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.BigInteger;
import java.util.*;

public class Main {
   public static void main(String[] args) throws IOException
   {
	   (new Main()).solve();
   }
   public void Main() {
   }
   

   void solve()  throws IOException {
	  //BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
	  //Scanner in = new Scanner(System.in);
	   MyReader in = new MyReader();
	  PrintWriter out = new PrintWriter(System.out);
     // Scanner in = new Scanner(new FileReader("input.txt"));
	//  PrintWriter out = new PrintWriter("output.txt");
	  int n = in.nextInt();
	  String a = in.readLine();
	  String b = in.readLine();
	  int m = a.length();
	  int k = b.length();
	  int d = m * k;
	  int t = n % d;
	  int countD1 = 0, countD2 = 0;
	  int countT1 = 0, countT2 = 0;
	  for (int i = 0; i < d; i++) {
		  char cA = a.charAt(i % m);
		  char cB = b.charAt(i % k);
		  if (cA != cB) {
			  if ((cA == 'R' && cB == 'S') || (cA == 'S' && cB == 'P') || (cA == 'P' && cB == 'R')) {
				  countD1++;
				  if (i < t) {
					  countT1++;
				  }
			  } else {
				  countD2++;
				  if (i < t) {
					  countT2++;
				  }
			  }
		  }
	  }
	  int count1 = countD1 * (n / d) + countT1;
	  int count2 = countD2 * (n / d) + countT2;
	  
	 out.println(count2 + " " + count1);
	out.close(); 
   }     

};


class MyReader {
	private BufferedReader in;
	String[] parsed;
	int index = 0;
	
	public MyReader() {
		in = new BufferedReader(new InputStreamReader(System.in));
	}
	
	public int nextInt() throws NumberFormatException, IOException {
		if (parsed == null || parsed.length == index) {
			read();
		}
		return Integer.parseInt(parsed[index++]);
	}
	
	private void read() throws IOException {
		parsed = in.readLine().split(" ");
		index = 0;
	}
	
	public String readLine() throws IOException {
		return in.readLine();
	}
	
};