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.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.Scanner;


public class Main {
    public static void main(String[] args)  throws Exception{
        new Main().run();
    }
    
    private void run() throws Exception{
        Scanner input = new Scanner(System.in);
        int n = input.nextInt();
        char[] sta1 = input.next().toCharArray();
        char[] sta2 = input.next().toCharArray();
        int i = 0;
        int len1 = sta1.length;
        int len2 = sta2.length;
        int ni = 0;
        int p = 0;
        int size = lcm(len1, len2);
        int tmp = size;
        while(tmp > 0){
            int i1 = i%len1;
            int i2 = i%len2;
            int win = rps(sta1[i1], sta2[i2]);
            if(win == 1)
                p++;
            else if(win == -1)
                ni++;
            tmp--;
            i++;
        }
        ni *= n/size;
        p *= n/size;
        
        int remain = n - (n/size)*size;
        
        while(remain > 0){
            int i1 = i%len1;
            int i2 = i%len2;
            int win = rps(sta1[i1], sta2[i2]);
            if(win == 1)
                p++;
            else if(win == -1)
                ni++;
            remain--;
            i++;
        }
        
        System.out.println(ni + " " + p);
    }
    
    private static int rps(char a, char b){
        if(a == 'R'){
            if(b == 'R')
                return 0;
            if(b == 'S')
                return 1;
            if(b == 'P')
                return -1;
        }
        if(a == 'S'){
            if(b == 'S')
                return 0;
            if(b == 'P')
                return 1;
            if(b == 'R')
                return -1;
        }
        if(a == 'P'){
            if(b == 'P')
                return 0;
            if(b == 'R')
                return 1;
            if(b == 'S')
                return -1;
        }
        return 0;
    }
    
    private static int gcd(int a, int b){
        if(b > a){
            int tmp = a;
            a = b;
            b = tmp;
        }
        if(b == 0)
            return a;
        return gcd(b, a-b);
    }
    
    private static int lcm(int a, int b){
        return a*b/gcd(a,b);
    }
}
