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.io.*;
public class RockPaperScissors 
{
	public static void main(String[] args)
	{
		Scanner in = new Scanner(System.in);
		
		int n = in.nextInt();
		
		char[] nike = in.next().toCharArray();
		char[] poly = in.next().toCharArray();
		
		int m = nike.length;
		int k = poly.length;
		
		int lcm = m * (k / gcd(m, k));
		
		int nPinches = 0;
		int pPinches = 0;
		
		for(int x = 0; x < lcm; x++)
		{
			int winner = play(nike[x % nike.length], poly[x % poly.length]);
			
			if(winner == 1)
			{
				nPinches += n / lcm;
				
				if(x < n % lcm)
				{
					nPinches++;
				}
			}
			else if(winner == 0)
			{
				pPinches += n / lcm;
				
				if(x < n % lcm)
				{
					pPinches++;
				}
			}
		}
		
		System.out.println(nPinches + " " + pPinches);
	}
	
	public static int gcd(int a, int b)
	{
		if(b == 0)
		{
			return a;
		}
		else
		{
			return gcd(b, a % b);
		}
	}
	
	public static int play(char n, char p)
	{
		if(n == p)
		{
			return -1;
		}
		else if(n == 'R')
		{
			if(p == 'P')
			{
				return 1;
			}
			else
			{
				return 0;
			}
		}
		else if(n == 'P')
		{
			if(p == 'S')
			{
				return 1;
			}
			else
			{
				return 0;
			}
		}
		else
		{
			if(p == 'R')
			{
				return 1;
			}
			else
			{
				return 0;
			}
		}
	}
}
