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.*;
import java.math.*;
import java.io.*;
public class Main
	{
	public static void main(String args[])	throws IOException
		{
		Scanner c=new Scanner(System.in);
		int n=Integer.parseInt(c.nextLine());
		char s1[]=c.nextLine().toCharArray();
		char s2[]=c.nextLine().toCharArray();
		int m=s1.length;
		int k=s2.length;
		int lcm=(m*k)/gcd(m,k);
		int N_loss=0;
		int P_loss=0;
		for(int i=0;i<lcm;i++)
			{
			int i_m=i%m;
			int i_k=i%k;
			if(s1[i_m]==s2[i_k])
				continue;
			else if((s1[i_m]=='P'&&s2[i_k]=='R')||(s1[i_m]=='R'&&s2[i_k]=='S')||(s1[i_m]=='S'&&s2[i_k]=='P'))
				P_loss++;
			else
				N_loss++;
			}
		P_loss*=(n/lcm);
		N_loss*=(n/lcm);
		
		for(int i=0;i<(n%lcm);i++)
			{
			int i_m=i%m;
			int i_k=i%k;
			if(s1[i_m]==s2[i_k])
				continue;
			else if((s1[i_m]=='P'&&s2[i_k]=='R')||(s1[i_m]=='R'&&s2[i_k]=='S')||(s1[i_m]=='S'&&s2[i_k]=='P'))
				P_loss++;
			else
				N_loss++;
			}
		System.out.println(N_loss+" "+P_loss);
		}
	public static int gcd(int i, int j)
		{
		if(i<j)
			return gcd(j,i);
		if(j==0)
			return i;
		else
			return gcd(j,i%j);
		}
	}

//must declare new classes here