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.awt.*;
import java.awt.event.*;
import java.awt.geom.*;
import java.io.*;
import java.math.*;
import java.text.*;
import java.util.*;

public class Main {
	static BufferedReader br;
	static StringTokenizer st;
	static PrintWriter pw;

	public static void main(String[] args) throws IOException	{
		br = new BufferedReader(new InputStreamReader(System.in));
		pw = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
		int n = readInt();
		String a = nextToken();
		String b = nextToken();
		int mod = lcm(a.length(), b.length());
		int tempL = 0;
		int tempR = 0;
		for(int i = 0; i < mod; i++)	{
			int now = score(a.charAt(i%a.length()), b.charAt(i%b.length()));
			if(now == -1)
				tempL++;
			else if(now == 1)
				tempR++;
		}
		int l = tempL * (n/mod);
		int r = tempR * (n/mod);
		n %= mod;
		for(int i = 0; i < n; i++)	{
			int now = score(a.charAt(i%a.length()), b.charAt(i%b.length()));
			if(now == -1)
				l++;
			else if(now == 1)
				r++;
		}
		pw.println(l + " " + r);
		pw.close();
	}

	public static int score(char a, char b)	{
		if(a == b)
			return 0;
		if(a == 'P')
			if(b == 'R')
				return 1;
			else
				return -1;
		if(a == 'R')
			if(b == 'S')
				return 1;
			else
				return -1;
		if(a == 'S')
			if(b == 'P')
				return 1;
			else
				return -1;
		return 0;
	}

	public static int lcm(int a, int b)	{
		return a * b / gcd(a,b);
	}

	public static int gcd(int a, int b)	{
		return a%b==0 ? b : gcd(b, a%b);
	}

	public static long readLong() throws IOException	{
		return Long.parseLong(nextToken());
	}
	public static double readDouble() throws IOException	{
		return Double.parseDouble(nextToken());
	}
	public static int readInt() throws IOException	{
		return Integer.parseInt(nextToken());
	}
	public static short readShort() throws IOException	{
		return Short.parseShort(nextToken());
	}
	public static String nextToken() throws IOException	{
		while(st == null || !st.hasMoreTokens())	{
			if(!br.ready())	{
				pw.close();
				System.exit(0);
			}
			st = new StringTokenizer(br.readLine());
		}
		return st.nextToken();
	}
}