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.PrintStream;
import java.util.Scanner;

/**
 * @author Roman Elizarov
 */
public class Krok2012_1_A {
	public static void main(String[] args) {
		new Krok2012_1_A().go();
	}

	char[] a;
	char[] b;

	int ra;
	int rb;

	private void go() {
		Scanner in = new Scanner(System.in);
		PrintStream out = System.out;
		int n = in.nextInt();
		a = in.next().toCharArray();
		b = in.next().toCharArray();
		int mk = a.length * b.length;
		imitate(mk, n / mk);
		imitate(n % mk, 1);
		out.println(ra + " " + rb);
	}

	private void imitate(int mk, int rep) {
		int ai = 0;
		int bi = 0;
		for (int i = 0; i < mk; i++) {
			char ac = a[ai++];
			if (ai >= a.length)
				ai = 0;
			char bc = b[bi++];
			if (bi >= b.length)
				bi = 0;
			if (ac != bc) {
				boolean win;
				switch (ac) {
				case 'R':
					win = bc == 'S';
					break;
				case 'P':
					win = bc == 'R';
					break;
				case 'S':
					win = bc == 'P';
					break;
				default:
					throw new IllegalArgumentException();
				}
				if (win)
					rb += rep;
				else
					ra += rep;
			}
		}
	}
}
