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.BufferedReader;
import java.io.File;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.io.StreamTokenizer;


public class UMain {

	public static void main(String[] Args) throws IOException
	{
		new UMain().Run();
	}
	
	StreamTokenizer St;
	PrintWriter Pw;
	
	int n;
	int KolA,KolB;
	int LoseA=0, LoseB=0;
	String SA,SB;
	
	public void Reading() throws IOException 
	{
		File f2=new File("output.txt");
		Pw=new PrintWriter(f2);
		File f1=new File("input.txt");
		//St=new StreamTokenizer(new BufferedReader(new FileReader(f1)));
		St=new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
		St.nextToken();
		n=(int)St.nval;
		St.nextToken();
		SA=St.sval;
		St.nextToken();
		SB=St.sval;
		KolA=SA.length();
		KolB=SB.length();
	}
	
	public void Count(int von, int bis)
	{
		int indA=(von-1)%KolA,indB=(von-1)%KolB;
		char cA,cB;
		for (int i=von; i<=bis; i++)
		{
			cA=SA.charAt(indA);
			cB=SB.charAt(indB);
			switch (cA)
			{
			case 'R':
				if (cB=='S')
					LoseB++;
				else
					if (cB=='P')
						LoseA++;
				break;
			case 'S':
				if (cB=='P')
					LoseB++;
				else
					if (cB=='R')
						LoseA++;
				break;
			case 'P':
				if (cB=='S')
					LoseA++;
				else
					if (cB=='R')
						LoseB++;
				break;
			}
			indA++;
			indB++;
			if (indA>=KolA)
				indA=0;
			if (indB>=KolB)
				indB=0;
		}
	}
	
	public void Writing() throws FileNotFoundException
	{
		File f2=new File("output.txt");
		//Pw=new PrintWriter(f2);
		Pw=new PrintWriter(new OutputStreamWriter(System.out));
		Pw.println(String.valueOf(LoseA)+" "+String.valueOf(LoseB));
		Pw.flush();
	}
	
	public void Run() throws IOException
	{
		Reading();
		int zn=KolA*KolB;
		if (zn<=n)
		{
			Count(1,zn);
			int buf=n/zn;
			LoseA*=buf;
			LoseB*=buf;
			Count(buf*zn+1,n);
		}
		else
			Count(1,n);
		Writing();
	}
	
}
