nextToken());
	}
	
	private long nextLong () throws Exception {
		return Long.parseLong(nextToken());
	}
	
	private double nextDouble () throws Exception {
		return Double.parseDouble(nextToken());
	}
	
	@Override
	public void run() {
		try {
			in = new BufferedReader(new InputStreamReader(System.in));
			out = new PrintWriter (System.out);
			solve ();
		} catch (Exception e) {
			throw new RuntimeException(e);
		} finally {
			out.close();
		}
	}
	
	public static void main(String[] args) {
		new Thread(null, new Solution(), "", 1<<26).start();
	}

}