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.*;
import java.math.*;
import java.text.*;
public class Main
{
    static class Reader 
    { 
        private InputStream mIs;private byte[] buf = new byte[1024];private int curChar,numChars;public Reader() { this(System.in); }public Reader(InputStream is) { mIs = is;} 
        public int read() {if (numChars == -1) throw new InputMismatchException();if (curChar >= numChars) {curChar = 0;try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}if (numChars <= 0) return -1; }return buf[curChar++];} 
        public String nextLine(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isEndOfLine(c));return res.toString() ;} 
        public String s(){int c = read();while (isSpaceChar(c)) c = read();StringBuilder res = new StringBuilder();do {res.appendCodePoint(c);c = read();}while (!isSpaceChar(c));return res.toString();} 
        public long l(){int c = read();while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }long res = 0; do{ if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read();}while(!isSpaceChar(c));return res * sgn;} 
        public int i(){int c = read() ;while (isSpaceChar(c)) c = read();int sgn = 1;if (c == '-') { sgn = -1 ; c = read() ; }int res = 0;do{if (c < '0' || c > '9') throw new InputMismatchException();res *= 10 ; res += c - '0' ; c = read() ;}while(!isSpaceChar(c));return res * sgn;} 
        public double d() throws IOException {return Double.parseDouble(s()) ;}
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
        public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
        public int[] arr(int n){int[] ret = new int[n];for (int i = 0; i < n; i++) {ret[i] = i();}return ret;}
    }
    
    
 
           //       |----|       /\      |    |   -----   |
           //       |   /       /  \     |    |     |     |
           //       |--/       /----\    |----|     |     |
           //       |   \     /      \   |    |     |     |
           //       |    \   /        \  |    |   -----   -------

    public static int GCD(int a, int b) 
    {
       if (b==0) 
       return a;
       return GCD(b,a%b);
    }
    public static int check(char a,char b)
    {
        if(a==b)return 0;
        if(a=='R')
        {
            if(b=='P')
            return -1;
            return 1;
        }
        if(a=='P')
        {
            if(b=='S')
            return -1;
            return 1;
        }
        if(a=='S')
        {
            if(b=='R')
            return -1;
            return 1;
        }
        return 0;
    }
    public static void main(String args[])throws IOException
    {
        PrintWriter out=new PrintWriter(System.out);
        Reader sc=new Reader();
        int n=sc.i();
        String s1=sc.s();
        String s2=sc.s();
        int l1=s1.length();
        int l2=s2.length();
        int lcm=(l1*l2)/(GCD(l1,l2));
        int loss1[]=new int[lcm+2];
        int loss2[]=new int[lcm+2];
        for(int i=0;i<lcm;i++)
        {
            int a=check(s1.charAt(i%l1),s2.charAt(i%l2));
            if(a==0)
            {
                loss1[i+1]=loss1[i];
                loss2[i+1]=loss2[i];
            }
            if(a==-1)
            {
                loss1[i+1]=loss1[i]+1;
                loss2[i+1]=loss2[i];
            }
            if(a==1)
            {
                loss1[i+1]=loss1[i];
                loss2[i+1]=loss2[i]+1;
            }
        }
        if(n<=lcm)
        out.println(loss1[n]+" "+loss2[n]);
        else
        {
            int times=n/lcm;
            int lossa=loss1[lcm]*times+loss1[n%lcm];
            int lossb=loss2[lcm]*times+loss2[n%lcm];
            out.println(lossa+" "+lossb);
        }
        out.flush();
    }
}