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.*;

public class Main {

	public static void main(String[] args) throws Exception {
		PrintWriter out = new PrintWriter(System.out, true);
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		// StringTokenizer st = new StringTokenizer(in.readLine(),"+=");
		// Scanner s = new Scanner(System.in);
		long n = Long.parseLong(in.readLine());
		String s1 = in.readLine();
		String s2 = in.readLine();
		int s1l = s1.length();
		int s2l = s2.length();
		
		long c = s1l*s2l/gcd(s1l,s2l);
		
		long res1 = 0;
		long res2 = 0;
		
		if(c >= n) {
			for(int i = 0;i < n;i++) {
				if(s1.charAt(i%s1l) == 'R' && s2.charAt(i%s2l) == 'S') res2++;
				if(s1.charAt(i%s1l) == 'S' && s2.charAt(i%s2l) == 'P') res2++;
				if(s1.charAt(i%s1l) == 'P' && s2.charAt(i%s2l) == 'R') res2++;
				if(s2.charAt(i%s2l) == 'R' && s1.charAt(i%s1l) == 'S') res1++;
				if(s2.charAt(i%s2l) == 'S' && s1.charAt(i%s1l) == 'P') res1++;
				if(s2.charAt(i%s2l) == 'P' && s1.charAt(i%s1l) == 'R') res1++;
			}
			out.println(res1+" "+res2);
		}else{
			for(int i = 0;i < c;i++) {
				if(s1.charAt(i%s1l) == 'R' && s2.charAt(i%s2l) == 'S') res2++;
				if(s1.charAt(i%s1l) == 'S' && s2.charAt(i%s2l) == 'P') res2++;
				if(s1.charAt(i%s1l) == 'P' && s2.charAt(i%s2l) == 'R') res2++;
				if(s2.charAt(i%s2l) == 'R' && s1.charAt(i%s1l) == 'S') res1++;
				if(s2.charAt(i%s2l) == 'S' && s1.charAt(i%s1l) == 'P') res1++;
				if(s2.charAt(i%s2l) == 'P' && s1.charAt(i%s1l) == 'R') res1++;
			}
			if(n/c != 0) {
				res1 *= n/c;
				res2 *= n/c;
			}
			n %= c;
			for(int i = 0;i < n;i++) {
				if(s1.charAt(i%s1l) == 'R' && s2.charAt(i%s2l) == 'S') res2++;
				if(s1.charAt(i%s1l) == 'S' && s2.charAt(i%s2l) == 'P') res2++;
				if(s1.charAt(i%s1l) == 'P' && s2.charAt(i%s2l) == 'R') res2++;
				if(s2.charAt(i%s2l) == 'R' && s1.charAt(i%s1l) == 'S') res1++;
				if(s2.charAt(i%s2l) == 'S' && s1.charAt(i%s1l) == 'P') res1++;
				if(s2.charAt(i%s2l) == 'P' && s1.charAt(i%s1l) == 'R') res1++;
			}
			
			out.println(res1+" "+res2);
		}

	}
	
	public static long gcd(long a, long b) {
		if(b == 0) return a;
		return gcd(b,a%b);
	}

}