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.Arrays;
import java.util.NoSuchElementException;
import java.util.Scanner;

    public class Test {
		static StringBuilder sb = new StringBuilder();
		static boolean isnew = true;
		static boolean ssharp;
		static int count = 0;
            public static void main(String args[]){
                    Scanner input = new Scanner(System.in);
                    int round = input.nextInt();
                    String nik = input.next();
                    String pol = input.next();
                    janken(round,nik,pol);
                    	
            }
            
            public static void janken(int round, String nik, String pol){
            	int nikl = nik.length();
            	int poll = pol.length();
            	int nikc = 0;
            	int polc = 0;
            	int lcms = (nikl*poll)/gcd(nikl,poll);
            	if(round <= lcms){
            		for(int i = 0 ; i < round ; i++){
            			int nikb = i % nikl;
            			int polb = i % poll;
            			if((nik.charAt(nikb) == 'P' && pol.charAt(polb) == 'R') || (nik.charAt(nikb) == 'S' && pol.charAt(polb) == 'P') || (nik.charAt(nikb) == 'R' && pol.charAt(polb) == 'S')){
            				polc++;
            			}else if((nik.charAt(nikb) == 'R' && pol.charAt(polb) == 'P') || (nik.charAt(nikb) == 'P' && pol.charAt(polb) == 'S') || (nik.charAt(nikb) == 'S' && pol.charAt(polb) == 'R')){
            				nikc++;
            			}
            		}
            	}else{
            		for(int i = 0 ; i < lcms ; i++){
            			int nikb = i % nikl;
            			int polb = i % poll;
            			if((nik.charAt(nikb) == 'P' && pol.charAt(polb) == 'R') || (nik.charAt(nikb) == 'S' && pol.charAt(polb) == 'P') || (nik.charAt(nikb) == 'R' && pol.charAt(polb) == 'S')){
            				polc++;
            			}else if((nik.charAt(nikb) == 'R' && pol.charAt(polb) == 'P') || (nik.charAt(nikb) == 'P' && pol.charAt(polb) == 'S') || (nik.charAt(nikb) == 'S' && pol.charAt(polb) == 'R')){
            				nikc++;
            			}
            		}
            		//System.out.println(lcms);
            		int nokori = round % lcms;
            		polc = polc * (round/lcms);
            		nikc = nikc * (round/lcms);
            		for(int i = 0 ; i < nokori ; i++){
            			int nikb = i % nikl;
            			int polb = i % poll;
            			if((nik.charAt(nikb) == 'P' && pol.charAt(polb) == 'R') || (nik.charAt(nikb) == 'S' && pol.charAt(polb) == 'P') || (nik.charAt(nikb) == 'R' && pol.charAt(polb) == 'S')){
            				polc++;
            			}else if((nik.charAt(nikb) == 'R' && pol.charAt(polb) == 'P') || (nik.charAt(nikb) == 'P' && pol.charAt(polb) == 'S') || (nik.charAt(nikb) == 'S' && pol.charAt(polb) == 'R')){
            				nikc++;
            			}
            		}
            	}
            	System.out.println(nikc+" "+polc);
            }
            
            public static int gcd(int x,int y){
            	int r;
            	while((r = x % y) != 0){
            		x = y;
            		y = r;
            	}
            	return y;
            }
          

    }

