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.*;
public class Main{
	public static int a=0;
	public static int b=0;
	/**
	 * @param args
	 */
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		Scanner input=new Scanner(System.in);
		
		while(input.hasNext()){
			a=0;b=0;
			int size=input.nextInt();
			String a1=input.next();
			String b1=input.next();
			int p=a1.length();
			int q=b1.length();
			int g=gcd(p,q);
			int j=0,k=0;
			if(size<=g)
			for(int i=0;i<size;i++){
				j=i%a1.length();
				k=i%b1.length();
				
				judge(a1.charAt(j),b1.charAt(k));
			}
			else {
				int l=size/g;
				int mod=size%g;
				for(int i=0;i<g;i++){
					j=i%a1.length();
					k=i%b1.length();
					
					judge(a1.charAt(j),b1.charAt(k));
				}
				a=a*l;
				b=b*l;
				for(int i=0;i<mod;i++){
					j=i%a1.length();
					k=i%b1.length();
					judge(a1.charAt(j),b1.charAt(k));
				}
				
			}
			System.out.println(a+" "+b);
		}
	}
public static void judge(char c,char d){
	if(c=='R'&&d=='S')b++;
	if(c=='R'&&d=='P')a++;
	if(c=='S'&&d=='P')b++;
	if(c=='S'&&d=='R')a++;
	if(c=='P'&&d=='R')b++;
	if(c=='P'&&d=='S')a++;
}
public static int gcd(int a,int b){
  	 int m1=a;
  	  int n1=b;
  	 int k=a%b;
  	  while(k!=0)
  	  {
  	   m1=n1;
  	   n1=k;
  	   k=m1%n1;
  	  }
  	  return a*b/n1;

  }
}
