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.util.*;
// warm-up
// Should have seen this the first time. Super optimized
public class RockPaperScissors {

	static void solve() {
		Scanner sc = new Scanner(System.in);
		int n=sc.nextInt(), f=0, s=0, i=0, j=0, k=0, o=0, p=0;
		String A = sc.next(); 
		String B = sc.next();
		int l=A.length(), r=B.length(), len=(l==r) ? l : (l*r), noc=len, w=n%len;
		while (noc-->0) {
			char a = A.charAt(i), b = B.charAt(j);
			if (a=='R') { if (b=='S') ++s; if (b=='P') ++f; }
			else if (a=='P') { if (b=='R') ++s; if (b=='S') ++f; }
			else if (a=='S') { if (b=='P') ++s; if (b=='R') ++f; }
			i+=(i+1==l) ? -i : 1;
			j+=(j+1==r) ? -j : 1;
			if (--w==0) { o=f; p=s; }
		}
		f+=(((n/len)-1)*f)+o;
		s+=(((n/len)-1)*s)+p;
		System.out.println(f+" "+s);
		sc.close();		
	}

	public static void main(String args[]) {
		solve();
	}

}

